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1. ee 2 ADin 3 Filter Switch DAout ADin Filter Switch DAout LQG LQG PID J PID J Filter i y Switch DAout ADin H Filter i Switch DAout LQG TE Er EA delete LQG 7 PID J PID J Filter i Switch DAout ADin rite f Switch DAout LQG new GPC GPC PID 4 o Copy variables Switch Filter i Switch DAout oio PID 5 ADin Update shadow lt PID ADin Filter GPC Switch Filter DAout Him H DAout DAout GPC PID ADin H Filter GPC Switch Figure 8 The internal structure during an edit session where one block is re placed by another dimension variables connected to it are updated This update is made syn chronously throughout the system There is no restriction in what data types that may be used in connections of type one and two 5 On line Configurations PALSJO allows the block configuration to be edited without having to stop and restart the system It is handled by using two identical sets of blocks called running and shadow The running configuration is the set of 98 6 Conclusion blocks that are executing and the shadow configuration is us
2. System gt BlockType Calculate Update b lt Add Remove GetChild int Algorithms Container A Calculate O 6 Update emove th erase atest nag ERRE ee GetChild int Filter Observer Controller Calculate Calculate Calculate Sporadic Periodic Update Update Update i Calculate Calculate i Update Update Figure 2 A user defined block is inherited from the pre defined class Algorithms Container is a super class designed to administer and encapsulate a set of blocks Two subclasses Periodic and Sporadic are available They are both used for man aging the execution of other blocks programmer does not have to deal with any traditional real time program ming Furthermore it is possible for the systems to arrange the blocks so that the execution is optimized The Framework and its Classes The inheritance structure of the block type library is shown in Fig 2 The super block to all block classes is BlockType which contains the basic functionality that a class needs to be integrated into the PALSJO envi ronment The subclasses implement the abstract methods Calculate and Update Two subclasses from BlockType exist One is Container de signed to encapsulate other blocks and the other is Algorithms the super class for all user defined PAL blocks Two subclasses from Container are available Periodic and Sporadic These are used to manage the execu
3. X2 xB x1 0 2 0 2 0 15 4 bo ots J E 0 1 L 0 1 E L 0 05 4 t 0054 E 0 0 r r 0 100 200 300 0 100 200 300 Uh ybrid x2 02 1 L 0 15 4 L 0 8 F 0 6 L 014 HA AA E F 4 ss E 0 4 0 05 a N 0 2 H I 0 4 E 0 L A 0 05 r 0 100 200 300 0 0 1 0 2 X1 Figure 10 Lyapunov based switching for the double tank system Compare Fig ure 9 This supervisory scheme may lead to two types of chattering behav ior One is only related to the time optimal controller and is due to the nonlinearities The nonlinear switching curve lies above the linear see Figure 7 That causes the trajectory of the nonlinear system to cross the linear switching curve and the control signal goes from 0 to 1 somewhat too late or too early One way to remove this problem is to introduce a hys teresis when going from minimum to maximum control signal in the time optimal controller There can also be chattering between the PID and the time optimal controller if their corresponding Lyapunov functions have the same value One solution to this problem is to add and remove the constant A as discussed in the section on Lyapunov functions modifica tions The Heating Ventilation Process In practical applications it can be an advantage to approximate the switch ing curves with simpler functions To investigate the behavior for such approximations the switching curves for the system in Equation 5 were approximated with five straight lines As can b
4. Pini outi sel Process 1 1 Mutex 1 Pnz otz Sa Process 2 Computer 1 rescuvestcompuer i D HEEE i Fie Edit View Simulation Format Tools Pera P A Out1 Out 2 E a Schedule Kernel LE Mutex 1 Time offset 0 Figure 14 The simulation model is defined by a block diagram There are two blocks for the dynamic processes and one block for the computer The control tasks are implemented as MATLAB files control tasks running in the virtual computer Three types of output sig nals from the kernel block are plotted The first type of output signals are the control signals u1 and u2 which are fed to the dynamic processes The second type of output signals are the execution traces The task ac tivation graph shows the state of each task at every point in time This signal is fed to the plot named Schedule A task can be either running high blocked medium or sleeping low The Mutex 1 signal indicates when the mutual exclusion monitor with the same name is occupied Sim ilar to the task activation graph there is one line for each task where high means that the task is inside the monitor medium that the task is waiting to get in and low that the task is outside the monitor Example 3 below shows the initialization script used for the simula 48 6 Simulation o
5. 138 7 References Zhao Q C and D Z Zheng 1999 Stable real time scheduling of a class of pertubed hds In Proceedings of the 14th World Congress of IFAC vol J pp 91 96 IFAC Beijing P R China 139 Paper 4 A Feedback Scheduler for Real time Controller Tasks Appendix A Proof and Continuation of Theorem 1 Proof To find out how J depends on the sampling interval it remains to investigate S Equation 3 is differentiated with respect to h IA ei LS gl le ol ls all ol dS pT le rje fir SUE del dQ al sio ry 2 e de Rearranging the terms yields o AJE glleg ol 0 0 0 g8 G 0 T Tr7 2 rT a where the block matrix W is defined as T S r r 51 a dh The following Lyapunov equations for E and e are obtained by extract ing elements from Equation 8 and introducing Y Pb TL dS q aS TI T will LT W dh a EA dL rds I I Y I W Ta Geo a The derivative dk is needed later for the calculation of the second deriva tive of J To calculate W formulas for Yu 22 and L are needed Since dh gt dt dh ADS 140 Appendix A Proof and Continuation of Theorem 1 and Se is given from Equation 4 it is straightforward to calculate do dr dQa sth yh an Ae dh AT B Ah e Qe W can now be written as w r E r 10 1 lo 1 Ab Ar B S r 9 rT S A Ar B and now let W be ee oe er PTAT LTB SY PT S
6. Paper 1 A Tool for Interactive Development of Embedded Control Systems Johan Eker Abstract Embedded control systems are today created using tools that give insuf ficient support for rapid prototyping and code reuse New tools for im plementation of embedded controllers are necessary This paper presents a software framework for implementation of embedded control systems The PAL language is presented PAL is designed to support implementa tion of control algorithms in particular A run time system called PALSJO is also introduced Algorithms written in PAL may be executed in the PALSJO system The PALSJO system is designed to allow on line system configuration and reconfiguration 69 Paper 1 A Tool for Interactive Development of Embedded Control Systems 70 1 Introduction 1 Introduction This paper presents the P LSJ system for development of embedded con trol systems P LSJ is an experimental environment designed to support code reuse and rapid prototyping To facilitate this and to relieve the con trol engineer of real time programming obstacles the controller descrip tion language PAL was created Algorithms are designed and packaged so that code reuse becomes straightforward It is difficult to design reusable real time code using general purpose languages such as C C Timing requirements and algorithm specifica tions are hard to separate and it becomes cumbersome to use the same code module in two real tim
7. Report TFRT 7443 Depart ment of Automatic Control Lund Institute of Technology Lund Swe den David R and H Alla 1992 Petri Nets and Grafcet Tools for modelling discrete events systems Prentice Hall International UK Elmqvist H 1985 LICS Language for implementation of control systems Report TFRT 3179 Department of Automatic Control Lund Institute of Technology Lund Sweden Integrated Systems 1996a AutoCode User s Guide Integrated Systems Inc 3260 Jay Street Santa Clara CA 95054 3309 USA Integrated Systems 1996b SystemBuild User s Guide Integrated Sys tems Inc 3260 Jay Street Santa Clara CA 95054 3309 USA Le Lann G 1996 The ariane flight 501 failure a case study in sys tem engineering for computing systems In Hand Out European Ed ucational Forum School on Embedded System European Educational Forum Lewis R 1995 Programming industrial control systems using IEC 1131 3 The Institution of Electrical Engineers London U K MathWorks 1997 Simulink Real Time Workshop The MathWorks inc 24 Prime Park Way Natick MA 01760 1500 Schneider S A V Chen and G Pardo Castellote 1995 The control shell component based real time programming system In IEEE Con ference on Robotics and Automation Real Time Innovations Inc 954 Aster Sunnyvale California 94086 Seto D B H Krogh L Sha and A Chutinan 1998 Dynamic con trol system upgrad
8. of how a control algorithm may be separated from application specific information through use of contracts All information that is related to the implementation of this specific hybrid controller is found in the contract Note that y2 is not used by the PI block O A System with Feedback Scheduling Consider a system where several control loops are executing on the same hardware Furthermore let the number of loops vary with time Fig ure 8 illustrates this system The CPU consumption of a controller may be changed by adjusting its sampling frequency The problem is twofold First the system must be kept schedulable in spite of the changes in workload due to tasks arriving or tasks changing modes Secondly the global control performance of the system should be op timized This can be done by associating a cost function QoS with each controller The cost function indicates how the control performance de pends on the level of alloted resources The task of the parent block is to 114 4 The FRIEND Language Block E Negotiation Ctrl 1 Ctrl 2 I Ctrl n I ul y u2 y2 Un Yn Y Plant 1 Plant 2 Plant n Figure 8 Several control loops execute at the same CPU and are competing for the computing resources If the number of control tasks change during run time the task schedule must be recalculated in order to avoid overload optimize the overall control performance i e min QoS 5 Q
9. J 1998 RealTime Control Systems with Delays PhD thesis ISRN LUTFD2 TFRT 1049 SE Department of Automatic Control Lund Institute of Technology Lund Sweden Ryu M and S Hong 1998 Toward automatic synthesis of schedulable real time controllers Integrated Computer Aided Engineering 5 3 pp 261 277 Ryu M S Hong and M Saksena 1997 Streamlining real time con troller design From performance specifications to end to end timing constraints In Proceedings of the IEEE Real Time Technology and Applications Symposium Seto D J P Lehoczky and L Sha 1998 Task period selection and schedulability in real time systems In Proceedings of the 19th IEEE Real Time Systems Symposium Seto D J P Lehoczky L Sha and K G Shin 1996 On task schedulability in real time control systems In Proceedings of the 17th IEEE Real Time Systems Symposium pp 13 21 Shin K G and C L Meissner 1999 Adaptation of control system per formance by task reallocation and period modification In Proceedings of the 11th Euromicro Conference on Real Time Systems pp 29 36 Stankovic J C Lu and S Son 1999 The case for feedback control real time scheduling In Proceedings of the 11th Euromicro Conference on Real Time Systems pp 11 20 van Loan C 1978 Computing integral involving the matrix exponen tial IEEE Transactions on Automatic Control No AC 23 pp 395 404
10. JJ 1200 pi vi in I Figure 4 The cost J h as a function of the sampling interval for the pendulum The plot shows the graph for 3 14 full 3 77 dot dashed and 4 08 dashed The peaks are due to the resonance frequencies of the pendulum Static Optimization For the class of systems for which the cost functions are convex ordi nary optimization theory may be applied The optimization criterion in Equation 1 has nonlinear constraints and is first rewritten By optimiz ing over the frequencies instead of the sampling intervals the following optimization problem is given min V f Ji 1 fi i 1 subject to Cf lt U ref Elfs fa The Kuhn Tucker conditions see for example Fletcher 1987 give that if f A fa is an optimal solution then VA f AC 0 AlUrer CTF 0 5 A gt 0 where V is the gradient and C Cj C 132 5 A Feedback Scheduler Recursive Optimization Since changes in the computer load U ef and the execution times C change the optimization problem they need to be resolved at each step in time In principle one can repeat the solution to the static optimization problem at each step in time However instead of looking for a direct solution we will consider a recursive algorithm Assume that we have a solution f k at step k which is optimal or close to optimal We will now construct a recursive algorithm to compute new values for f and A Let the executio
11. To design such a feedback scheduler two problems are studied The first is to find a suitable performance index and calculate how it depends on the sampling frequency The second problem is to design an optimization routine It is assumed that measurements or estimates of the execution times and system workload are available from the real time kernel at run time As a performance index a linear quadratic LQ formulation is used The controllers are state feedback algorithms designed to minimize this quadratic cost function The performance index is calculated as a func tion of the sampling interval Given this control performance indicator an optimization routine is designed The optimization routine aims at finding the control performance optimum given a desired CPU utiliza tion level workload and the execution times for the tasks The global cost function that should be minimized consists of the sum of the cost function of each control loop The minimization is performed subject to a schedulability constraint The minimization of the global cost function constitutes a nonlinear programming problem The solution of this prob lem is facilitated by the knowledge of the first and second derivatives of the cost functions with respect to the sampling rate Expressions for the derivatives are calculated and used in the optimization Using a feedback scheduling strategy it is now possible to design real time control systems that are more robust aga
12. are block oriented similar to how systems are described in the simulation environments Simulink Real time Work shop and SystemBuild Autocode Complex controllers are formed by com bining a number of basic building blocks Many features in PALSJO were inspired by LICS Elmgvist 1985 and SIM2DDC Dahl 1990 both pre vious research projects at the Department Ideas from the Simplex Seto et al 1998 project on fault tolerant controllers have also influenced this work Another interesting tool is ControlShell RealTimeInnovations 1995 a C class library combined with graphical editors The authors believe the goals stated in Section 1 have been reached with the P LSJ framework The on line configuration feature has however created a new set of problems First the current switching mechanism is too crude It is necessary to give the control engineer more power to specify how the switch shall be performed There are also a number of other problems that have to be faced For example is it possible to predict the consequences of replacing one real time task with another Will all tasks still be schedulable in the new configuration and if so how will the system behave during the actual switching of the tasks How can controllers be 99 Paper 2 A Flexible Interactive Environment for Embedded Controllers designed so that they can be switched in and out without problems The next step is to address some those issues Better language is nee
13. extends implements extends Figure 6 The relations of the Friend language components supervisor is used to select which sub controller that should be active and typically only one controller is affecting the plant at each point in time The supervisor uses a set of switching rules to decide when to change the active controller Consider an example with a hybrid controller where Aea ais n supervisor u2 H Co H y u gt process H C H Figure 7 A hybrid controller consists of several sub controllers C A supervisor is used for selecting which control signal u u to be fed to the process each sub controller is associated with a function V The idea is to use the controller corresponding to the smallest value of the function V For more on this switching criterion see Malmborg 1998 This hybrid controller is implemented in block B which consists of the two sub controllers C and D see Figure 2 Block B is a negotiator block and block C and D are algorithm blocks Block B decides when and how the blocks C and D shall execute Example 1 shows the outline of the FRIEND code for such a hybrid controller 111 Paper 3 A Contract Based Language for Embedded Control Systems EXAMPLE 1 interface SISO Y Yref input real u output real The SISO interface defines a block interface with two input signals and one output signal The signals may at run tim
14. gies into an embedded spacecraft system flight software system engi neering for new millennium In Aerospace Conference vol 2 pp 409 420 IEEE Malmborg J 1998 Analysis and Design of Hybrid Control Systems PhD thesis ISRN LUTFD2 TFRT 1050 SE Department of Auto matic Control Lund Institute of Technology Lund Sweden 118 6 References Meyer B 1992 Applying design by contract Computer 25 10 pp 40 51 Natarajan S and K Lin 1988 FLEX towards flexible real time pro grams In Proceedings of the International Conference on Computer Languages IEEE Rosu D K Schwan and S Yalamanchili 1998 Fara a framework for adaptive resource allocation in complex real time systems In Proceedings of the 4th IEEE Real Time Technology and Applications Symposium pp 79 84 IEEE Stankovic J C Lu and S Son 1999 The case for feedback control real time scheduling In Proceedings of the 11th Euromicro Conference on Real Time Systems pp 11 20 119 Paper 3 A Contract Based Language for Embedded Control Systems 120 Paper 4 A Feedback Scheduler for Real time Controller Tasks Johan Eker Per Hagander and Karl Erik rz n Abstract The problem studied in this paper is how to distribute computing re sources over a set of real time control loops in order to optimize the total control performance Two subproblems are investigated how the control performance
15. however we need to store the value of u between two invocations of the myController function Configuration Before a simulation can start the user must define what tasks that should exist in the system what scheduling policy should be used whether any common resources exist etc The initialization is performed in a Matlab script EXAMPLE 3 Three dummy tasks are initialized in the script below The tick size of the kernel is set to 0 001 s and the scheduling type is set to rate monotonic The dummy code segment empty models a task that computes nothing for a certain amount a time Each task is assigned a period and a deadline which is equal to the period function rtsys rtsys_init 1 RM 2 DM 3 Arbitrary FP 4 EDF rtsys st 1 rtsys tick_size 0 001 T 0 10 0 08 0 06 Task Periods D 0 10 0 08 0 06 Deadlines C 0 02 0 02 0 02 Computation times rtsys Tasks code1 code empty 1 C 1 code2 code empty 1 C 2 code3 code empty C 3 rtsys Tasks 1 task Task1 code1 T 1 D 1 rtsys Tasks 2 task Task2 code2 T 2 D 2 rtsys Tasks 3 task Task3 code3 T 3 D 3 The initialization script is given as a parameter to a Computer block in 155 Paper 5 A Matlab Toolbox for Real Time and Control Systems Co Design a Simulink model Simulating the model for one second produces among other things the schedule plot shown in Figure 9 O Sch
16. p2 daout new AnalogOut pcl gt p1 adin y gt p1 filter u pel gt p1 filter y gt p2 pid u pel gt p1 filter y gt p2 rst u pcl gt p2 pid y gt p2 switch ul pcl gt p2 rst y gt p2 switch u2 pcl gt p2 switch y gt p2 daout u pcl gt p1 tsamp 0 010 pcl gt p2 tsamp 0 050 O The Periodic block executes its child blocks according to a schedule automatically created on line Since the child blocks are executed syn chronously no data sharing problems will arise Mutual exclusion is thus handled automatically by the system The data flow mechanism is imple mented so that unnecessary copying is avoided 4 PAL P lsj Algorithm Language PAL is a block based imperative language for implementation of embed ded controllers It is designed to support and simplify the coding of control algorithms Language constructs for both periodic algorithms and sequen 75 Paper 1 A Tool for Interactive Development of Embedded Control Systems tial algorithms are available Furthermore complex data types such as polynomials and matrices are fully supported For a more in depth de scription see Blomdell 1997 which this section is based upon Blocks and Modules Algorithms are described as input output blocks New values for the out put signals are calculated based on the values of the inputs the internal states and the parameters A PAL block has the following structure EXAMPLE 2 module MyPI block PI r y u
17. plementing and supervising control applications It supports sequential algorithms expressed using Grafcet notation and algebraic algorithms expressed with implicit equations The SattLine language is based on LICS Elmgvist 1985 which has also inspired the work with P LSJ The IEC 1131 3 Lewis 1995 programming standard consists of five different ways of representing control algorithms The five different lan guages are Structured Text Function Block Diagram Ladder Diagram Instruction List and Sequential Function Charts Structured Text is a Pascal type language with a structure similar to PAL Function Block Di agram is a graphical language for specifying data flows through function blocks Ladder Diagram is another graphical language that is used for 21 Introduction expressing ladder logic The fourth language is Instruction List which is a low level assembler language Sequential Function Chart is a graphi cal language for implementing sequential algorithms similar to Grafcet The textual representation of Sequential Function Chart was used as a starting point when implementing support for Grafcet in PALSJO There are currently several initiatives trying to turn Java into a full fledged alternative for implementation of embedded systems The J Con sortium has a working document Core Real Time Extensions for the Java Platform J Consortium 1999 trying to establish a real time standard The PERC virtual machine wh
18. sizes of aggegate data types is motivated by the need for synchronized size changes In a situation where an output polynomial is connected to an input polynomial and the degrees are changed it is necessary for this change to be done simultaneously throughout the system Dimension vari ables are used in Fig 6 where in1 is an input array with n elements and in2 is an array of m inputs n dimension m dimension inl input array 1 n of real in2 array 1 m of input real 1 gt 1 inl in2 _ n n Figure 6 The input signal can be declared either as an input array or as an array of inputs Dimension variables can be used to specify the size Connections There are three types of connections in P LSJ 1 Output signal to input signal 96 4 Signal Management 2 Output signal to parameter 3 Dimension to dimension The first type of connection is the most common It is used to sim ply transfer data from one block to another during the execution of the calculate update procedures The second type of connection is intended for adaptive systems and is more expensive regarding computation time The reason for this is that it Periodic LPL Ft Output to parameter Periodic gt Calculate Request indirect calculation M parameters Parameter Server Figure 7 To handle connections of the type outpu
19. x t ui ui c x t 1 i t 1 n where the c x t represent different controllers In a hybrid control sys tem different controllers are switched in for different regions of the state space or in different operating modes There exist some switching schemes that guarantee stability see for example Johansson and Rantzer 1998 Ferron 1996 For the applica tions in this paper the min switch strategy described below is used The min switching strategy is defined as follows Let there be a Lya punov function V associated with each controller c in Equation 1 Fur thermore let the controller c be admissible only in the region Q The idea is then to use the controller corresponding to the smallest value of the Lyapunov function More formally DEFINITION 1 THE MIN SWITCHING STRATEGY Let f x be the right hand side of Equation 1 when control law c is used Use a control signal u such that So aifi x t 2 i 1 where gt 0 satisfies a 1 and a 0 if either x Q or if Vi x t gt min V x If only one controller achieves the minimum then a 1 for that controller and all the other q are zero O THEOREM 1 STABILITY OF HYBRID SYSTEMS Let the system be given by Equation 1 Introduce W as W min Vi Vo E Va 170 4 The Processes The closed loop system is then stable with W as a non smooth Lyapunov function if the min switch strategy is used O For a proof of the theo
20. 0 before it is switched out It is easily shown that the hybrid controller is globally stabilizing with this addition if it is stabiliz ing without it More information on chattering in hybrid systems can be found in Hay and Griffin 1979 Park and Barton 1996 4 The Processes The first process is a double tank system a standard laboratory process The second process is a real life process a heating ventilation system at a public school A Double Tank System The first process is the double tank system from our laboratory It consists of two water tanks in series see Figure 4 The goal is to control the level x2 of the lower tank and indirectly the level x of the upper tank The 171 Paper 6 Design and Implementation of a Hybrid Control Strategy x1 Ee x2 E Figure 4 The double tank process The input signal u is the voltage to the pump and the output signal y xa is the level of the lower tank two tank levels are both measurable The following state space description is derived Q x Bu A1 X1 A 24 X2 where the flow u into tank 1 is the control variable The inflow can never be negative and the maximum flow isi 27 1076 m s Furthermore in this experimental setting the tank areas and the outflow areas are the same for both tanks giving 41 02 The square root expression is derived from Bernoulli s energy equations amp f x u 3 A heating ventilation p
21. AY BL which now leads to the following expression and a may now be calcu lated dS raS ch cht W GE pd ree 110 TITS AY BL AT BJ SY dh dh THEOREM 2 The second derivative is given by BJ 11 ds dS Ry R J ae Ry 2 Geant SZ Bona 2 dS Ri d 2 li FAY AMAS SR where dS ds d T dS rdSd dW aa E Mea ae ah dE dY dL Sy AD AT BLT 141 Paper 4 A Feedback Scheduler for Real time Controller Tasks dw 1 y y ir ae alg ela ro e g dh dh dS dv TaT JT pT WTA LOB Ge Sap dS dv Der Aa SAY BL dY p OL r T dy dL Vane a po SA an dI dR R T ToT E ZAPRT R ATO dh tr Q1 ah dh Ri Ri Proof Proven with similar techniques as Theorem 1 LEMMA 1 The integral t T i e Qet Tdt 0 is calculated using the following equations taken from van Loan 1978 Consider the linear system eL aller o which has the following solution ello alizo xa t o AT x9 0 If a aml Lo ae 021 22 0 A then x1 t Y11x1 0 Y 12x2 0 x2 t Y21x1 0 Y22x2 0 142 Appendix A Proof and Continuation of Theorem 1 An alternative way of solving Equation 9 is xa t e xa 0 gt 1 Axi t Qe xo 0 t gt x1 t e x1 0 a eA QA tdtx2 0 0 Identification of the terms from the different solutions now gives r T e t QeA dr wi o 0 which concludes the lemma O 143 Paper 4 A Feedback Scheduler
22. Design and Implementation of a Hybrid Control Strategy Malmborg J 1998 Analysis and Design of Hybrid Control Systems PhD thesis ISRN LUTFD2 TFRT 1050 SE Department of Auto matic Control Lund Institute of Technology Malmborg J and J Eker 1997 Hybrid control of a double tank system In IEEE Conference on Control Applications Hartford Connecticut Morse A S 1995 Control using logic based switching In Isidori Ed Trends in Control A European Perspective pp 69 113 Springer Park T and P Barton 1996 State event location in differential algebraic models ACM Transactions on Modeling and Computer Simulation 6 2 p 137 Wall n A 1999 A tool for rapid system identification In Proceedings of the 1999 IEEE International Conference on Control Applications 188 Appendix A PAL Palsj Algorithm Language 1 Introduction PAL is a block based imperative language for implementation of embed ded controllers It is designed to support and simplify the coding of control algorithms Language constructs for both periodic algorithms and sequen tial algorithms are available and complex data types such as polynomials and matrixes are fully supported A brief introduction to the PAL language is given below For a more in depth description see Blomdell 1997 which this text is based upon 2 Blocks and Modules Algorithms are described as input output blocks New values for t
23. H 1985 LICS Language for implementation of control systems Report TFRT 3179 Department of Automatic Control Lund Institute of Technology Lund Sweden Elmavist H K J str m T Sch nthal and B Wittenmark 1990 Simnon User s Guide SSPA G teborg Sweden Elmqvist H and S E Mattsson 1997 Modelica The next generation modeling language an international effort In Proceedings of the 1st World Congress on System Simulation WCSS 97 Singapore Gerber R S Hong and M Saksena 1995 Guaranteeing real time requirements with resource based calibration of periodic processes IEEE Trans on Software Engineering 21 7 Gustafsson K 1991 Control theoretic techniques for stepsize selection in explicit Runge Kutta methods ACM Transactions on Mathematical Software 17 4 pp 533 554 Gustafsson K 1994 An architecture for autonomous control Report ISRN LUTFD2 TFRT 7514 SE Department of Automatic Control Lund Institute of Technology Lund Sweden Halbwachs N 1993 Synchronous programming of reactive systems Kluwer Academic Publishing Halbwachs N P Caspi P Raymond and D Pilaud 1991 The synchronous data flow programming language LUSTRE In Proceedings of the IEEE vol 79 64 9 References Hennessy J 1999 The future of systems research JEEE Computer August Henriksson R 1998 Scheduling Garbage Collection in Embedded Syste
24. Hybrid Control Strategy parameters 0w 0 0 06 0 7 1 0 are chosen to get a good behavior under load disturbances For the heating ventilation process the parameters in the closed loop characteristic equation are a 0 025 1 0 1 0 The controller pa rameters are chosen to give a well damped closed loop system but with approximately the same speed as the open system The controller could be more aggressively tuned than the currently used PID controller as the error and control signal never are large Time optimal controller design The problem of set point response can be viewed as a purely deterministic problem to change the process from one state to another in shortest pos sible time possibly without any overshoot subject to constraints on the control signal The constraints are typically bounds on the control signal or its rate of change This is an optimal control problem and the theory of optimal control see Lewis 1986 and Leitman 1981 is applied to derive minimum time strategies to bring the system as fast as possible from one set point to another The time optimal control is the solution to the following optimization problem T max 1 dt 7 0 under the constraints x 0 x2 21 TY ce Gh ae u E 0 1 This together with the system dynamics give the control law For a wide class of systems the solution to Equation 7 is of bang bang character where the optimal control signal switches between its
25. J and A Cervin A MATLAB Toolbox for Real Time and Control Systems Co Design To appear in Proceedings of the 6th International Conference on Real Time Computing Systems and Applications De cember 1999 Hong Kong China Contributions A toolbox for simulation of embedded systems is designed and imple mented The control algorithm the dynamic process and the underlying real time kernel is viewed as one system and its behavior is investigated through simultaneous simulation of both the process dynamics and the real time kernel The toolbox also supports simulation of distributed con trol systems connected by a network Paper 6 This paper presents the design of a hybrid controller for a heating ven tilation process Eker J and J Malmborg Design and Implementation of a Hybrid Con trol Strategy IEEE Control Systems Magazine vol 19 number 4 August 1999 Contributions A hybrid control strategy based on Lyapunov function arguments is first designed A simplified version of the control law is then proposed and 14 3 Implementation of Control Systems implemented on a commercial embedded control system The controller is tested on a heating ventilation process with good results Related publications Malmborg J and J Eker Hybrid Control of a Double Tank System In Proceedings of the IEEE International Conference on Control Appli cations October 1997 Hartford Connecticut Other Related P
26. KeepFilling end KeepFilling step StopFilling pulse activate CloseV1 end StopFilling step EmptyTank pulse activate OpenV2 end EmptyTank 199 Appendix A PAL P lsj Algorithm Language transition from nit to StartFilling when Start transition from StartFilling to KeepFilling StartHeating when L1 transition from StartHeating to StopHeating when T gt Tref transition from StopHeating to StartHeating when T lt Tref transition from KeepFilling to StopFilling when L2 transition from StopFilling StopHeating to EmptyTank when true transition from EmptyTank to Init when not L1 action OpenV1 begin V1 false end OpenV2 action CloseV1 begin V1 false end CloseV1 action OpenV2 begin V 2 false end OpenV2 action CloseV2 begin V 2 false end CloseV2 action Heat begin Q Ll end Heat action NoHeat begin Q false end NoHeat end boiler end grafcet 200 9 References 9 References str m K J and B Wittenmark 1995 Adaptive Control second edition Addison Wesley Reading Massachusetts Blomdell A 1997 PAL the PALSJ6 algorithm language Report ISRN LUTFD2 TFRT 7558 SE Department of Automatic Control Lund Institute of Technology Lund Sweden David R and H Alla 1992 Petri Nets and Grafcet Tools for modelling discrete events systems Prentice Hall International UK Davis R B 1997 Newmat A matri
27. an observer or a filter can be used 182 7 Implementation Typically this information is needed by the whole set of controllers and thus the controller itself can be implemented as a hybrid system consist ing of one global periodic task that handles the filtering of process data and a set of controllers that can be either active or inactive Many hybrid controllers have the same sort of demands on the programming language Implementing complex control algorithms puts high demands on the software environment Automatic code generation and verification are needed together with advanced debugging and testing facilities The Double Tank System The hybrid controller for the double tank system was implemented in PAL for use in the P LSJ real time environment PAL Blomdell 1997 is a dedicated control language with support for hybrid algorithms Furthermore the language supports data types such as polynomials and matrices which are extensively used in control the ory PAL has a run time environment PALSJO Eker and Blomdell 1996 that is well suited for experiments with hybrid control P LSJ was de veloped to meet the needs for a software environment for dynamically configurable embedded control systems PALSJO features include rapid pro totyping code re usability expandability on line configurability portabil ity and efficiency For a more exhaustive description of PAL and P LSJ see Eker 1997 The Heating Venti
28. are empty i e x gt 0 The switching times are determined by the new and the old set points In practice it is preferable to have a feedback loop instead of pre calculated switching times Hence an analytical solution for the switching curves is needed For the linearized equation for the double tank systems it is possible to derive the switching curve ax b xa x1 lla bi 1 In bal where i takes values in 0 1 The time optimal control signal is u 0 above the switching curve and u 1 below see Figure 7 The fact that the nonlinear system has the same optimal control se quence as the linearized system makes it possible to simulate the non linear switching curves and to compare them with the linear switching curves Simulation is done in the following way initialize the state to the value of a desired set point and simulate backwards in time Note that the linear and the nonlinear switching curves are quite close for the double tank model see Figure 7 The diagonal line is the set of equilibrium points a oe Figure 7 shows that the linear switching curves are always below the nonlinear switching curves This will cause the time optimal controller to switch either too late or too soon 177 Paper 6 Design and Implementation of a Hybrid Control Strategy T T T X1 0 0 05 0 1 0 15 0 2 Figure 7 Switching curves for different set points for the double tank system The set points lie
29. be fed to the process Using a hybrid control scheme it is possible to combine several control al gorithms and thus get a controller that consists of several subcontrollers each designed for a special purpose An example of a multi control ar chitecture is shown in Figure 2 The basic idea here is that the process outputs y are fed back to a set of controllers Then each controller cal culates a candidate control signal Which control signal is finally used is decided by the supervisor For an overview of hybrid systems see Bran icky 1995 Antsaklis and Nerode 1998 Antsaklis et al 1998 Branicky et al 1998 168 2 The Controller Structure A Two Mode Hybrid Controller A controller structure with two sub controllers and a supervisory switch ing scheme will be used The time optimal controller is used when the states are far away from the reference point Coming closer the PID con troller will automatically be switched in to replace the time optimal con troller At each different set point the controller is redesigned keeping the same structure but using reference point dependent parameters Figure 3 describes the algorithm with a Grafcet diagram see David and Alla 1992 Grafcet also known as Sequential Function Charts SFC is a graphical language for implementation and specification of sequential algorithms A Grafcet consists of steps and transitions A step corresponds to a state and can be active or inactive Eac
30. be possible to extend the system with new data types and classes while it is operating Furthermore it should be possible to replace a running algorithm The PALSJO environment provides a framework designed to support on line configurations and code reuse The control algorithm coding is made off line and the system configuration is made on line The system may also be reconfigured on line without stopping the system Basic Idea Many control systems have a similar internal structure The same kind of building blocks are used and their internal communication follows certain patterns There are usually functions for e User interaction The operator must be able to set and inspect parameters and variables make mode changes start and stop oper ation etc e Task management Scheduling of real time activities 86 2 PAL PALSJO Algorithm Language e Data logging Logging of events signals etc e Network interaction Managing the communication with other controllers and with the host system The code for these functions can only be reused if it is implemented in a flexible modular fashion with well defined interfaces Modules for a number of these basic common activities could then be arranged in a framework Then the user of such a framework only needs to add code that is specific for a certain application i e only the control algorithm Design Goals A number of important issues were taken into account when the frame wor
31. changed by the user code while the parameters remain constant throughout the execution To capture the timely behavior of a task the associated code is divided into one or several code segments see Figure 5 The execution time of a segment is determined dynamically at its invocation Normally the seg ments are executed in order but this may be changed by kernel function calls from the user code On a finer level actual execution of statements in a code segment can only occur at two points at the very beginning of the code segment in the enterCode part or at the very end of the code segment in the exitCode part see Figure 6 Typically reading of input signals locking of resources and calculations are performed in the enterCode part Writing of output signals unlocking of resources and other kernel function calls 151 Paper 5 A Matlab Toolbox for Real Time and Control Systems Co Design Code Code Code Segment Segment Segment 1 2 to time Figure 5 The execution structure of a task The flexible structure supports data dependent execution times and advanced scheduling techniques enterCode xitCode dnde Execution Time Figure 6 A code segment is divided in two parts the enterCode part and the exitCode part are typically performed in the exitCode part The following examples illustrate how code segments can model real time tasks EXAMPLE 1 A task
32. code that fits into the framework The framework has classes for real time scheduling network interface and user interaction The control algorithm coding is made off line and the system configuration is made on line The system may also be reconfigured on line without stopping the system Related Work Two previous research projects at the Department of Automatic Con trol in Lund that have influenced this work are LICS Elmqvist 1985 and Sim2DDC Dahl 1990 The Simplex Seto et al 1998 project at Carnegie Mellon University has inspired the support for variable struc ture controllers Other interesting systems are the ControlShell frame work Schneider et al 1995 and the port based object approach built on top of the Chimera system Stewart et al 1993 8 References str m K J and B Wittenmark 1997 Computer Controlled Systems third edition Prentice Hall Upper Saddle River New Jersey Blomdell A 1997 PAL the PALSJ6 algorithm language Report ISRN LUTFD2 TFRT 7558 SE Department of Automatic Control Lund Institute of Technology Lund Sweden 81 Paper 1 A Tool for Interactive Development of Embedded Control Systems Cervin A 1999 Improved scheduling of control tasks In Proceedings of the 11th Euromicro Conference on Real time Systems Euromicro Department of Automatic Control Lund Institute of Technology Sweden In Submission Dahl O 1990 SIM2DDC User s manual
33. control algo rithms On the other hand the true objective of real time scheduling for control is to allocate limited computing resources in such a way that the state estimation and control algorithms can ensure stability and optimize the performance of the system The computing resources could include CPU time and communication bandwidth The approach taken in Paper 4 is based on using dynamic feedback be tween the scheduler and the control loops The idea of feedback has been used informally for a long time in scheduling algorithms for applications where the dynamics of the computation workload cannot be characterized accurately For instance the VMS operating system uses multi level feed back queues to improve system throughput and Internet protocols use feedback to help solve the congestion problems Recently under the title of quality of service QoS the idea of feedback has also been exploited in multi media scheduling R amp D Given this one might expect that the use of feedback in the schedul ing of feedback control systems would have been naturally an active area On the contrary the scheduling research of feedback control systems are dominated by open loop analytic scheduling methods such as rate or dead line based algorithms This is not an accident but rather the consequence of some serious theoretical challenges that require the close cooperation between control and scheduling communities The Vision The work in this the
34. control and much of the work in this thesis is directly or indirectly inspired by his ideas Thanks for being so generous I truly enjoyed working with J rgen Malmborg on the hybrid controller project I have spent many good times together with him and Johan Nils son I would like to thank all the people who work or have worked at the department during these five years Per Hagander made sure that I got a Riccati equation into the thesis Bo Bernhardsson has read and commented on various manuscripts He is always willing to switch focus and help out Anton Cervin did a great job on the toolbox He also read different versions of the papers turning proof reading into an art form FIpA has provided excellent computer facilities Anders Robertsson was very helpful in getting the robotics experiments to work John Hauser vigorously played the devil s advocate and pointed out some blank spots in the thesis Klas Nilsson came with some useful last minute comments Paolo Tona did great work putting PALSIMART together Thank you all Acknowledgments This work has been supported by the Swedish National Board for In dustrial and Technical Development NUTEK I would also like to thank the Swedish real time research network ARTES for their support of my work Finally thanks to all my friends and family for supporting and encour aging me and for giving me so many good reasons not to work Most of all thanks to Lotta for being the apple of my ey
35. extreme values For problems with a two dimensional state space the strategy can be expressed in terms of a switching curve that separates the state space into two subsets where the control signal assumes either its high or low value This changes the control principle from feed forward to feedback Equilibrium points and switching curves around these may be derived from the state space representations These switching curves may then be used as reference trajectories For many systems analytic expressions for the switching curves are hard to derive The solution is then to use approximate switching curves If the system is known it is easy to get numerical values for the switching curves through simulation 176 5 Controller Design The Hamiltonian A x u A for the double tank system described by Equation 3 is H 1 41 a x1 bu Aa ay x1 ayxa with the adjoint equations E H E SE o Az 0 a A2 The complete solution to these equations is not needed to derive the opti mal control signal It is sufficient to note that the solutions to the adjoint equations are monotonic The switching function from solving Equation 8 is o A bu It gives the optimal control signal sequence that minimizes H u and the possible control sequences are then 0 1 1 0 0 1 For linear systems of order two there can be at most one switch between the maximum and minimum control signal value it is assumed that the tanks never
36. for Real time Controller Tasks 144 Paper 5 A Matlab Toolbox for Real Time and Control Systems Co Design Johan Eker and Anton Cervin Abstract The paper presents a Matlab toolbox for simulation of real time control systems The basic idea is to simulate a real time kernel in parallel with continuous plant dynamics The toolbox allows the user to explore the timely behavior of control algorithms and to study the interaction be tween the control tasks and the scheduler From a research perspective it also becomes possible to experiment with more flexible approaches to real time control systems such as feedback scheduling The importance of a more unified approach for the design of real time control systems is discussed The implementation is described in some detail and a number of examples are given 145 Paper 5 A Matlab Toolbox for Real Time and Control Systems Co Design 146 1 Introduction Single CPU System Real Time Kernel Task 1 Task 2 j 2 y2 u3 y3 Plant 1 Plant 2 Plant 3 Figure 1 Several control loops execute concurrently on one CPU The interaction between the control tasks will affect the control performance Task 3 j y u Y 1 Introduction Real time control systems are traditionally designed jointly by two dif ferent types of engineers The control engineer develops a model for the plant to be controlled designs a control law and tests it in
37. for aggregate data types It gets its value upon block creation and may not be assigned within the algorithm section The value of a dimension variable can only be set by the runtime system There is a special data type sampling interval for handling the period time for periodic processes The sampling time is set by the user or the run time system Below is an example of more complex data types n dimension inl input array 1 n of real m dimension in2 array 0 m of input real out input matrix 1 n 1 m of real par parameter polynomial n of real There are built in functionality to fully support the use of matrices and polynomials Function libraries for Diophantine equation solving recur sive model estimation etc are available Events All procedures in PAL when executed in the P LSJ environment are reg istered as events For example let the procedure Reset below be defined in the block Estim The Reset procedure may then be called from the PCL command line by the following command pcl gt process block new Estim pcl gt process block Reset TT Paper 1 A Tool for Interactive Development of Embedded Control Systems Grafcet Grafcet see David and Alla 1992 is a convenient and powerful way of implementing sequential algorithms There exist constructs in PAL for ex pressing Grafcet algorithms These constructs are steps actions and tran sitions Grafcet statements are expressed in PAL
38. h The controller u Lx t that minimizes the cost is given by solving the stationary Riccati equation with respect to the matrices S and L S LTGL LG GL G where Q T ir slo Ti Qs 3 where G I ST Qsd and h Qa Qe dt a 4 The minimal value of J is given by Astr m and Wittenmark 1997 Gustafsson and Hagander 1991 as 1 2 mind h trSR J where h J tr Ri t dt In order to use the cost function in the optimization it is useful to know the derivatives with respect to the sampling period 129 Paper 4 A Feedback Scheduler for Real time Controller Tasks THEOREM 1 The first derivative of J is given as dJ 1 dS dR d 2 trSR J where dS _ 7 dS a eat g TL W AN eee Td E id E TL TAT L7B S TL TL S A TL BL The matrix R is calculated using the expressions in Equation 1 Ri Y LW yo where pet ta y 0 Woe O AT dR _ An ATh aa Rie dj ah trQi R1 a See Appendix A for the proof The expression for the second derivative of the cost functions is also given there EXAMPLE 1 Consider the linearized equations for a pendulum 0 1 0 del a Co fea gy edt do y 1 0 x Reelo e 0 0 The natural frequency is o the damping d 2 0 with 0 2 and b 09 9 81 If a 1 the equations describe the pendulum in the upright 130 5 A Feedback Scheduler position and if a 1 they describe
39. implementing a control loop can often be divided into two parts one that calculates a new control signal and one that updates the con troller states The first part called Calculate Output has a hard timing constraint and should finish as fast as possible The timing requirement for the second part Update State is that it must finish before the next invocation of the task Two code segments are appropriate to model the task LOOP E E Read Inputs Code Cade CalculateOutput Segment Segment Write Outputs E UpdateState al a END The enterCode of the first segment contains the reading of the measure ment signals and the calculation of a new control signal In the same seg 152 4 Using the Simulator ment in exitCode the control signal is sent to the actuator The control delay of the controller is thus equal to the execution time of the first seg ment The enterCode of the second code segment contains Update State When the last segment has completed the task is suspended until the next period by the kernel O EXAMPLE 2 The structure of a periodic task that first calculates some data and then writes to a common resource could look like this LOOP Calculate Lock Mutex Code Code WriteData Segment Segment e l Unlock Mutex Sleep A END Again two code segments can capture the timely behavior The first code segment contains the Calculate statement loc
40. informally for a long time in scheduling algorithms for applications where the dynam ics of the computation workload cannot be characterized accurately The VMS operating system for example uses multi level feedback queues to improve system throughput and Internet protocols use feedback to help solve the congestion problems The idea of feedback has also been ex 123 Paper 4 A Feedback Scheduler for Real time Controller Tasks Desired Load gt Exec Times Performance gt Feedback Scheduler Sampling Rates Figure 1 New sampling rates are calculated based on the desired CPU load the execution times of the controllers and the performance of the controllers ploited in multi media scheduling R amp D recently under the title of quality of service QoS In this paper we want to schedule a set of real time control loops to maximize their total performance The number of control loops and their execution times may change over time and the task schedule must hence be adjusted to maintain optimality and schedulability Since the optimizer works in closed loop with the control tasks it is referred to as a feedback scheduler The feedback scheduler adjusts the control loop frequencies to optimize the control performance while maintaining schedulability The input signals are the performance levels of each loop their current ex ecution times and the desired workload level see Figure 1
41. may be organized in a hierarchical fashion and by the full block name all the blocks above in the hierarchy is meant In the example below the full name for the second block is S Input 203 Appendix B PCL P lsj Configuration Language pcl gt S new Periodic pc1x gt S Input new Analogln Periodic is a predefined block type There are three predefined block types Periodic Aperiodic and Remotelo0 All other block types must be imported from either block libraries supplied by the user at linkage time or from the P lsj standard library see the use statement below delete A block is deleted using the delete command pcl gt delete lt block name gt with To avoid repeating the block path name the with command is available It works similarly to the with statement in Modula 2 and Pascal EXAMPLE 1 pcl gt use MyBlocks pel gt f pcl gt S new Periodic pclx gt with S pel S gt adin new AnalogIn pel S gt control new PI pcl S gt daout new AnalogOut pel S gt pel S gt refgen out gt control yr pcl S gt adin out gt control y pcl S gt control u gt daout in pcl S gt endwith pcl gt reset This command is used to remove all blocks from the workspace and clears all system variables All processes must be stopped before this operation is possible pcl gt reset 204 2 Keywords quit Stops the run time system and exits to the surrounding shell All processe
42. modules for these basic common activities are arranged in a framework the user of such a frame work only needs to add the code that is specific for a certain application In the case of embedded control systems the necessary code is typically the control algorithm 17 Introduction The PALSJO environment is an attempt to provide such a framework The project was outlined in 1994 Gustafsson 1994 as a part of the project Autonomous Control The goal was to create an environment for experiments in automatic control Initially a C class library was proposed but the library soon became very large and cumbersome to use A set of C pre processor macros were created in order to support use of the framework These worked reasonably well but to further ease the use of the framework a new language with a compiler was created The language is called PAL which stands for PALSJO Algorithmic Language Blomdell 1997 and was designed to support controller implementation Control algorithms can often be described as a combination of periodic tasks and finite state machines PAL supports those types of algorithms The finite state machine is supported in form of Grafcet David and Alla 1992 Furthermore the language supports data types such as polynomials and matrices which are extensively used in control theory The P LSJ system consists of two main parts a compiler and a frame work The compiler reads algorithms specified in PAL and
43. new BlockTypeA pcl gt s BlockB new BlockTypeB pc1 gt s BlockA out gt s BlockB in O If a connection results in an algebraic loop the system will give a warning When this occurs the blocks cannot be sorted according to data flow The execution order will then be determined from the order the blocks were added to the Periodic block The Disconnect Operator To break up a connection the disconnect operator is applied on the input signal To disconnect the blocks in the previous example the following command is given pcl gt s BlockB in Macro Operator It is possible to use macros to simplify system configuration A macro file consists of a set of PCL commands A PCL macro may have arguments Below a macro with two arguments is shown 211 Appendix B PCL P lsj Configuration Language 1 new Periodic with 1 2 new PI endwith All occurrences of 1 are replaced by the first argument and all occur rences of 2 is replaced by the second argument and so on A macro is called using the following syntax lt macro name gt pari par2 A call to the macro above would thus have the following look pcl gt macroname S A The default file extension for all macro files is pcl The Move Operator gt The move operator is used to move blocks from one location to another For example from the workspace to a Periodic block or from one Periodic block to another This is demonstrated by an example The
44. overall system remains schedulable during and after the mode change A simple mode change protocol was suggested in Sha et al 1989 The protocol assumes that an on line record of the total utilization is kept A task may be deleted at any time and its utilization may be reclaimed by a new task at the end of the period of the old task The new task is accepted if the resulting task set is schedulable according to the rate monotonic analysis The locking of semaphores according to the priority ceiling protocol during the mode change is also dealt with In Tindell et al 1992 it was pointed out that the analysis of Sha et al was faulty Tasks may miss their deadlines during a mode change even if the task set is schedulable both before and after the switch The tran sient effects of a mode change can be analyzed by extending the deadline monotonic framework Formulas for the worst case response times of old and new tasks across the mode change were given New tasks may be given release offsets relative to the mode change request to prevent dead lines to be missed It is interesting to note that under EDF scheduling the reasoning about the utilization from Sha et al 1989 actually seems to hold In Buttazzo et al 1998 EDF scheduling of a set of tasks with deadlines equal to their periods is considered It is shown that a task can decrease its period at its next release as long as the total utilization remains less than one
45. programming the larger and more inefficient the resulting programs usually become Distributed control systems are common in the process and manu facturing industry and are typically programmed using sequential func tion charts function block languages or relay or ladder diagram lan guages Distributed control systems and programmable logic controllers 16 3 Implementation of Control Systems share many of the characteristics of embedded systems Many of these systems have the bizarre property that the order of execution depends on the order in which the systems are configured This can lead to many strange effects particularly when changes are made Several real time languages have been proposed One is the functional language Erlang Armstrong et al 1993 developed by the Swedish tele com industry It has built in support for concurrency and error recovery Erlang is aimed for use in soft real time systems and it also has mech anisms for on line code replacement The language HI Pearl is an ex tension of the Pearl programming language augmented with real time constructs Stoyenko and Halang 1993 Pearl was designed in the late 1960 s as a process control language for industrial automation problems Real Time Euclid offers similarly to HI Pearl schedulability analysis of the compiled code Kligerman and Stoyenko 1986 It is a Pascal style language where all constructs are space and time bounded Hence re cursion and dyn
46. resulting sys tems in Example 4 and Example 5 are equivalent EXAMPLE 5 pel gt pcl gt s new Periodic pcl gt BlockA new BlockTypeA pcl gt BlockB new BlockTypeB pcl gt BlockA gt s pcl gt BlockB gt s pc1 gt s BlockA out gt s BlockB in 212 LUND INSTITUTE OF TECHNOLOGY Lund University ISSN 0280 5316 ISRN LUTFD2 TFRT 1055 SE
47. tasks running on separate CPUs The locks and the events are designed similarly to how monitors and events are implemented in a standard real time kernel i e using queues associated with the monitor for storing tasks blocking on locks or events The execution time used for trying but failing to lock is in the example above zero Network Blocks It is possible to include more than one Computer block in a Simulink model and this opens up the possibility to simulate much more complex systems than the ones previously discussed Distributed control systems may be investigated Furthermore fault tolerant systems where for re dundancy several computers are used for control could also be simulated In order to simulate different communication protocols in such systems communication blocks for sending data between the different Computer blocks are needed Figure 14 shows a simulation setup for a simple dis tributed system where the controller and the actuator and sensor are located at different places Besides the kernel blocks there is a network block for communication The network block is event driven and each time any of the input signals change the network is notified The user needs to implement the network protocol since the blocks simply provides the mechanisms for sending data between kernels 161 Paper 5 A Matlab Toolbox for Real Time and Control Systems Co Design High Level Task Communication One of the main reasons
48. the Computer block it is possible to study details about the execution of different tasks stance possible to study the schedule i e a plot that shows when different tasks are executing at run time Further statistics about the execution is stored in the workspace and may be analyzed when the simulation has stopped Controller Implementation It is highly desirable that the design of the kernel is flexible and al lows components to be reused and replaced Much effort has been put into writing control algorithms in Matlab and these algorithms should be straightforward to reuse In the toolbox a control algorithm can be implemented as a code segment with the following format function exectime states myController flag states params switch flag case 1 Y enterCode y analogIn params inChan states u lt place control law here gt exectime 0 002 case 2 exitCode analogOut params outChan states u end 154 4 Using the Simulator The input variables to myController are the state variables states and the controller parameters params The flag is used to indicate whether the enterCode or the exitCode part should be executed If the enterCode part is executed the function returns the execution time estimate exectime and the new state variables The control signal is sent to the plant in the exitCode part REMARK 1 The output signal u is not normally regarded as a state variable in a controller In this example
49. the concepts of the P LSJ framework and details of the run time system are discussed The proposed language FRIEND is designed to give high level support for implementation of flexible control systems The main concept is to use contracts to specify when and how control algorithms can be used FRIEND is presented in Paper 3 with a discussion on flexible systems and some code examples 4 The Robot Pendulum Controlling the inverted pendulum is a classical problem in control labo ratories The pendulum process provides a suitable test bench for control algorithms as well as for real time control applications Since the process is both nonlinear and unstable it gives rise to a number of interesting problems Its unstable nature makes it a good process for testing real time controllers since if the timing fails the pendulum is likely to fall down The goal with the control is to bring the pendulum from the downward position to the upward position and keep it stabilized The ABB Irb 2000 industrial robot used in the experiments is shown in Figure 3 The robot holds the shaft of the pendulum using a gripper that is attached to the robot wrist see Figure 4 Joint 1 of the robot is then used for swinging up and balancing the pendulum The Model The design of the controller is based on the following linear model of the pendulum on the robot X1 X2 x Ax BT where x X3 ss gt D X4 23 Introduction Figure 3 The ABB Irb20
50. the controlled plant This includes computational phases input and output actions and blocking of common resources other than the CPU Figure 3 shows the activation graph for the low priority task from Figure 2 and how it interacts with the continuous plant The controller samples the continuous measurement signal from the plant y and writes new control outputs u Figure 4 provides a schematic view of how we simulate the system A model of a real time kernel handles the scheduling of the control tasks and is also responsible for properly interfacing the tasks with the physical environment The outputs from the kernel model i e the control signals are piecewise constant The plant dynamics and the plant outputs i e the measurement signals are continuous 3 The Simulation Model The heart of the toolbox is a Simulink block an S function that simu lates a tick driven preemptive real time kernel The kernel maintains a number of data structures that are commonly found in a real time ker nel a set of task records a ready queue a time queue etc At each clock 150 3 The Simulation Model tick the kernel is responsible for letting the highest priority ready task i e the running task execute in a virtual CPU The scheduling policy used is determined by a priority function which is a function of the at tributes of a task For instance a priority function that returns the period of a task implements rate monotonic schedul
51. the pendulum in the downward position The incremental covariance of ve is Rj dt which corresponds to a disturbance on the control signal The cost functions J for the closed loop control of the inverted pen dulum as a function of the sampling interval is shown in Figure 3 The corresponding function for the stable pendulum is shown in Figure 4 Cost 15000 10000 f 5000 Figure 3 The cost J h as a function of the sampling interval for the inverted pendulum The plot shows the graph for 3 14 full 3 77 dot dashed and 4 08 dashed Figure 4 clearly demonstrates that faster sampling not necessarily gives better control performance Sampling the pendulum as slowly as this is however unrealistic The rule of thumb from str m and Wittenmark 1997 is to chose the sampling rate as oh 0 2 0 6 O 5 A Feedback Scheduler In this section a feedback scheduler see Figure 2 for a class of control systems with convex cost functions is proposed Standard nonlinear pro gramming results are used as a starting point for the feedback sched uler design First an algorithm using the cost functions presented in the previous section is designed and then an approximate less computation intense algorithm is presented Simulation results for a system with three control loops are also given 131 Paper 4 A Feedback Scheduler for Real time Controller Tasks Cost 1800 T TY A 1600 1 I I 1400 i
52. the top negotiator A negotiator block may be viewed as a virtual computer with a set of available resources 4 The Friend Language Does the world really need another language and why cannot the pro posed structure with contracts and negotiators be implemented using for example Java The answers to those questions lie in what we are trying to achieve with FRIEND The goal is to design a language that gives good support in writing adaptive control applications using contracts In the same way that you could write object oriented code in plain C or write numerical software in Cobol contract based control software can be im plemented in the language of your choice We believe however that the quality of the resulting application will be higher if the design paradigm and the implementation paradigm are the same Hence the introduction of a new programming language This section gives an introduction to FRIEND and the syntax of the language is presented by examples 109 Paper 3 A Contract Based Language for Embedded Control Systems block algorithm negotiatior Figure 5 The block the algorithm and the negotiator are the three types of block in FRIEND The Components FRIEND is a small block based imperative language and is a continuation of the PAL PALSJ6 project see Eker 1997 Blomdell 1997 In FRIEND there are four main components e The Algorithm An algorithm is a bloc
53. this section two different ap proaches to simulation of embedded control systems are discussed First the PALSIMART simulation environment in which PAL blocks may be simulated is presented Second a MATLAB Simulink toolbox for inte grated simulation of process dynamics and discrete controllers running in a virtual computer is introduced The toolbox is the subject of Paper 5 PALSIMART Rapid prototyping of advanced control systems can be properly supported provided that the design phase is closely coupled to the real time imple mentation In many systems once the controller is designed and tested in simulation the control algorithm must be rewritten usually from scratch in another environment for real time embedded implementation Apart from an obvious overhead this procedure may as well cause significant deviations from the predicted behavior due to the basically different na ture of the underlying code One possible rapid prototyping approach mentioned earlier and in deed the most widespread so far consists of using commercial tools like Simulink together with Real Time Workshop or SystemBuild together with AutoCode One problem with this approach is that the languages used in simulation may not be suitable for designing real time applica tions With PALSIMART another approach was chosen based on the in tegration of the control description language PAL and the CACSD envi ronment SIMART see M Saad et al 1997 SIMART
54. three different scheduling strategies The dashed line shows the ideal behavior and the dotted line shows the reference signal The plot show the WCET scheduling top Average scheduling middle and Feedback scheduling bottom Average Case Scheduling The average case scheduling scenario allows deadlines to be missed and instead tries to keep a high utilization level The sampling intervals h 2 6 s ha 1 8 s ha 1 3 s are calculated to give approximately 80 utilization Actual utilization in simulation is 78 5 This approach will favor the controllers with high priorities Controller 1 however misses a lot of deadlines with poor performance as a result The output from the system controlled by Controller 1 is shown in Figure 22 middle 61 Introduction Strategy Vi Vo V3 Uef WCET 0 21 0 20 0 15 32 7 Average 0 21 0 05 0 037 78 5 Feedback 0 067 0 067 0 095 80 Table 1 The different scheduling strategies are compared in terms of the addi tional cost due to scheduling The U y is the actual utilization from the simulation The feedback scheduling strategy distributes the computing resources more evenly over the tasks which results in lower total cost Feedback Scheduling The feedback scheduling approach tries to achieve both high utilization and few missed deadlines Each task is associated with a cost function which reflects how the task performance relates to the sampling inter val The cost function is given by E
55. to be active The decision of the supervisor is based on so called switching rules which in FRIEND are conveniently expressed in terms of contracts The paper is organized as follows Section 2 gives some motivation and overview of related work The concept of FRIEND is presented in Section 3 and the outline of the language is presented by two examples in Section 4 A summary is then given in Section 5 2 Related Work How can software be designed so that it can reconfigure itself and load and unload software modules on line in order to cope with changes in the environment Such an adaptive behavior could prove useful in an embedded control system The number of real time tasks the available resources and the usage thereof would then be allowed to change with time A simple example of such a scenario is an embedded control system where new control loops are added from time to time Since it is a real time system care must be taken to ensure that enough computing and network resources are available for all tasks A change in the task set re 105 Paper 3 A Contract Based Language for Embedded Control Systems quires the task schedule to be recomputed By introducing a feedback loop between the control loops and the kernel an adaptive real time system can be formed Figure 1 illustrates this setup The real time scheduler Real Time y Scheduler Performance Available amp resources validity Controller Inp
56. with a textual represen tation that is based on Sequential Function Charts in TEC 1131 Lewis 1995 A Grafcet designed to control a boiler process is shown in Figure 2 Each state in a sequential algorithm is defined as a step in Grafcet A step may be active or inactive Several steps may be active at the same time A Grafcet must have an initial step The syntax for defining a step is illustrated below initial step Init pulse activate CloseV2 end Init step StartHeating activate Heat end StartHeating step StopHeating pulse activate NoHeat end StopHeating A transition has a set of input steps a set of output steps and a condition All input steps must be active and the condition must be true for the transition to be fireable When a transition is fired all output steps become active transition from StartFilling to KeepFilling StartHeating when Ll transition from Start Heating to Stop Heating when T gt Tref A block algorithm may be described using both the calculate update procedures and one or or several Grafcets This is useful when an algo rithm is composed of one periodic part and one sequential part Consider for example a hybrid controller The control law is conveniently expressed using Grafcet where each step corresponds to a sub controller Assume that several of the control laws used are of state feedback type and that all plant states cannot be measured In this case we need to estimate the stat
57. 00 robot and the pendulum used in the experiment and 7 is the torque applied to joint 1 of the robot The states and are the angle and the angular velocity of the pendulum see Figure 5 The position and velocity of joint 1 are denoted and 4 respectively The model used in the control design is very much simplified First it is assumed that the system may be viewed as two decoupled sub systems one describing the pendulum and one describing the robot arm position The Corioli forces due to the rotation and the interaction between the pendulum and the arm are neglected Let us first look at the pendulum and model it as if attached to a cart running on a straight track see Figure 5 The input signal u to the pendulum is the acceleration of the pivot i e the acceleration of the cart 24 4 The Robot Pendulum Joint 3 Joint 4 Joint 2 Joint 1 Figure 4 The pendulum is held by the gripper on the robot The equation of motion of the inverted pendulum is given by d o dr 9 qa Vosin 0 u g cos 0 where 00 yg9 l is the natural frequency for small oscillations around the stable equilibrium and g is the gravity The input signal u is the acceleration of the pivot When the pendulum is attached to the robot it can be approximated by u 1 where l is the length of the robot arm The equation of motion can be written as dx1 dix ap 7 2 dx2 y ea o sin x U g 0 cos x1 where x 0 and x2 0 09 The i
58. 1 1 of real x1hat 0 0 x2hat 0 0 dx1hat 0 0 dx2hat 0 0 real theta Hat 0 0 dthetaHat 0 0 real xr 0 0 E 2 0 real on false boolean k 280 0 parameter real w0 6 3 parameter real n 0 35 parameter real minTh 0 1 maxTh 0 45 parameter real h sampling interval calculate begin dxlhat w0 x2hat K2 1 1 x th theta Hat dx2hat w0 sin x1hat w0 u 9 81 x cos x1hat K2 2 1 th theta Hat xlhat x1hat dxlhat h x2hat x2hat dx2hat h thetaHat x1hat dthetaHat w0 x x2hat end calculate update begin xhat A22 x xhat B2 xu K1 x xhat 1 1 end update action off begin u 0 0 end off action swing begin E 0 5 x dtheta Hat dthetaHat w0 w0 cos th 1 0 u sign dthetaHat x cos th sat n 9 81 k E end swing 4 The Robot Pendulum action catch begin xr x u L 1 1 th L 2 1 dtheta Hat end catch action stabilize begin u L 1 1 th L 2 1 dthetaHat L 3 1 xhat 1 1 xr L 4 1 xhat 2 1 end stabilize initial step step1 activate off end stepl step step2 activate swing end step2 step step3 activate catch end step3 step step4 activate stabilize end step4 transition from step1 to step2 when on transition from step2 to step3 when th gt minTh and th lt maxTh
59. 3 Design controller params ctrl_design omega i T i Initialize control code states xhat 0 0 The controller reads from input i params inChan i The controller writes to output i params outChan i sfbcode code myController states params Create task tasks i task Task num2str i sfbcode T i T i end rtsys tasks tasks O The outputs from a simulation of this system are a set of continuous signals from the plants together with an activation graph It is hence possible to evaluate the performance of the real time systems both from a control design point of view and from a scheduling point of view 5 A Co Design Example Using the simulator it is possible to evaluate different scheduling policies and their effect on the control performance Again consider the problem of controlling three inverted pendulums using only one CPU see Figure 11 The inverted pendulum may be approximated by the following linear dif ferential equation 00 0u 9 157 Paper 5 A Matlab Toolbox for Real Time and Control Systems Co Design where 00 y 9 l is the natural frequency for a pendulum with length l The goal is to minimize the angles so for each pendulum we want to minimize the accumulated quadratic loss function Ji t a 6 s ds 1 Three discrete time controllers with state feedback and observers are de signed Sampling periods for the controllers are chosen according to the desired
60. 4 z 0 05 4 E 0 T T T T T 0 y T T T y 0 100 200 300 0 100 200 300 Uh ybrid x2 0 2 1 L 0 8 F 0 15 4 E PS ini 0 6 E 0 1 F 0 4 F S 0 2 F 0 05 4 z S 0 L T T 0 7 T T x 0 100 200 300 0 0 05 0 1 0 15 0 2 x1 Figure 9 Simulation of the simple switching strategy for the double tank system Lower left figure shows the control signal The time optimal controller makes one extra min max switch because of the nonlinearity Catching regions are shown in lower right sub figure tions are defined as T x X1 x X1 V R P 0 R PID x 2 0 7 xy x2 ait X3 x X3 Vro remaining time to reach new set point The second Lyapunov function is associated with the time optimal control law and is the time it takes to reach the new setpoint starting from the current position in the state space if time optimal control is used The state xs is the integrator state in the PID controller and x is its steady state value As in the previous simulation set the parameters y and 0 are used to shape the catching region The new state x3 is preset to its value at the new equilibrium point i e e any time there is a set point change This state is not updated until after the first switch to PID control Using this method a similar two dimensional catching region as in the case with the simple switching strategy is created The simulation results are presented in Figure 10 180 6 Simulations
61. 81 2 A Flexible Interactive Environment for Embedded Con GOMES 2 iee son Sch ae a dh os en Seen ne Sects Sean nen Sonor os ae A A 83 1 Introduction e 85 2 PAL P LSJ Algorithm Language 87 3 The P LSJ framework 00 00005 90 4 Signal Management 96 5 On line Configurations 98 6 Conclusion e 99 7 Acknowledgment 0 0000 ee eens 100 8 References is ideie as te Jeda fe A 100 3 A Contract Based Language for Embedded Control Sys tems ie Rachie suk hh ets tn ies es Gus Benes Has he he eee 103 1 Introduction 0 o 105 Contents 4 5 2e Related Work 6s 3 50 6 8 80 Se bobo bod do de A 105 3 Friendly Concepts 0 0 00 ee eee eee 107 4 The FRIEND Language 0 0000 2a 109 De MUMMY hoot e ws oe oo ss te Se ee eee ee ee ee ee 117 6 References 2 56 2 b 84 Bh 648 bf 6 bo bad bd bo bd Add 117 A Feedback Scheduler for Real time Controller Tasks 121 Th APAEROMUCEIONS so oe A a on a Mond A amp Bard 123 2 Integrated Control and Scheduling 125 3 Problem Statement 00002 ee eee 128 Av COST WUNnCtIONS r y se Fee aa sk a a ee hl ask a laa a eae ge ad aed 128 5 A Feedback Scheduler 131 6 Conclusion s s ar e a e ated ia 136 7 References 137 Appendix A Proof and Continuation of Theorem 1 140 A Matlab Toolbox for Real Time and Control
62. 96b The same control algorithm description may then be used both in simulation and in implementation This is practical if simulation is the main goal and implementation is just a feature It may however be a serious draw back if the main goal is to implement a safe and efficient controller One drawback with code generation is that it does not take into account the fact that sampling delay can be significantly reduced by rearranging the code see Astr m and Wittenmark 1997 Another drawback is that most simulation languages are not designed to deal with execution in real time and therefore lack the necessary functionality It would be better to use a tool that is designed especially for controller implementations but that also supports simulation in some way The requirements of a real time lan guage are typically quite different from those of a simulation language For example the weak typing in MATLAB where basically everything is 85 Paper 2 A Flexible Interactive Environment for Embedded Controllers matrices is useful while designing and during simulations as the control engineer does not have to worry about data types and variable allocations During implementation on the other hand strong typing and no global variables are needed to create safe real time systems If a simulation fails due to a programming error it is usually easy to correct it and restart the simulation However if the controller fails during an experiment in
63. Close Step3 Catch Upright Step4 Stabilize Stop Falling Figure 6 The Grafcet which describes the switching rules for the hybrid pendu lum controller The pendulum standing in the upright position corresponds to zero energy The algorithm used for controlling the energy was proposed in Wiklund et al 1993 str m and Furuta 1996 and is given as u satag RE sign 0 cos 0 where k and n are design parameters The function sat saturates when its argument is larger than n times the gravity g When the pendulum is close to the upright equilibrium the catching controller is switched in The task for this controller is to as smoothly as possible hand over the control from the swing up mode to the stabilizing mode The controller used in the experiments is the following state feedback controller u l x laxo This controller stabilizes the pendulum but takes no concern to the po sition of the pivot To balance the pendulum at the upright equilibrium another state feedback controller is used The control law is the following u l1x1 laxo l3 x3 Xr laxa where x is the desired position of joint 1 The controller parameters are calculated using pole placement design 27 Introduction Designing an Observer In order to implement the control laws discussed above both the angle and the angular velocity values are needed Since no angular velocity measurement is available this must be esti
64. Flexible Embedded Control Systems Design and Implementation Johan Eker Flexible Embedded Control Systems Design and Implementation Flexible Embedded Control Systems Design and Implementation Johan Eker Lund 1999 Till Lotta Department of Automatic Control Lund Institute of Technology Box 118 S 221 00 LUND Sweden ISSN 0280 5316 ISRN LUTFD2 TFRT 1055 SE 1999 by Johan Eker All rights reserved Printed in Sweden by Wallin Dahlholm Boktryckeri AB Lund 1999 Contents Acknowledgments aaa aaa 9 Introduction e 11 T Motivation eat ara 11 2 Outline and Summary of Contributions 12 3 Implementation of Control Systems 15 4 The Robot Pendulum 23 5 Feedback Scheduling 36 6 Simulation of Embedded Control Systems 44 7 Implementation of a Hybrid Controller 52 8 A Unifying Example 54 9 References e 63 1 A Tool for Interactive Development of Embedded Control Systems a III rd Bb es de 69 1 Tatroductio ee PRP alaala a ala alaala aiii a 71 2 The P LSJ System ee ee 71 3 Configuring the SysteM 74 4 PAL P lsj Algorithm Language 75 5 Calculate and Update 79 6 On Line Configurations 81 o A NN 81 By References cu bid hts ds Ga hy ek A
65. Model and optimal control theory IEEE Trans Automatic Control 43 1 p 31 David R and H Alla 1992 Petri Nets and Grafcet Tools for modelling discrete events systems Prentice Hall Eker J 1997 A Framework for Dynamically Configurable Embedded Controllers Lic Tech thesis ISRN LUTFD2 TFRT 3218 SE Depart ment of Automatic Control Lund Institute of Technology Lund Swe den Eker J and A Blomdell 1996 A structured interactive approach to embedded control In The 4th International Symposium on Intelligent Robotic Systems Lisbon Portugal Elmqvist H K J str m T Sch nthal and B Wittenmark 1990 Simnon User s Guide SSPA G teborg Sweden Ferron E 1996 Quadratic stabilizability of switched systems via state and output feedback Technical Report CICS P 468 Center for intelligent control systems MIT Cambridge Massachusetts 02139 U S A Hay J L and A W J Griffin 1979 Simulation of discontinuous dy namical systems In Proc of the 9th IMACS Conference on Simulation of Systems Sorrento Italy Johansson M and A Rantzer 1998 Computation of piecewise quadratic lyapunov functions for hybrid systems IEEE Transactions on Automatic Control 43 4 pp 555 559 Special issue on Hybrid Sys tems Leitman G 1981 The Calculus of Variations and Optimal Control Plenum Press New York Lewis F L 1986 Optimal Control Wiley 187 Paper 6
66. PCL P lsj Configuration Language 203 T Introduction bd oot ce ee heh ie he hes Bie hod a 203 Di Keywords si su S fa Je i oe S Sa Je ele Ja Jade Ia fe ote belo ie B amp R eS 203 3 Operators ya w ke a RR RR a a e a 208 Contents Acknowledgments Starting on my first day of undergraduate studies in Lund I heard peo ple talking about Professor str m Nobody seemed to know what he did They had just heard about him A couple of years later when 1 did my master s thesis at the department I got to know the object of all the ru mors Karl Johan str m has so much energy and such a drive that it is hard not to the get carried away And I was Now the thesis is written and I owe my gratitude to many people who have helped me along the way My main thanks go to my supervisors Karl Johan str m and Karl Erik Arz n without whom this thesis would never have been completed Karl Erik has done a great job in reading and improving this thesis and for this I am very grateful Karl Johan s overwhelming enthusiasm has kept me going when things felt tough Working with Karl Johan and Karl Erik has been a great pleasure and lots of fun Many thanks to Anders Blomdell the best programmer I have ever met for always being anxious to deconstruct my vague ideas Thanks to my roommate and dear friend Erik M llerstedt for putting up with my mood swings and for solving those equations for me Lui Sha changed my view on embedded
67. RIEND supports the implementation of flexible control systems through the use of contracts In FRIEND a control algorithm may be associated with a contract which defines the expected behavior of the algorithm The contracts allow the run time system to distinguish between blocks that are working correctly or incorrectly The notion of contracts in the language supports the development of systems with a high level of adaptivity and fault tolerance Paper 4 A feedback scheduler algorithm is presented Given that all the control tasks are associated with cost functions it finds the optimal set of sam 13 Introduction pling frequencies Eker J P Hagander and K E Arz n A Feedback Scheduler for Real time Control Tasks In submission to Control Engineering Practice Contributions A feedback loop between the control tasks and the real time kernel is designed based on LQG cost functions How the cost depends on avail able computing resources is investigated and an algorithm for finding the optimal resource allocation scheme is proposed Related publications rz n K E B Bernhardsson J Eker A Cervin K Nilsson P Pers son and L Sha Integrated Control and Scheduling Technical Re port ISRN 7586 Department of Automatic Control Lund Institute of Technology August 1999 Lund Paper 5 A toolbox that supports simulation of closed loop embedded control sys tems at task level is presented Eker
68. Report TFRT 7443 Depart ment of Automatic Control Lund Institute of Technology Lund Swe den David R and H Alla 1992 Petri Nets and Grafcet Tools for modelling discrete events systems Prentice Hall International UK Eker J 1997 A Framework for Dynamically Configurable Embedded Controllers Lic Tech thesis ISRN LUTFD2 TFRT 3218 SE Depart ment of Automatic Control Lund Institute of Technology Lund Swe den 100 8 References Elmqvist H 1985 LICS Language for implementation of control systems Report TFRT 3179 Department of Automatic Control Lund Institute of Technology Lund Sweden Gamma E R Helm J R and J Vlissides 1995 Design Patterns Elements of Reusable Object Oriented Software Adison Wesley Read ing Massachusetts Integrated Systems 1996a AutoCode User s Guide Integrated Systems Inc 3260 Jay Street Santa Clara CA 95054 3309 USA Integrated Systems 1996b SystemBuild User s Guide Integrated Sys tems Inc 3260 Jay Street Santa Clara CA 95054 3309 USA Lewis R 1995 Programming industrial control systems using IEC 1131 3 The Institution of Electrical Engineers London U K MathWorks 1997 Simulink Real Time Workshop The MathWorks inc 24 Prime Park Way Natick MA 01760 1500 RealTimelInnovations 1995 ControlShell Object Oriented Framework fro Real Time System Software Real Time Innovations Inc 155A Moffet Park Drive Suite 111 S
69. Robertsson A J Eker K Nilsson and R Johansson Application Spe cific Control for Industrial Robots Poster presentation at the 3rd Por tuguese Conference on Automatic control Controlo98 1998 Lisboa Portugal Eker J A Framework for Dynamically Configurable Embedded Control lers Licentiate Thesis ISRN LUTFD2 TFRT 3218 SE Department of Automatic Control Lund Institute of Technology November 1997 Lund Eker J and A Blomdell Patterns in Embedded Control Technical Re port TFRT 7567 Department of Automatic Control Lund Institute of Technology December 1997 Lund Eker J and A Blomdell A Structured Interactive Approach to Em bedded Control In Proceedings of 4th International Symposium on Intelligent Robotic Systems July 1996 Lisboa Portugal Eker J and K J str m A C Class for Polynomial Operations Technical Report TFRT 7541 Department of Automatic Control Lund Institute of Technology December 1995 Lund Paper 3 Based on the experiences from P LSJ and PAL a new language called FRIEND is proposed The FRIEND language supports the implementation of flexible embedded control systems by providing mechanisms for adding and removing code on line Eker J and A Blomdell A Contract Based Language For Embedded Control Systems In submission to the 25th IFAC IFTP Workshop on Real Time Programming WRTP 2000 Palma de Mallorca Spain Contributions F
70. SIMNON see Elmqvist et al 1990 The lack of an integrated tool like the PALSIMART environment previously de scribed forced us to use four different languages during the development The simulations were coded in OMOLA Andersson 1994 for the OMSIM simulation tool The first real time implementation of the controller was made in PAL and later translated into Forth The Forth code was tested on the real time simulation of the process A flavor of the Forth code is given in Example 5 below 52 7 Implementation of a Hybrid Controller DIANA Z Control He GT UTE 9 A203 A2t Figure 16 The air temperature control loop The water flow to the heat exchanger is controlled by a valve via the control signal u The output is the air temperature T after the fan EXAMPLE 5 A fragment of the Forth code for the PID sub controller Even a simple algorithm like this becomes quite complex due to the lack of proper lan guage support PAR REF 2 PAR y1 20 F PAR EE P2 PAR EE 20 PAR K 20 Fx 2DUP PAR P P2 PAR 11 20 PAR Di 20 PAR D 20 Fx PAR D2 20 PAR yiold 20 PAR y1 20 F Fx F 2DUP PAR D P2 F F PAR UU P2 O The process diagram is shown in Figure 16 The temperature T of the in flow air is controlled by adjusting the flow of hot water in a heat exchanger The control signal for the hot water valve is u The previously installed controller worked well when the proc
71. Summary A brief overview of state of the art in integrated control and scheduling was given Three papers in this thesis relate to this type of work Pa per 4 presents a feedback scheduling algorithm which optimizes control performance with respect to available computing resources The FRIEND language in Paper 3 is designed to support the implementation of control systems that are adaptive to changes in resources Using the toolbox pre sented in Paper 5 it is possible to study how CPU scheduling algorithms and network protocols affect the control performance 43 Introduction One could argue that this type of research is uninteresting and soon to be superfluous The computing power increases rapidly today and prices are going down Why then bother with scheduling at all Just buy another set of CPUs and give each task its own one and the need for scheduling is gone This is probably true for some applications On the other hand the more powerful the CPUs get the more software can and will be put onto them Available CPU power will almost always be used no matter speed or number of processors Furthermore adding more CPUs may solve the scheduling problem but will instead worsen the network congestion problem 6 Simulation of Embedded Control Systems The complexity of embedded control systems often makes it difficult to investigate all their properties analytically It is therefore necessary to have good simulation tools available In
72. Systems Co Designs o epa 50 le R RR de BeBe Wl Be Be a Wh Be A 145 Ty Introduction ss ari dao te Se se st te Ee E a a E i 147 2 THE Basic Idea m sect d heh G a a 148 3 The Simulation Model 150 4 Using the Simulator 153 5 A Co Design Example 157 6 Simulation Features 159 To CONCIUSIONS Alles 162 8 Acknowledgments e 163 9 References 163 Design and Implementation of a Hybrid Control Strategy 165 1 Introduction e 167 2 The Controller Structure 168 3 Stabilizing Switching Schemes 170 4 The Processes eee ee es 171 5 Controller Design 175 6 Simulations 2 ee a e AE E E AE AE AE A E AE AE E E E EE N 178 Yo Implementation s s e s ses T S 182 8 Experimentin n e ete e a t e Attalo 184 9 SUMMATY sar eieaa i ADO 186 10 References eee ee 186 PAL P lsj Algorithm Language 189 1 Introduction aoaaa a 189 2 Blocks and Modules 189 3 Block Variables vo aaa 190 4 Interface Modifiers 190 5 Scalar Data Types Da aaa aca he ee 191 Contents 6 Aggregate Data Types 192 7 Expressions and Statements 193 8 Procedures Functions and Events 194 9 Referentes cia ie Dkk Bi ie ita 201 B
73. Technical Report RJ 243 San Jos Research Laboratory IBM San Jos California str m K J and B Wittenmark 1997 Computer Controlled Systems third edition Prentice Hall Buttazzo G G Lipari and L Abeni 1998 Elastic task model for adaptive rate control In Proceedings of the IEEE Real Time Systems Symposium Fletcher R 1987 Practical Methods of Optimization second edition Wiley Gill P E W Murray and M H Wright 1981 Practical Optimization Academic Press Gustafsson K and P Hagander 1991 Discrete time LQG with cross terms in the loss function and the noise description Report TFRT 7475 Department of Automatic Control Lund Institute of Technology Lund Sweden 137 Paper 4 A Feedback Scheduler for Real time Controller Tasks Kosugi N A Mitsuzawa and M Tokoro 1996 Importance based scheduling for predictable real time systems using MART In Proceed ings of the 4th Int Workshop on Parallel and Distributed Systems pp 95 100 IEEE Computer Society Kosugi N and S Moriai 1997 Dynamic scheduling for real time threads by period adjustment In Proceedings of the World Congress on Systems Simulation pp 402 406 Kosugi N K Takashio and M Tokoro 1994 Modification and adjust ment of real time tasks with rate monotonic scheduling algorithm In Proceedings of the 2nd Workshop on Parallel and Distributed Systems pp 98 103 Nilsson
74. This section describes the design of the subcontrollers for each of the processes First the design of the PID controller for both the double tank system and the heating ventilation process is presented Next the time optimal controller is discussed for both of the plants PID controller design A standard PID controller of the form 1 K 1 sT Grip K ems a with an additional lowpass filter on the derivative is used The design of the PID controller parameters K Tz and Ty is based on the linear second order transfer function k G s s s a1 s a2 Both the double tank system and the heating ventilation system may be written in this form The PID controller parameters are then derived with a pole placement design method where the desired closed loop character istic equation is s 00 s 26 s 07 For the double tank system the sub controller designs are based on a linearized version of Equation 3 a elole 6 For the tank system a az a and k ba compare Equation 6 The parameter b has been scaled so that the new control variable u is in 0 1 The parameters a and b are functions of q p and the reference level around which the linearization is done It is later shown how the neglected nonlinearities affect the performance To be able to switch in the PID controller a fairly accurate knowledge of the parameters is needed The 175 Paper 6 Design and Implementation of a
75. a ADP 2000 comes with some predefined objects and a limited number of mathematical functions 8 Experiments The theory and the simulations have been verified by experiments For simplicity only the simple switching strategy previously presented was implemented Figure 12 shows the results of that experiment with the double tanks x2 x x i Ya 0 12 _ gt __ o 2 Wee ee o o 50 100 150 200 250 300 350 0 002 0 04 0 08 008 01 012 O14 O16 018 02 Figure 12 The double tank system The simple switching strategy is us The noise level is rather high which is visible during PID control The measurements from the lab process have a high noise level as can be seen in Figure 12 A first order low pass filter 1 ista is used to eliminate some of it To further reduce the impact of the noise a filter is added to the derivative part of the PID controller in a standard way 184 8 Experiments The parameters in the simulation model were chosen to match the parameters of the lab process It is thus possible to compare the experi mental results directly with the simulations A comparison of Figures 9 and 12 shows a close correspondence between simulation and experimen tal results During experiments it was found that the model mismatch i e the difference between the linear and the nonlinear switching curves did not affect the performance in the sense of fast trackin
76. a2 transition from s1 to s2 when tl transition from s2 to s1 when t2 calculate begin end calculate update begin end update end Steps 3 The P lsj framework Fig 1 shows the inheritance structure of the framework using using ob ject diagram notation see Gamma et al 1995 The functionality of the framework can be divided into three different parts the User Interface handles commands from the operator the Network Communication trans mits and receives data over the network and the Workspace Manager ad ministers the blocks and the block type libraries The fourth component is the block type library which contains the super class for all user defined block classes and a set of system classes used for execution 90 3 The PALSJO framework User Network Block Type Interface Communication Library O Workspace Manager ZN User ze Block Figure 1 The framework handles the user interaction the network communica tion and the block administration Definition of a Block A block is the smallest programming entity in the P LSJ environment and is defined as a seven tuple B I O P S E L A A block can have A set of input signals 7 An input signal must be connected to an output signal Input signals may not be assigned values in the PAL code A set of output signals O An output signal may be connected to an input signal A set of parameters P Para
77. amic memory allocation are not allowed The language FLEX Natarajan and Lin 1988 is designed to support the implementa tion of dynamic and flexible real time systems By incorporating impreci sion in the language FLEX makes it possible to adjust execution times of tasks so that deadlines may be met The synchronous language approach has emerged as a paradigm well suited for design and implementation of safety critical real time systems Halbwachs 1993 Benveniste and Berry 1991 At the design level the synchronous languages use a concurrent task model but after compilation the program is completely sequential The resulting programs are deterministic and possible to analyze There are currently a number of synchronous languages available among which Esterel Boussinot and de Simone 1991 Lustre Halbwachs et al 1991 and Signal Halbwachs 1993 are the most well known There is an obvious need for languages dedicated towards special prob lem domains General purpose languages may be used for implementing real time embedded control systems but it is unnecessarily awkward and time consuming By using languages targeted for real time systems the programmer will be better supported in the task of writing safe and pre dictable software P lsj Many control systems have a similar internal structures There are for example functions for control logic sequencing user communication task management and data logging If the software
78. and Autocode generate static systems i e it is not possible to make any changes to the system without recompilation An other tool that generates real time code from a simulation description is Sim2DCC Dahl 1990 Control algorithms are coded and simulated in the Simnon simulation environment Elmqvist et al 1990 and translated to Modula 2 code using Sim2DCC Sequential algorithms are implemented using the graphical GrafEdit interface Simulink is used both as the simulation environment and the real time controller in Blomdell 1999 Simulink is executed on a slightly modified Linux operating system There are blocks for reading from analog inputs and writing to analog outputs There are also timer blocks handling the sampling rate This set up offers a simple way to test algorithms in a near real time environment ControlShell RealTimeInnovations 1995 is an advanced tool for de signing complex real time control systems It consists of a C class library in combination with graphical editors which are used for configuring con trol applications ControlShell is block based and the blocks are imple mented in C ControlShell gives the programmer great freedom and it allows an application to be reconfigured without recompilation A commercial system that has some basic ideas in common with the P LSJ system is SattLine Johannesson 1994 It is a system for pro gramming PLC systems It consists of a graphical environment for im
79. and their influence on the control performance 7 Implementation of a Hybrid Controller Paper 6 describes the design and implementation of a hybrid control strat egy for a heating ventilation system in a school in Klippan a small town not far from Lund The project which mainly consisted of control de sign also gave some valuable insights through the use of commercial control hardware software While the design and the test implementa tions were made in the lab using P LSJ the actual implementation was programmed in Forth on a Diana ADP 2000 system The Diana ADP 2000 manufactured by Diana Control AB is mainly used in heating ventilation applications The software is quite flexible and it is possible to install new controller code without having to rebuild the system A unit can contain several control loops and on large installations several units can be interconnected in a network In the network configuration one of the control units is a master and the others are slaves The master unit can be reached over a modem connection and from the master it is possible to communicate with all the others It is possible to log data change parameters and download new code for every controller over the network The identification experiments presented in Paper 6 were made over a telephone connection from Lund Before trying the controller on the heating ventilation process it was tested against a process simulation implemented in real time
80. anging control algorithms even if the new algorithm would give better performance and costs reduction 2 The Palsj System The internal structures for many controller implementations are very similar The same kind of building blocks are used and their internal communication follows certain patterns There are functions for user in teraction task management data logging network interaction etc The main idea with the P LSJ project is to capture the common behavior of 71 Paper 1 A Tool for Interactive Development of Embedded Control Systems A I1IBrcC D kX Figure 1 Control systems are conveniently described using block diagrams typical control systems If those common features can be encapsulated in a framework then the size of the code that needs to be written for each new application can be significantly reduced Further it is possible to in troduce a suitable abstraction level that will support control algorithms in particular The goal is to give a high level of support for those com mon features and let the control engineer focus on the control algorithm implementing The user of such a framework only needs to add the code that is specific for a certain application i e the control algorithm P lsj System Model Control engineers extensively describe control system using block dia grams see Figure 1 A block diagram contains information of the algo rithms an
81. anguage PCL Instances of the system blocks Periodic and Sporadic are created to manage the execution Consider the block diagram in Fig 3 It consists of six blocks An analog input block followed by a pre filter two controllers in parallel a switch and an analog output block The pre filter is used to reduce the noise from the measurement signal and is executed at a higher sampling rate than the control blocks The desired real time behaviors are the following e Execute LQG PID Switch and Analog Out at a slower sampling rate e Execute Analog In and Filter at a higher sampling rate To configure the system to get the this behavior two instances of the system block Periodic are created one for each sampling rate The PCL commands to achieve this are the following EXAMPLE 3 pel gt f pcl gt pi new Periodic pcl gt p2 new Periodic pcl gt p1 adin new Analogln 93 Paper 2 A Flexible Interactive Environment for Embedded Controllers pcl gt p1 filter new Filter pcl gt p2 lqg new LQG pcl gt p2 pid new PID pcl gt p2 switch new Switch pcl gt p2 daout new AnalogOut pclx gt pcl gt p1 adin y gt pl filter u pcl gt p1 filter y gt p2 pid u pcl gt p1 filter y gt p2 laqg u pcl gt p2 pid y gt p2 switch ul pcl gt p2 lqg y gt p2 switch u2 pcl gt p2 switch y gt p2 daout u pcl gt p1 tsamp 0 010 pcl gt p2 tsamp 0 050 O The execution model used is shown in Fig 4 Th
82. arts the enter part which is executed when the segment is started and exit part which is executed when the execution time of the segment has passed In Ex ample 3 each of the code objects rCode and oCode consists of two code segments These four segments are shown in Example 4 below Task Code Code Code Code Segment Segment Segment Figure 15 Each task is associated with a code object which consists of one or more code segments EXAMPLE 4 function exectime states rsegl flag states params switch flag case 1 enterCode if lock M1 data readData M1 if data lt 2 await E1 exectime 0 else exectime 0 003 end else exectime 0 end case 2 exitCode unlock M1 end function exectime states rseg2 flag states params switch flag case 1 enterCode y analogIn params inCh states u 50 y exectime 0 003 case 2 exitCode 50 6 Simulation of Embedded Control Systems analog0ut params outCh states u end function exectime states osegl flag states params switch flag case 1 Y enterCode y analogIn params inCh states u 20 y exectime 0 002 case 2 exitCode analog0ut params outCh states u end function exectime states oseg2 flag states params switch flag case 1 Y enterCode if lock M1 data readData M1 writeData M1 data t1 exectime 0 003 else exectime 0 end case 2 exitCod
83. at it fulfills some requirements in order to work correctly with the rest of the blocks This type of guarantees may be expressed with contracts The resources of block B are distributed be tween the blocks D E and F by the supervision logic of block B The process of distributing resources among child blocks is in FRIEND called negotiation The reasons for dividing blocks into subcomponents are e Better reuse of control algorithms by letting the control algorithm be described in an algorithm block and the application specific in formation in a contract e Better support for on line controller upgrades By introducing inter faces it becomes easy to check whether or not the block reads and writes signals as specified Furthermore the interface may contain signal data logs needed to assign correct values to the controller states before switching in 19 Introduction Interface Block Signals i Jep dr Block supervision logic Figure 2 A controller in FRIEND may be organized in a hierarchical fashion The interfaces between blocks at different levels in the hierarchy are called contracts Better support for building systems with a high level of adaptivity The negotiator decides which of its sub blocks should execute when and how New blocks may be added on line As long as there is a negotiator that is familiar with the contract of the new block it is possible for the system to a
84. ated in the enterCode part The enterCode part of the second code segment contains the Lock Mutex and WriteData statements while exitCode contains the Unlock Mutex statement When the last segment has completed the task is suspended until the next period by the kernel O 4 Using the Simulator From the user s perspective the toolbox offers a Simulink block that mod els a computer with a real time kernel Connecting the Computer block s inputs and outputs representing for instance A D and D A converters to the plant a complete computer controlled system is formed see Figure 7 Mux Inputs Outputs Demux Input Socket Computer Output Socket Figure 7 The simulation environment offers a Simulink Computer block that can be connected to the model of the plant dynamics Plant Dynamics 153 Paper 5 A Matlab Toolbox for Real Time and Control Systems Co Design The plant dynamics may have to be controlled by several digital con trollers each implemented as a periodic control task in the computer Besides the controllers other tasks could be executing in the computer for instance planning tasks supervision tasks and user communication tasks Opening up the Computer block the user may study detailed informa tion about the execution of the different tasks see Figure 8 It is for in Kernel Inputs S Function Sampling instants El Control instants Figure 8 Inside
85. ated to preserve the consistency of data By grouping blocks together the execution gets more efficient Con sider for example ifeach block was running as a separate process instead First there would be a problem with data latency since the processes are running without synchronization If all blocks execute with the same sam pling interval it is be possible that data would be delayed by one sample for each block from input to output Another disadvantage would be the overhead introduced due to the context switching when processes are stopped and restarted 95 Paper 2 A Flexible Interactive Environment for Embedded Controllers 4 Signal Management PAL has a set of predefined data types Among those are regular scalar ones e g real integer string Furthermore there are aggregate types such as arrays matrices and polynomials The availability of arithmetic oper ations for polynomials and matrices makes it straightforward to express control algorithms see Example 4 EXAMPLE 4 A matrix 1 2 1 2 of real B x matrix 1 2 1 1 of real u input real x Axx B xu O The size of the aggregate data types cannot be changed from within the PAL code They may however be parameterized using dimension vari ables Dimension is a special parameter type used for defining the sizes of aggregate data types The value of a dimension variable can only be set by the runtime system The need of a special data type for handling
86. auseplot asynchronous start synchronous stop synchronous DIMENSIONS ___________ ooo GRAP CET 32 22223 uia oda ee oe oe ee Ss oe Block list Input Buffers Output Buffers Export Buffers Execution order In a similair fashion information about the block regul can be retrieved pclx gt s regul BlockType PI Block Name regul Block 1D 4 SIGNAL iets A begs 3 a it ed Be input r double mot connected input y double mot connected input u double mot connected output v double 0 000000 state I double 0 000000 state e double 0 000000 PARAMETERS _______ tsamp int 100 offset int 0 slave int 1 K double 0 500000 Ti double 10000 00 Tr double 10000 00 bi double 5 000E 6 210 3 Operators br double 10 00E 6 DIMENSIONS 30 o ia a A A GRAPE CE TS a es A a A pclx gt The Connect Operators gt and lt After blocks have been allocated and assigned to Periodic blocks they must be connected to form an excutable system Output signals and input signals are connected using the connection operators gt and lt In the following example two blocks and a Periodic block are allocated The output signal out in BlockA is connected to the input signal in in BlockB A connection is valid only if the input and the output signals are of the same data types and have the same sizes EXAMPLE 4 pcl gt pcl gt s new Periodic pcl gt s BlockA
87. bandwidths 3 5 and 7 rad s respectively and the CPU resources available The execution times of the control tasks 7 are all 28 ms and the periods are T 167 ms T 100 ms and 73 71 ms Task objects control input output signals e Ty Ta T3 Kernel Figure 11 The setup from described in Section 5 Three inverted pendulums with different lengths are controlled by three control tasks running on the same CPU are created according to Example 4 Also similar to Example 1 the con trol algorithm is divided into two code segments Calculate Output and Update State with execution times of 10 and 18 ms respectively In a first simulation the control tasks are assigned constant priori ties according to the rate monotonic schema and the two code segments execute at the same priority In a second simulation the Calculate Out put code segments are assigned higher priorities than the Update State segments according to iterative priority deadline assignment algorithm suggested in Cervin 1999 The accumulated loss function for the slow pendulum T 167 ms is easily recorded in the Simulink model and the results from both simulations are shown in Figure 12 A close up inspection of the schedule produced in the second simulation is shown in Figure 13 It can be seen that the faster tasks sometimes allow the slower tasks to execute and in this way the control delays in the slower co
88. bedded systems are found in mechatronic sys tems such as industrial robots in aerospace applications such as airplanes and satellites in vehicular systems such as cars and in consumer elec tronic products Embedded controllers are often complex systems con 15 Introduction sisting of several concurrent tasks such as low level feedback control su pervision logic data logging and user communication Special language support is needed in order to implement embedded control systems in an easy and straightforward way Control laws are conveniently described using polynomials or matrices and access to these data types is an ad vantage Furthermore many algorithms are described as a combination of periodic behavior and sequential logic Any good language should support both of these descriptions Finally it should be easy to reuse algorithms from one application to another One of the problems with reusing real time algorithms is that statements describing the algorithm are often mixed with statements specifying the real time behavior Code reuse may be better supported by separating the algorithm code and the real time specific information Implementing embedded control systems is an error prone and complicated task The nondeterministic nature of the programs makes them hard to test and verify A program that works in one environ ment may fail in another One reason for this is the dynamic allocation of resources For example a change i
89. bles A plant model is then chosen in a similar way 46 6 Simulation of Embedded Control Systems The resulting PALSIMART framework is presented in Figure 13 Any PAL coded algorithm can be easily appended to a control library that is available both to SIMART and to P LSJ run time system After the con troller has been validated through simulation the same PAL block with the exact same C coding can be tested in the P LSJ run time environ ment Testing the controller in the simulation environment ahead of the experiments on the real process substantially reduces prototyping time The main asset of PALSIMART with respect to other available pro totyping systems is that algorithm coding is identical regardless of use the same blocks are used both in simulation and real time and the same behavior is expected With no need for code rewriting the creation of a versatile library of control algorithms is straightforward PALSIMART currently runs on Sun Solaris workstations A Windows NT version is under development A Toolbox for Simulation of Embedded Systems Paper 5 presents a MATLAB Simulink toolbox for simulation of embed ded systems There currently exist many tools for simulation of control systems for example Simnon Elmgvist 1973 OMSIM OMOLA Ander sson 1994 Modelica Elmqvist and Mattsson 1997 Simulink Math Works 1996 and SystemBuild Integrated Systems 1996b Similarly there are many tools available for s
90. ccept it and reconfigure itself The FRIEND framework does not give any solutions to the design of con tracts or negotiation procedures FRIEND merely provides the necessary mechanism for creating flexible and adaptive control software Related Work There are several widely used prototyping systems today for example Au tocode Integrated Systems 1996a which generates real time code from SystemBuild models Integrated Systems 1996b or Real time Work shop MathWorks 1997 which generates real time code from Simulink models MathWorks 1996 The models are implemented graphically us ing block diagrams In both SystemBuild and Simulink the user has a 20 3 Implementation of Control Systems palette of pre defined blocks for defining controllers To create user defined blocks from which code may be generated SystemBuild has a language called BlockScript which is a simple block description language with sup port for basic data types such as floats integers and booleans Autocode generates C or Ada code from BlockScript blocks A template file is used for customizing the generated code for different target environments The template description is made in a template programming language and makes it possible to generate code that is tailor made for a special system User defined blocks for Real time Workshop must me written as C MEX S functions which are standard C functions with a specified interface Both Real time Workshop
91. ce it may optimize the system with respect to available computing resources The actual calculations of the new sampling intervals H are however omitted Block E listens to three events resourceChange new Block and delete Block which are caused by the run time system The event resourceChange is caused when the resources available for block E changes The events new Blocks and delete Blocks are caused when blocks are added or removed When the events occur new sampling intervals are calculated for the child blocks The new blocks are then started by the schedule procedure and will execute as periodic threads 116 5 Summary algorithm F extends PI a parameter real fulfills myContract C3 QoS a sampling interval dQoS 2 p x sampling interval Block F extends the PI algorithm by adding a contract 5 Summary This paper outlines the language FRIEND which is designed for the im plementation of flexible embedded control systems The main goal is to support systems with an adaptive quality of service level and systems with feedback scheduling The main idea is to separate the controller block into different parts that carry specific information i e the actual algorithm the contract the interface and the negotiator The algorithm describes an input output block The contract describes how and when the controller should be used The interface describes how the controller is connected to the environme
92. ception is Stankovic et al 1999 where it is pro posed to use a PID controller as an on line scheduler under the notion of Feedback Control EDF The measurement signal the controlled variable is the deadline miss ratio for the tasks and the control signal is the re quested CPU utilization Changes in the requested CPU are effectuated by two mechanisms actuators An admission controller is used to con trol the flow of workload into the system and a service level controller is used to adjust the workload inside the system The latter is done by changing between different versions of the tasks with different execution time demands A simple liquid tank model is used as an approximation of the scheduling system Using a controller approach of the above kind it is important to be able to measure the appropriate signals on line e g to be able to measure the deadline miss ratio the CPU utilization or the task execution times An event feedback scheduler is proposed in Zhao and Zheng 1999 Several control loops share a CPU and only one controller may be active at each time instant The strategy used is to activate the controller connected to the plant with the largest error Similar ideas are found in Arz n 1999 which suggests an event based PID controller that only executes if the control error is larger than a specified threshold value Admission controller Load reference L Feedback gt scheduler ES A ea
93. computations IEEE Trans on Computers Liu J W K Shih K J Lin R Bettati and J Y Chung 1994 Imprecise computations Proceedings of the IEEE Jan pp 83 983 MathWorks 1996 Simulink Dynamic System Simulation for MATLAB The MathWorks inc 24 Prime Park Way Natick MA 01760 1500 MathWorks 1997 Simulink Real Time Workshop The MathWorks inc 24 Prime Park Way Natick MA 01760 1500 M Saad M J Chebassier and P Tona 1997 Advanced control using the CACSD package SIMART In IFAC Conference on Systems Structure and Control Bucharest Romania Nakajima T 1998 Resource reservation for adaptive QoS mapping in real time Mach In Proceedings of the Sixth International Workshop on Parallel and Distributed Real Time Systems Nakajima T and H Tezuka 1994 A continuous media application supporting dynamic QoS control on real time Mach In Proceedings of ACM Multimedia 94 Natarajan S and K Lin 1988 FLEX towards flexible real time pro grams In Proceedings of the International Conference on Computer Languages IEEE 66 9 References NewMonics 1999 Making Java Applications a Reality in Embedded Sys tems Today NewMonics Inc 1755 Park Street Suite 260 Naperville IL 60563 http www newmonics com Persson P 1998 A tool measuring and analyzing real time task exe cution times Project Report Real Time Systems Course Department of Au
94. computer To the right the three double tanks are controlled by a real slower computer The behavior of the ideal system is used as a reference when evaluating the performance of the real system Figure 20 shows the level of the lower tanks when controlled by the ideal computer 57 Introduction Setpoint Responses with Optimal Computer 2 io Lower tank 1 o 0 100 200 300 400 500 600 Lower tank 2 o 0 L L 1 L L 0 100 200 300 400 500 600 0 2 T T ard po 3 Z 0 1F k J o S 0 L L L sE L 0 100 200 300 400 500 600 time s Figure 20 The level of the lower tanks when controlled by the ideal computer The simulations display very good setpoint responses and steady state behavior To compare different scheduling strategies the control performance needs to be quantified somehow This is a difficult task even for a single non hybrid controller We decided to measure the accumulated squared distance between the outputs of the ideal system Yideal and the outputs of the real system Yeal during a simulation of length Ty Tsim 0 The function V is called the performance loss due to scheduling It gives a rough estimate of the performance of the real system by judging all devi ations from the ideal system as undesired Typically the outputs from the real system are delayed compared to the outputs from the ideal
95. d control strategy for two different plants are presented The ideas were first tested in the labora tory on a double tank system and later applied to a heating ventilation system in a public school The experiments were performed in two differ ent software environments but with the same basic control algorithm The main focus of this work has been to apply optimal control theory and hybrid control theory to realistic processes using as simple methods as possible This means taking hardware and software limitations into account when designing the control algorithm In practice we have been forced to simplify and approximate the control strategy A positive aspect 167 Paper 6 Design and Implementation of a Hybrid Control Strategy of this has been that we have found a fairly easy way of synthesizing our controller This in turn makes the control strategy much more acces sible for industrial use A Lyapunov based strategy is first investigated theoretically and simulated A simplified version of this controller is then implemented for two different processes This paper is based on work found in Malmborg 1998 Eker 1997 and Malmborg and Eker 1997 2 The Controller Structure ul fo 1 supervisor ua A x u u process u ad l Figure 2 A multi controller architecture used in Morse 1995 Several con trollers C execute in parallel and a supervisor is used to select which control signal u uy to
96. d how they are interconnected Real time code could be gener ated from this this simple system description but the resulting system would be equally simple Ifinstead some additional real time information were added to the block diagram its real time behavior would become much more precise Figure 2 shows a system with some extra real time specifications The kind of information is which blocks should be mapped onto which real time tasks which signal connections are synchronous and which are asynchronous etc In P LSJ blocks are implemented in the language PAL PALSJO Algorithm Language Control systems are then configured on line using the script language PCL PALSJO Configuration Language The additional real time information discussed above is hence in P LSJ added on line In P LSJ it is allowed to edit the system config uration without halting it first Figure 3 shows the structure of a PALSJO application Two user defined processes execute in the workspace which is connected to modules managing operator communication network com munication plant IO etc When an application is written in PAL for the PALSJO system only the tasks specific to the application must be imple mented by the control engineer In Figure 3 there are two processes that execute the actual control application from Figure 1 and these processes are created on line by the user Each of these processes consists of a two PAL blocks Each PAL block has a set of fu
97. data type maps down onto an external polyno mial package Eker and Astr m 1995 7 Expressions and Statements An expression yields a value The value domain of an expression is deter mined by the operation and the operands Statements are used to describe the execution of an algorithm A statement may consist of expressions declarations and statements Below are the expressions and statements available in PAL e Unary Expressions A unary expression is an expression which only involves one operand There are three types of unary expres sions in PAL Referencing a variable Arithmetic negation e g pi Logical negation e g not bad e Binary Expressions A binary expression is an expression which involves two operands There are three types of binary expressions in PAL Arithmetic expressions i e mod or div Relational expressions i e lt lt lt gt gt or gt Polynomial evaluation that returns the value of the polynomial in a specific point e Other Expressions In PAL there are two other types of expres sions 193 Appendix A PAL P lsj Algorithm Language Indexing e g x i which returns a specific part of an array matrix or polynomial Function calls A function reads input parameters and returns a value e Assignment A variable is assigned using the assignment opera tor in input real out output real K parameter real out K in e Th
98. ded for writing controllers that can be switched in and out by a supervisor PALSJO is currently available for Motorola 68000 VME Power PC VME and Windows NT P LSJ is implemented on top of the STORK real time kernel Andersson and Blomdell 1991 STORK is a public domain real time kernel available for Windows NT Motorola 68000 Motorola Power PC and Sun Solaris 2 x The real time performance achieved on a Motorola 68040 are sampling intervals of around 5 milliseconds The Power PC version is about 10 100 times faster 7 Acknowledgment This work was sponsored by National Swedish Board of Technical Devel opment NUTEK under contract P9040 2 The authors wish to thank the anonymous reviewers for valuable comments 8 References Andersson L and A Blomdell 1991 A real time programming envi ronment and a real time kernel In Asplund Ed Vational Swedish Symposium on Real Time Systems Technical Report No 30 1991 06 21 Dept of Computer Systems Uppsala University Uppsala Sweden str m K J and B Wittenmark 1995 Adaptive Control second edition Addison Wesley Reading Massachusetts str m K J and B Wittenmark 1997 Computer Controlled Systems third edition Prentice Hall Upper Saddle River New Jersey Blomdell A 1997 The P LSJ algorithm language Master s thesis Department of Automatic Control Lund Institute of Technology Dahl O 1990 SIM2DDC User s manual
99. depends on the sampling interval and how a recursive re source allocation optimization routine can be designed Linear quadratic cost functions are used as performance indicators Expressions for calcu lating their dependence on the sampling interval are given An optimiza tion routine called a feedback scheduler that uses these expressions is designed 121 Paper 4 A Feedback Scheduler for Real time Controller Tasks 122 1 Introduction 1 Introduction Control design and task scheduling are in most cases today treated as two separate issues The control community generally assumes that the real time platform used to implement the control system can provide de terministic fixed sampling periods as needed The real time scheduling community similarly assumes that all control algorithms can be modeled as periodic tasks with constant periods hard deadlines and known worst case execution times This simple model has made it possible for the con trol community to focus on its own problem domain without worrying how scheduling is being done and it has released the scheduling community from the need to understand how scheduling delays impact the stability and performance of the plant under control From a historical perspec tive the separated development of control and scheduling theories for computer based control systems has produced many useful results and served its useful purpose Upon closer inspection it is however quite cl
100. development of embedded real time systems Effort has been put on designing a system that allows the en gineer to work interactively PALSJO is highly modular and components may be added while the system is running on line Control algorithms are coded in a dedicated controller description language called PAL In PAL control algorithms are described in terms of blocks that read input signals and calculate output signals Compilation of PAL blocks results in C code which is subsequently compiled and linked to the P LSJ run time sys tem The system is configured i e blocks are instantiated and connected on line using PCL Data is exported over the network to stand alone tools used for plotting and logging The run time system supports on line edit 22 4 The Robot Pendulum ing of a running configuration hence blocks in a running controller can be replaced without stopping the system Scheduling and synchronization problems encountered in many real time systems are avoided by exploit ing features of PAL control algorithms that make it easier to find a logical order of execution PALSJO is primarily designed to run in a host target configuration and currently runs on Sun Solaris VME m68k VME ppc and Windows NT A complete description of the PALSJO environment in cluding the run time system the PAL compiler and the PAL language can be found in Eker 1997 Paper 1 gives an introduction to P LSJ and PAL Paper 2 focuses more on
101. during runtime could cause the overall control performance to be quite poor Feedback Scheduling Feedback scheduling in this example means that task periods are as signed on line depending on the modes of the different controllers The underlying scheduling principle is rate monotonic scheduling The feed back scheduler is activated each time a control task switches mode The feedback loop between the scheduler and the control tasks is illustrated in Figure 21 In this example we assume that each controller has an associated known cost function Ji a B h 1 where h is the sampling frequency for task i The goal for the feedback scheduler is to optimize the total performance i e n minimize Y Ji i 1 subject to the utilization constraint gt Ci hi U i 1 59 Introduction ModeChanges Feedback Frequencies Scheduler Control Control Control Task 1 Task 2 Task 3 Figure 21 A feedback loop is formed between the control tasks and the sched uler The control tasks notify the scheduler of their current mode The scheduler then adjusts the frequencies of the control tasks so that the CPU load becomes the desired where U is the desired utilization and C is the execution time for task i The execution time of the feedback scheduler itself is zero in the simula tions We do however reserve some slack for the feedback scheduler by se
102. e Johan 10 Introduction 1 Motivation The number of embedded systems is increasing rapidly Processors ship ped for embedded systems are already outnumbering processors for desk top systems According to Hennessy 1999 the ratio between the number of 32 and 64 bit processors aimed for embedded systems and desktop sys tems is expected to increase to three to one in the next five years If 8 and 16 bits processors are also considered the difference becomes even more profound The large number of embedded systems puts high demands on the software These systems are expected to function more or less au tonomously and must be robust and adaptive to changes The advantage of using a system may easily be overshadowed by the cost of a failure If for example the cruise controller of a car fails ever so rarely the potential benefits from using it become very small Most embedded systems today are designed in an ad hoc fashion They are tuned for well defined software and hardware environments and val idated through extensive testing If the conditions change the behavior of the system may be unpredictable For example the failure of the Ariane 5 rocket was due to the use of a code module from Ariane 4 which caused a fault when executed on a more modern processor Le Lann 1996 The more we start to depend on embedded control systems for critical tasks the higher are the demands on reliability and safety Maneuvering sys tems in a
103. e cause E1 unlock M1 end a The functions lock unlock await cause readData and writeData are toolbox functions implementing the mutual exclusion monitor with the associated event In the initialization script above the scheduling type was set by giving a priority function The priority function defines the criterion according to which the ready queue is sorted A number of different strategies is available and it is also straightforward for the user to implement a new strategy The priority function for the rate monotonic case is the following function prio prioRM task prio task period In Example 3 Task1 has the shortest period and since rate monotonic priority assignment is used it gets the highest priority A low number corresponds to a high priority 51 Introduction Summary The PALSIMART environment allows the use of exactly the same PAL code and C code in both simulation and implementation By bridging the gap between simulation and implementation the prototyping time is shortened The MATLAB Simulink toolbox supports task level simulation of closed loop embedded controllers This opens up the possibility to eval uate different scheduling strategies from a control performance point of view The toolbox does also support simulation of computer networks which makes it possible to investigate and simulate distributed control systems For example it is possible to look at time delays in networks
104. e Waa 1 1 E i Kernel _ Execution i Resource statistics allocations I J 1 i Requests Events Figure 2 The real time kernel is connected in a feedback loop with the feedback scheduler and the admission controller 127 Paper 4 A Feedback Scheduler for Real time Controller Tasks 3 Problem Statement Consider a control system where several control loops share the same CPU Let the execution times of all tasks and the system workload be available from the real time kernel at all times Furthermore associate each controller with a function which indicates its performance The ex ecution times the number of tasks and the desired workload may vary over time The aim of the feedback scheduler is to optimize the total con trol performance while keeping the workload at the desired level Two separate modules are used see Figure 2 The feedback scheduler adjusts the sampling intervals to control the workload The workload ref erence is calculated by the admission controller which contains high level logic for coordinating tasks The tasks and the feedback scheduler communicate using requests and events A task can send a request for more computing resources and the scheduler may grant this by replying with the appropriate event The kernel manages the tasks at the low level i e task dispatching etc The feedback scheduler gets execution statistics such as the actual execution times of the tasks and the system w
105. e be connected to input and output signals of other blocks interface MISO extends SISO y2 input real The SISO interface is extended with an additional input signal and given the name MISO interface PI_pars K Ti parameter real As shown in PI_pars an interface may also define block parameters contract C1 negotiates sampling interval duration WCET duration QoS real sampling interval gt QoS requires invocation lt WCET The contract C1 requires that any block that fulfills it agrees with the following e The duration of an invocation must be less than WCET seconds If the duration of an invocation exceeds WCET an exception will be raised and the parent block will be notified e A relation between the sampling interval and the quality of ser vice QoS must be given in the block contract C2 extends C1 requires V real requires interface io MISO 112 4 The FRIEND Language The contracts C1 is extended to also require that e The MISO interface must be implemented e There must be an expression for calculating V algorithm PI I 0 0 state real implements io SISO pars PI_pars calculate io u pars K io y ef 10 y I update I I pars K pars Ti io y ef 10 y The implementation of the PI controller is divided into two parts cal culate and update An algorithm block calculates new output signals based on the input s
106. e control tasks must be able to express the quality of the control performance in relation to needed resources if and how the sampling rate and deadline may be adjusted and what the consequences will be Paper 4 investigates how the LQ cost depends of the sampling rate and how this may be used in a feedback scheduling loop Designing a Feedback Scheduler Viewing a computing system as a dynamical system or as a controller is an approach that has proved to be fruitful in many cases For example the step length adjustment mechanism in numerical integration algorithms can be viewed as a Pl controller Gustafsson 1991 and the traveling salesman optimization problem can be solved by a nonlinear dynamical system formulated as a recurrent neural network This approach can also be adopted for real time scheduling i e it is possible to view the on line scheduler as a controller Important issues that then must be decided are what the right control signal measurement signals and setpoints are what the correct control structure should be and which process model that 38 5 Feedback Scheduling may be used Using a controller approach of the above kind it is important to be able to measure the appropriate signals on line for example the deadline miss ratio controller performance the CPU utilization or the task execution times Control and Scheduling Co Design A prerequisite for an on line integration of control and scheduling the or
107. e following command pal fig grafcet pal to be executed while the step is active action OpenV1 begin V1 true end OpenV1 action CloseV1 begin V1 false end CloseV1 An action can be activated in a number of different ways for example e activate Action the action is executed as long as the step is active 198 StartHeating Heat KeepFilling T gt Tref L2 StopHeating NoHeat StopFilling CloseV1 T lt Tref true EmptyTank Openv2 8 Procedures Functions and Events e pulse activate Action the action is executed one time only when the step becomes active A transition has a set of input steps a set of output steps and a condition All input steps must be active and the condition must be true for the transition to be fireable When a transition is fired all output steps become active transition from nit to StartHeating StartFilling when Start transition from StartHeating to StopHeating when T gt Tref An Example The PAL code for the Grafcet in Figure 2 is the following module grafcet block boiler L1 L2 Start input boolean T input real Tref parameter real V1 V2 Q output boolean initial step Init pulse activate CloseV2 end Init step StartHeating activate Heat end StartHeating step StopHeating pulse activate NoHeat end StopHeating step StartFilling pulse activate OpenV1 end StartFilling step
108. e functionality is veri fied through testing This makes them very sensitive to changes in the operating conditions for example decreased network bandwidth or less available CPU power From a control engineering point of view the control tasks run in open loop i e there is no feedback between the control tasks and the underlying real time kernel The purpose of feedback in automatic control is to adjust the control signal to accommodate for the control er ror The same principle could be applied to real time systems by viewing the resource allocation level as the process output and the priority of the tasks as the control signal This paper proposes a controller description language FRIEND designed to support implementation of adaptive and flexible real time control systems The objectives of the FRIEND project are to give good high level support for flexible control systems and to simplify the design of embedded systems with quality of service reason ing and feedback scheduling A controller in FRIEND is associated with a contract which specifies how the controller performance depends on the available resources This information may be used by a supervisor to distribute resources to optimize the system in some respect The FRIEND language also addresses the implementation of so called hybrid control systems see Branicky et al 1998 A hybrid controller consists of a set of sub controllers and a supervisor that selects which sub controller
109. e if Statement Conditional execution is constructed using the if statement if a true then i i l elsif b true then i i 2 else i i 3 end if e The for statement One or more statements are repeated using the for statement for i 1 to N do sum sum vecli end for 8 Procedures Functions and Events A procedure is a subprogram which consists of a sequence of statements A procedure has a head and a body The head defines the name of the procedure and the interface used for calling the procedure The body of the procedure contains the statements that are executed when the pro cedure is called Parameters to a procedure can either be input or out put Input parameters are passed by value while output parameters are passed by reference Parameters of type array are however always passed by reference It is not allowed to assign values to input parameters in side the function body In Example 3 the implementation of a function which performs dyadic decomposition is shown The algorithm is taken from str m and Wittenmark 1995 Three functions RowAsRealArray 194 8 Procedures Functions and Events RealArrayAsRow and DyadicReduction are called in the code but not de fined there The first two are built in functions for converting data from a matrix row to an array and back The definition of the third function is omitted for simplicity EXAMPLE 3 procedure LDFilter theta output array 0 n in
110. e is executed 88 2 PAL PALSJO Algorithm Language Grafcet Grafcet David and Alla 1992 is a convenient and powerful tool for im plementing sequential algorithms Grafcet statements are expressed in PAL with a textual representation based on Sequential Function Charts in IEC 1131 Lewis 1995 An example of a Grafcet in PAL is shown in Example 2 As shown in Example 2 a block algorithm may be described using both the calculate update procedures and one or more Grafcets This is useful when an algorithm is composed of one periodic part and one sequential part Consider for example a hybrid controller The control law are conveniently expressed using Grafcet where each step corresponds to a sub controller Assume that several of the control laws used are of state feedback type and that all plant states cannot be measured In this case the states need to be estimated It is desireable to have an estimator inside the block but not to have an estimator in each step By implementing the estimator in the calculate update section the estimates are available for all the control laws 89 Paper 2 A Flexible Interactive Environment for Embedded Controllers EXAMPLE 2 block Steps t1 2 input boolean initial step sl activate al end sl step s2 pulse activate a2 end s2 action al begin end al s2 a2 action a2 begin t2 end
111. e scenarios for a dramatic example of this see Le Lann 1996 If instead real time code is generated from a simula tions environment code reuse may be better supported Examples of simu lation environments that support code generation are SystemBuild Inte grated Systems 1996a Integrated Systems 1996b and Simulink Math Works 1997 A problem with code generators is that they may give large and inefficient programs The real time specifications in simulation mod els are usually very sparse and this makes it difficult to generate opti mized real time code Code generators usually do not take into account that the sampling delay can be reduced significantly by rearranging the code see str m and Wittenmark 1997 Development tools of today have a very low degree of interactivity The control application is designed compiled and tested If any errors are found the plant must be stopped and restarted before the user can test the corrected version There is a great need for a higher level of interactivity when developing real time control systems It must be possible to insert and delete algorithms without having to stop the plant and recompile the whole application More flexible control software is not only needed in the control labs but also in the industry The software in embedded controllers needs to be upgraded periodically Since the cost for shutting down a manufacturing cell is high the upgrade might not be feasible just for ch
112. e seen in Figure 11 the 181 Paper 6 Design and Implementation of a Hybrid Control Strategy overall performance did not deteriorate very much The main difference from using the theoretically correct switching strategy is that a few ex tra min max switches are needed Simulations to test the method s ro bustness to process variations were also made There was no significant decrease in performance for process parameter variations of 50 T Tref T 0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400 T Figure 11 Simulation of the ventilation model for the school in Klippan The affine approximation of the ideal switching curves is seen together with two set point change trajectories in the last sub plot 7 Implementation The traditional way of implementing real time systems using languages such as C or ADA gives very poor support for algorithms expressed in a state machine fashion The need for a convenient way to implement hybrid systems is evident The programming language must allow the designer to code the controller as a state machine as a periodic process or as a combination of both The latter alternative is particularly useful in the case where the controller is divided into several controllers sharing some common code A typical example of this is a state feedback controller for a plant where it is not possible to measure all states To get informa tion about the non measurable states
113. e system blocks Periodic and Sporadic are mapped down to threads in the real time kernel The threads are scheduled with fixed priority scheduling i j Design Level 1 1 1 eE e E EESE EEE Sosa E a eA ete Fisico Sis Concurrent Processes CD Figure 4 The Periodic and Sporadic blocks are mapped down to threads in the real time kernel Execution Level The Periodic block executes its child blocks according to the data flow between them using a schedule automatically created on line All timing and synchronization between the child blocks is taken care of by the scheduler in the Periodic block Since the child blocks are executed 94 3 The PALSJO framework Periodic Buffer Analog In Filter NN po ie Periodic Buffer Switch Analog pass by value lencia gt pass by reference Figure 5 A system with one process for down sampling the measurement signal and one process for the control algorithms sequentially no data sharing problems will arise The data flow mecha nism is implemented so that unnecessary copying is avoided Input signals in blocks are implemented as pointers which simply point at output sig nals see Fig 5 Thus no data needs to be copied when passing signals from one block to another within the same Periodic block For connected blocks belonging to different Periodic blocks mutual exclusion buffers are automatically cre
114. e user and the run time system but can only be assigned within the block i e in a PAL statement If the interface modifier is omitted state is used as default 5 Scalar Data Types The predefined scalar data type are the following real A real valued variable integer An integer valued variable string A text string str initial value string String concatenation is available using dimension An integer variable used to specify the dimension for aggregate data types n dimension A dimension variable can be used as an integer in expressions and statements It gets its value upon block creation and may not be assigned within the algorithm section The value of a dimension variable can only be set by the runtime system A dimension variable may be given a default value 191 Appendix A PAL P lsj Algorithm Language boolean A boolean valued variable being either true or false bool true boolean Predefined constants true or false Three logical operators and or and not sampling interval The period time for the block given in seconds The sampling time is set by the user or the run time system The sampling time is real valued 6 Aggregate Data Types The predefined aggregate data types are 192 array An array is a fixed sequence of elements of some scalar type The size of the array is given as the upper and the lower limits when defining the array instance The array s
115. e using the simplex architechture IEEE Control Systems 18 4 pp 72 80 Stewart D B R A Volpe and P K Khosla 1993 Design of dynami cally reconfigurable real time software using port based objects Ad vanced Manipulators Laboratory The Robotics Institute and Depart ment of Electrical and Computer Engineering Carnegie Mellon Uni versity 82 Paper 2 A Flexible Interactive Environment for Embedded Controllers Johan Eker and Anders Blomdell Abstract Today embedded control systems are created using tools that give insuffi cient support for rapid prototyping and code reuse New tools for the im plementation of embedded controllers are necessary This paper presents the experimental software framework PALSJO and the language PAL The P LSJ system is a rapid prototyping environment designed to support on line system reconfigurations and code reuse PAL is a new language designed for implementation of control algorithms 83 Paper 2 A Flexible Interactive Environment for Embedded Controllers 84 1 Introduction 1 Introduction The use of embedded control systems is growing rapidly Nowadays ad vanced control systems can be found in a wide range of areas from in dustrial processes and aeroplanes to consumer products such as washing machines and home stereo equipment In everyday life computers are be coming more and more indispensable for assistance Some tasks are non critical and may fail wit
116. e were actually two sets for each working point one for raising the temperature and one for lowering the temperature There was no significant difference in the models estimated from raising or lowering the temperature or at different set points Basically the only difference was in the static gain The identification experiments gave that b 0 03 SO es Cen CENA er EMITS was a reasonable model of the system During the experiments the pa rameter b had a variation of 20 At least part of the variation in this parameter is due to the outdoor temperature changes To raise the tem perature more energy needs to be added to the outdoor air when it is colder The chosen model is complicated enough to capture the dynamics of the system and still simple enough to allow an analytical solution to the time optimal control problem There is some freedom in choosing a state space representation for the transfer function in Equation 4 In the real process only one state the temperature is measurable and to simplify the filtering needed in the real time implementation the second state was chosen as the derivative of the temperature A suitable state space representation for simulation and implementation is the controllable form Alo ale y 1 0 x 5 174 5 Controller Design The parameters aj as are almost constant and only the gain b contributes to the process variations as a function of the working conditions 5 Controller Design
117. ear that neither of the above assumptions need necessarily be true Many of the computing plat forms that are commonly used to implement control systems are not able to give any deterministic guarantees This is especially the case when commercial off the shelf operating systems are used These systems are typically designed to achieve good average performance rather than high worst case performance Many control algorithms are not periodic or they may switch between a number of different fixed sampling periods Con trol algorithm deadlines are not always hard On the contrary many con trollers are quite robust towards variations in sampling period and re sponse time It is in many cases also possible to compensate for the varia tions on line by e g recomputing the controller parameters see Nilsson 1998 It is also possible to consider control systems that are able to do a tradeoff between the available computation time i e how long time the controller may spend calculating the new control signal and the control loop performance For more demanding applications requiring higher degrees of flex ibility and for situations where computing resources are limited it is therefore motivated to study more integrated approaches to scheduling of control algorithms The approach taken in this paper is based on dynamic feedback from the scheduler to the controllers and from the controllers to the scheduler The idea of feedback has been used
118. ed for editing All commands that deal with creating blocks moving blocks connecting blocks etc are done on the shadow configuration When the edit session is completed the shadow configuration becomes the running configuration The values of all internal states are copied to the shadow configuration before it is switched in The new shadow configuration is now updated and turned into an identical copy of the current running configuration The copying of variables could become a problem if the data set is large A better solution would be to pass a reference to the data set thus making the switch independent of the size of the data set An edit session is shown in five steps in Fig 8 Step one shows the initial state of the system There are two identical copies of the block configuration In step two the LQG block is deleted by the user This operations only affects the shadow configuration at this stage A new block called GPC is allocated and connected in step three Now the shadow configuration is a correct and executable configuration In step four a switch is made and the shadow configuration now becomes the running configuration Before the switch is performed the values of all variables are copied from the running configuration to the shadow configuration Finally the new shadow configuration is updated in step five 6 Conclusion The design of P LSJ has been inspired and influenced by a number tools System descriptions in P LSJ
119. edule 4 T T T T T T T Task1 Task2 Task3 3 5 2S r Pe 05 fi L fi i fi i Ll L i 0 Figure 9 The schedule resulting from the simulation in Example 3 The bottom graph shows when Task 1 is running high ready medium or blocked low The other two graphs represent Task 2 and Task 3 Connecting a Continuous Plant Figure 10 shows a Simulink diagram where a Computer block is connected to three pendulum models The continuous plant models are described by other Simulink blocks Angle Position noise J Pendulum 1 pilin Out Angle 3 In2 Out2 Position noise J gt 1n3 Out3 Pendulum 2 u Computer Angle Position noise J Pendulum 3 pu Figure 10 A Simulink diagram where three continuous pendulum models are connected with the real time kernel The simulation result from this system is both the activation graph and the output from the continuous plants 156 5 A Co Design Example A real time system with three control loops are created in Example 4 One code segment named myController is associated with each task EXAMPLE 4 function rtsys rtsys_init Scheduling type 1 RM 2 DM 3 FP 4 EDF rtsys st 1 rtsys tick_size 0 001 Desired bandwidths omega 3 5 7 Sampling periods T 0 167 0 100 0 071 for i 1
120. eduling Adjustment of task periods has also been suggested by others For example Kuo and Mok 1991 propose a load scaling technique to grace fully degrade the workload of a system by adjusting the task periods Tasks are assumed to be equally important and the objective is to min imize the number of fundamental frequencies to improve schedulability under static priority assignments In Nakajima and Tezuka 1994 a sys tem is presented that increases the period of a task whenever the deadline of the task is missed In Lee et al 1996 a number of policies to dynami cally adjust task rates in overload conditions are presented In Nakajima 1998 it is shown how a multimedia activity can adapt its requirements during transient overloads by scaling down its rate or its computational demands The MART scheduling algorithm Kosugi et al 1994 Kosugi et al 1996 Kosugi and Moriai 1997 also supports task period adjustments The system handles changes in both the number of periodic tasks and in the task timing attributes Before accepting a change request the system analyzes the schedulability of all tasks If needed it adjusts the period and or execution time of the tasks to keep them schedulable with the rate monotonic algorithm For the task execution time it is assumed that a minimum value exists in order for the task to guarantee a minimum level of service For the task period neither minimum nor maximum are assumed to exist The MART s
121. ef gref forceR gt gr forceR gref inhale gt gr inhale gref exhale gt gr exhale gref openclosed gt gr openclosed ji new IRB2000JointWrite 34 4 The Robot Pendulum End Effector IRB2000 JointWrite Gripper Ref ADn Pendul ER l ae E ointRea ontroller Ramp Ref Periodic IRB2000 JointWrite Figure 11 The PAL blocks used for controlling the robot The PCL script for creating this system is found in Example 2 ji joint 1 j4 new IRB2000JointWrite j4 joint 4 p2 new PendulumController thetaIn new ADIn jir new IRB2000JointRead jir joint 1 thetaIn out gt p2 thdirect jir y gt p2 xdirect ref4 new RampRef ref4 out gt p2 inref4 p2 ui gt ji tauExtern p2 u4 gt j4 qrExtern endwith s gref OpenClosed false s gref force 0 3 s tsamp 5 s start show s p2 u show s p2 thetaHat show s p2 dthetaHat show s p2 x s connect 35 Introduction Summary The implementation and design of a robot controller for balancing and swinging up the inverted pendulum was briefly presented The process model and the controller design were discussed To get good estimates of the angular velocities a nonlinear observer was used The implementation was presented with PAL and PCL code This application with PALSJO balancing the pendulum was also used in Henriksson 1998 to demonstrate scheduling principles for
122. elow are three examples of the available information when using the information operator 208 EXAMPLE 3 Including module built in Including module StandardBlocks PALSJO 3 Operators Copyright 1995 97 Department of Automatic Control Written by Johan Eker amp Anders Blomdell Lund Institute of Technology version Beta Sep 3 1997 bug report johane control lth se pcl gt use StandardBlocks pel gt pel gt s new Periodic pclx gt s adin new ADIn pcl gt s refgen new RefGen pel gt s regul new PI pcl gt s daout new DAOut pclx gt WORKSPACE Blocks workspace of type WorkspaceBlock id 0 s of type Periodic id 1 adin of type ADIn id 2 refgen of type RefGen id 3 regul of type PI id 4 daout of type DAOut id 5 DIMENSIONS Block libraries____________________ built in InSocket OutSocket Sporadic Periodic StandardBlocks ADIn DAOut RefGen PI SimplePI PID Filter Information about the Periodic block process is available in the same way If no object is specified then information about the run time system is retrived pclx gt s 209 Appendix B PCL P lsj Configuration Language BlockType Periodic Block Name s Block 1D 1 SIGNAL S Is it de er state running boolean false PARAMETERS 22 200 rt td et A tsamp int 2000 skip int prio int EVENTS connect asynchronous 5 5 disconnect asynchronous restartplot asynchronous p
123. emoving invalid nodes Block s is deleted Block b is deleted pcl gt 207 Appendix B PCL P lsj Configuration Language 3 Operators The predefined PCL operators are the following The Assignment Operator All parameters in a PAL block can be set by the user from the command line Below is an example of how this is done The first command sets the parameter Ti to 20 In this case Ti is a real valued variable but the same syntax is valid for integers pcl gt s b Ti 20 pcl gt s b1 parl false pcl gt s b1 par2 1 0 2 3 14 pcl gt s b1 par3 1 2 1 3 pel gt s bi par4 1 2 3 0 4 1 5 6 28 pari is a boolean parameter and may be assigned the values true or false par2 is an array with three elements par3 is a polynomial of degreee 2 and par4 is a two by three matrix The Event Operator It is possible to manually trigger the execution of block procedures An event requesting the execution is sent to the block The event simply consists of the name of the proceure Below a block procedure called on are executed pc1 gt s b2 on Events make it possible to construct blocks and systems that directly interacts with the user The Information Operator The information operator retrieves information about a system object A system object may be a single variable a block or the whole system The syntax is straightforward simply the desired system object followod by a question mark B
124. en in the PID mode for several samples and then the cycle repeats The relative execution times of the different modes were obtained by measurements on an existing PALSJO implementation of the hybrid con troller It was found that the Opt mode took about twice as long to execute as the PID mode and that the Ref mode had about six times the exe cution time of the PID mode In this example it is assumed that the execution times are constant in each mode and equal to Cp p 300 ms Cop 600 ms and Cres 1800 ms More on the measurements of exe 56 8 A Unifying Example Level 1 ol1_1 Level 19111 Level 2 H gt lt ol21 gt Level 29 12_1 u u mii y yt yi A ut ya 1 ls y2 gt y2 1 5 y2 loul Double Tank 1 lu Double Tank 1 Level 1H gt lt olt_2 gt Level 1 H gt lt I1_2 m re y2 Level 2 ol2_2 Level 2 12 2 3 y2 2 u2 az u gt lt m2 u2 u gt lt a yi yi re Dyer 2 ua pra yea ke y2 y2 ny ouble Tank 2 ny ouble Tank 2 yi3 Tou gy Double Tank no quar Double Tank a us Level 1H gt lt olt_3 3 2 3 cs Level 1H gt lt 11_3 yrer 3D yret_s Level 21 gt lt ol2_3 yret_ 3D y
125. ending the event connect to the Periodic block Below is an example of how this is done 206 2 Keywords pcl gt show process control u pcl gt show process l pc1 gt process connect pcl gt After the event connect is sent to process a socket is opened on the net work and the data transmission will start as soon as any client program on the host machine will connect hide The opposite of show is the command hide which removes a signal from the list of exported signals hide is used in the same way as show pcl gt hide lt block gt lt block gt lt signal gt break Several commands may be grouped together using curly brackets and such a set of commands is called an atomic operation i e all commands within the brackets will be interpreted as one complex command If the atomic operation is incorrect it will not be accepted by the system The command break can be used to leave an incorrect atomic operation and discard the edits In the example below the atomic operation is not correct since all input signals are not connected When the command break is used all edits made in the atomic operations are reversed and the running system remains unchanged pcl gt use StandardBlocks pcl gt pcl gt s new Periodic pcl gt use StandardBlocks pcl gt s b new PI pcl gt Error in b input signal r not connected gt Configuration invalid pclx gt pclx gt gt Now discarding all edits R
126. er parameters REDESIGN RECODING after validation Figure 13 The integrated environment The PALSIMART framework The PALSIMART environment is an integrated environment created start ing from three existing pieces of software the CACSD package SIMART the PALSJO run time system and the PAL meta compiler Its main purpose is to quicken prototyping of advanced controllers by letting real time al gorithms be analyzed and tested in simulation prior to on line implemen tation Using PAL to build control systems for real time applications enables the creation of a reusable library of control algorithms that are both easy to write and to implement Still the designer spends a considerable amount of time testing the control system under development by means of real time experiments PALSIMART supports the integration of PAL blocks into SIMART Allowing PAL blocks to execute in the SIMART sim ulation environment has some immediate benefits First the same PAL code may be used both in the simulation and in the real time controller Second it is possible to evaluate and test the controller code off line A screen shot from PALSIMART is shown in Figure 12 By double clicking on the PAL regulator block a list of available PAL modules and blocks will appear From this list the user chooses which PAL algorithm to be simulated Once a block is instantiated its parameters can be set and its variables can be connected to SIMART varia
127. ered during run time using PCL Instances of the system blocks Periodic and Sporadic are used to manage the exe cution The Periodic block executes its child blocks periodically according to the data flow between the child blocks All timing and synchronization between the child blocks is taken care of by the scheduler in the Periodic block Consider the block diagram in Figure 5 It consists of six blocks an analog input block followed by a pre filter two controllers in paral lel a switch and an analog output block The pre filter is used to reduce the noise from the measurement signal and is executed at a higher sam pling rate than the control blocks The desired real time behavior is the following e Execute RST PID Switch and Analog Out at a slower sampling rate e Execute Analog In and Filter at a higher sampling rate To configure the system to get this behavior two instances of the sys tem block Periodic are created one for each sampling rate The PCL commands to achieve this are the following 74 4 PAL P lsj Algorithm Language gt PID f Analog Filter gt Switch gt Azalog L gt RST Figure 5 The block diagram created in Example 1 EXAMPLE 1 pcl gt pl new Periodic pcl gt p2 new Periodic pcl gt p1 adin new AnalogIn pcl gt p1 filter new Filter pcl gt p2 rst new RST pcl gt p2 pid new PID pcl gt p2 switch new Switch pcl gt
128. es We want an estimator inside the block but we do not want to have an estimator in each step By implementing the estimator in the calculate update section the estimates are available for all the control laws 78 5 Calculate and Update Init CloseV2 Start StartFilling OpenV1 StartHeating Heat KeepFilling T gt Tref L2 StopHeating NoHeat StopFilling CloseV1 T lt Tref true EmptyTank Openv2 not L1 Figure 6 Grafcet for the controller of a boiler process This figure is generated by the PAL compiler 5 Calculate and Update Periodic algorithms in PAL are divided into the two sections calculate and update When a PAL block is executed new output values are calcu lated based on the values of the input signals and the states The values of the output signals are used as inputs to the next block in the signal flow path The two main reasons to divide the code into two parts are to minimize the sampling delay and to handle signal limitations correctly Minimizing Sampling Delay Consider the control system in Figure 7 First the value of the plant is sampled and then the signal propagates from the first block to the second one and so on In a control system
129. esigned keeping the same structure but using setpoint dependent parameters Figure 17 describes the algorithm with a Grafcet David and Alla 1992 This controller is used in Section 8 as an example of a con troller with highly varying execution times 8 A Unifying Example A feedback scheduling application is designed and simulated The feed back scheduling algorithm is loosely based on the work presented in Pa 54 8 A Unifying Example Single CPU System Real Time Kernel Task 1 Task 2 Yi u2 Task 3 Y2 re Figure 18 Several tank controllers execute concurrently on one hardware unit The interaction between the control tasks affects the control performance per 4 The simulations are made using the toolbox described in Paper 5 and the control problem is taken from Paper 6 Several double tank processes should be controlled by a single CPU system see Figure 18 Since the control tasks execute on the same CPU they will compete for the resources and interact with each other The goal of this example is to show how higher resource utilization and better con trol performance may be achieved by a more flexible scheduling approach The controller used in the simulation is the same as the one presented in Section 7 The computer executes each hybrid controller as a periodic real time task The execution times for the different modes va
130. ess was in steady state However the response to reference point changes was quite oscillative One solution to this problem is to use a hybrid controller consisting of two sub controllers one PID controller and one time optimal controller together with a super visory switching scheme In process control it is common practice to use PI control for steady state regulation and to use manual control for large 53 Introduction Init OffController NewRef Ref NewControllers not NewRef A A Opt OptController NewRef A A Close or Off not Close PID PIDController NewRef Off Figure 17 The Grafcet diagram for the hybrid controller consists of four steps The execution starts in the Init step Opt is the step where the time optimal con troller is active and PID is the step for the PID controller The Ref step is an intermediate state used for calculating new controller parameters changes In this case the PID steady state regulation is combined with a minimum time controller for the setpoint changes The time optimal controller is used when the states are far away from the reference point Coming closer the PID controller will automatically be switched in to re place the time optimal controller At each different setpoint the controller is red
131. eve on line interaction between control algorithms and the scheduler a number of issues must be considered Control design methods must take schedulability constraints into account It must be possible to dynamically adjust task parameters e g task periods in order to com pensate for changes in workload It can also be advantageous to view the task parameters adjustment strategy in the scheduler as a controller In this section an overview is given of the work that has been performed in these areas A more detailed survey on control and scheduling can be found in Arz n et al 1999 Control and scheduling co design A prerequisite for an on line integration of control and scheduling the ory is that we are able to make an integrated off line design of control algorithms and scheduling algorithms Such a design process should ide ally allow an incorporation of the availability of computing resources into the control design by utilizing the results of scheduling theory This is an area where so far relatively little work has been performed In Seto et al 1996 an algorithm was proposed that translates a system performance index into task sampling periods considering schedulability among tasks running with pre emptive priority scheduling The sampling periods were 125 Paper 4 A Feedback Scheduler for Real time Controller Tasks considered as variables and the algorithm determined their values so that the overall performance was optimi
132. f Embedded Control Systems tion in Figure 14 At the top some general settings are made A priority function prioRM which implements rate monotonic priority assignment is chosen and the tick size of the kernel is set to 1 millisecond Two peri odic tasks are then defined using the task function The first parameter is the name of the task followed by the code object the period and the deadline The code object contains the statements that are to be executed by the task EXAMPLE 3 function rtsys resources_init hh General settings rtsys prioFun prioRM rtsys tickSize 0 001 Create tasks TASK 1 rSegs rsegl rseg2 rParams inCh 1 rParams outCh 1 rCode code rSegs rParams rPeriod 0 012 rDeadline 0 012 rTask task Task1 rCode rPeriod rDeadline TASK 2 oSegs osegl oseg2 oParams inCh 2 oParams outCh 2 oCode code oSegs oParams oPeriod 0 017 oDeadline 0 017 oTask task Task2 oCode oPeriod oDeadline rtsys tasks rTask oTask hh Create mutexes mi mutex M1 mi data 0 rtsys mutexes m1 ih Create events el event E1 M1 rtsys events e1 O A code object is built up from code segments which is the smallest entity in the kernel and implemented as a MATLAB function The hierarchy of 49 Introduction objects is shown in Figure 15 A code segment has two p
133. face modifier data type The possible data types and interface modifiers are described below 4 Interface Modifiers The interface modifiers define how the variable interacts with the envi ronment i e other blocks and the user e Input The input modifier is used in variable declarations and in procedure heads indicating that the variable is an input An input variable may not be assigned a value e Output The output modifier is used in variable declarations and in procedure heads indicating that the variable is an output e Parameter The parameter modifier is used in variable declarations A parameter variable may not be assigned a value Parameters can only be set by the user or the run time system There are two types of 190 5 Scalar Data Types parameters direct and indirect A direct parameter is declared with data type and interface modifier An indirect parameter is a function of other parameters and may not be assigned directly in the PAL code For indirect parameters the data type is given implicitly from the relation with other direct parameters In Example 2 the indirect parameter c is declared as a function of the direct parameters a and b The data type of the c parameter will be real Notice that indirect parameters are declared using equality EXAMPLE 2 a parameter real b parameter real c a b O State The state modifier indicates that the variable is a state A state variable is visible to th
134. for designing the kernel and the network blocks was to facilitate the simulation of flexible embedded control system i e systems where the task set is allowed to change dynamically and the un derlying real time system must compensate for this From a control theory perspective we might say that we want to design a feedback connection between the control tasks and the scheduler see Figure 15 To support the Scheduler z Controllers Processes Cul Figure 15 The control tasks and the task scheduler are connected in a feedback loop simulation of feedback scheduling there must be ways for the tasks and the task scheduler to communicate Therefore the kernel also supports system level message passing between tasks 7 Conclusions This paper presented a novel simulator for the co design of real time sys tems and control systems The main objective is to investigate the conse quences on control performance of task interaction on kernel level This way scheduling algorithms may be evaluated from a control design per spective We believe that this is an issue of increasing importance There are many more things to be implemented and improved before this block set will become a truly useful tool Currently the kernel is tick based and has little support for external interrupts The next version of the kernel block will probably be event based in order to better support interrupts and event based sampling To make the si
135. g It resulted in a few more min max switches before reaching the target area where the PID controller took over However a good model of the static gain in the system is needed If there is a large deviation it cannot be guaranteed that the equilibrium points are within the catching regions The catching region is defined as an ellipsoid around the theoretical equilibrium points Field test Finally the hybrid control strategy was tested at the school in Klippan The results are shown in Figure 13 As expected there were a few ex tra min max switches due to approximation of the switching curve and probably also due to unmodeled dynamics and nonlinearities The param eter b was estimated from steady state values of the air temperature and the control valve position T Tref u 60 80 100 120 140 160 0 20 40 60 Figure 13 A 5 degree set point change using the hybrid controller Air tempera ture left and control signal right A similar set point change for the controller currently in use at the school showed that it took approximately twice as long time to reach the new set point However the main advantage with the proposed method is that it will not give a large overshoot even if started from a very low temperature It is not difficult to incorporate some process parameter estimation functions in the code This would give a good estimate of the static gain Po
136. g intervals has been investi gated Formulas for calculating the cost functions and their derivatives 136 7 References have been presented The feedback scheduler is demonstrated on a three control loops system and the result is promising The algorithm is how ever complex and quite computation intense The execution time needed for solving the optimization problem would probably exceed the execution times of most control tasks By instead using approximative cost functions good results may be achieved at much less computational cost Many questions have been left out in our discussion on feedback sched uling One thing that has been neglected is what happens during the transient phase when a sampling rate is changed This problem must be treated differently depending on the used scheduling algorithm e g EDF or RMS Using a feedback scheduler approach it would be possible to design real time plug and play control systems Tasks and resources are allowed to change and the system adapts on line 7 References Arz n K E 1999 A simple event based PID controller In Proceedings of the 14th World Congress of IFAC vol Q pp 423 428 IFAC Beijing P R China Arz n K E B Bernhardsson J Eker A Cervin K Nilsson P Persson and L Sha 1999 Integrated control and scheduling Report ISRN LUTFD2 TFRT 7586 SE Astr m K J 1963 On the choice of sampling rates in optimal linear systems
137. garbage collection in hard real time systems There the underlying memory allo cation and deallocation routines were replaced with functions supporting garbage collection 5 Feedback Scheduling Real time systems is an inter disciplinary research area that includes as pects of control engineering and computer science It is an area of vital importance to all control engineers Today almost all controllers are im plemented on digital form with a computer A successful implementation of a computer controlled system requires a good understanding of both control theory and real time systems Traditionally when implementing computer control systems the con trol community has assumed that the computer platform used can provide the deterministic equidistant sampling that is the basis of sampled com puter control theory However many of the computing platforms that are commonly used to implement control systems are not able to give any deterministic guarantees On the other hand the real time scheduling community generally as sumes that all control algorithms should be modeled as tasks that e are periodic with a set of fixed periods e have hard deadlines and e have known worst case execution times WCETs This simple model has permitted the control community to focus on its own problem domain without worrying about how scheduling is being done and it has relieved the scheduling community from the need to understand what impact sched
138. generates C code which fits into the framework The framework has classes for real time scheduling network interface and user interaction The control al gorithm coding is made off line and the system configuration is made on line using PCL PALSJO Configuration Language PCL is a simple lan guage for managing blocks and assigning variables The system may be reconfigured on line while the system is running Introductions to PAL and PCL are found in Appendix A and B Friend The more interactive way of working with embedded systems as pro posed in the PALSJO PAL project creates new problems P LSJ admits that blocks are changed on line Allowing blocks to be added or deleted dy namically will for example give rise to timing and scheduling problems In PALSJO it is entirely up to the user to make sure that nothing goes wrong There are no language constructs in PAL to assist the programmer The design of the FRIEND language addresses the need for built in lan guage support when implementing fault tolerant and adaptive embedded control systems Similarly to PALSJO PAL FRIEND is block oriented i e a control system is defined by a number of blocks and their interconnections To support implementation of control systems that allow blocks to be inserted and replaced on line the use of contracts is introduced The con tract defines the behavior of a block and may be used by the run time system to determine e Ifa new block can
139. gnal Pendulum Angle E Z gt o o E 0 5 10 0 5 10 __ Seconds Seconds Joint 1 position Angular velocity e 0 5 10 Q p D 2 0 5 0 E 0 5 amp 10 0 5 10 0 5 10 Seconds Seconds Figure 9 The control signal and the measurements logged during the swing up shown in Figure 10 The PAL Code Example 1 shows the PAL code for the pendulum controller The pendulum controller has one sequential part and one periodic part The sequential part is described as a Grafcet with four steps see Figure 6 In the initial step the output signal is set to zero In step 2 the swing up algorithm is switched in and when the pendulum comes close to the upright posi tion step 3 becomes active Finally when the pendulum has reached the upright position step 4 becomes active The periodic part implemented using the calculate and update sections contains the position and angle observers 30 4 The Robot Pendulum Figure 10 The robot swings up the pendulum by adding energy The signals from this experiment are presented in Figure 9 31 Introduction EXAMPLE 1 module Pendel function cos r input real real external cos function sin r input real real external sin block PendulumController 32 x th input real u 0 0 output real A22 parameter matrix 1 2 1 2 of real B2 K1 K2 parameter matrix 1 2 1 1 of real xhat matrix 1 2 1 1 of real L parameter matrix 1 4
140. h state may be associated with an action which is executed when the step is active A transition may fire if its condition is true and the the preceding step is active The Grafcet diagram for our hybrid controller consists of four states Initially no controller is in use This is the Init state Opt is the state where the time optimal controller is active and PID is the state for the PID controller The Ref state is an intermediate state used for calculating new controller parameters before switching to a new time optimal controller The signal Close tells if the controller should use the PID controller or Init OffController NewRef Ref NewControllers not NewRef Opt OptController NewRef d Close or Off not Close PID PIDController NewRef _ Off Figure 3 A Grafcet diagram describing the control algorithm 169 Paper 6 Design and Implementation of a Hybrid Control Strategy the time optimal controller Two different ways to calculate Close is given in the section on Lyapunov function modifications 3 Stabilizing Switching Schemes It is well known that switching between stabilizing controllers may lead to an unstable closed loop system lt is therefore necessary to have a switching scheme that guarantees stability Consider the system x f
141. he out put signals are calculated based on the values of the inputs the internal states and the parameters A PAL block has the following structure EXAMPLE 1 module examplel block block1 in input real out output real p parameter real i 1 0 real calculate begin out i in end calculate update begin i i p 189 Appendix A PAL P lsj Algorithm Language end update end block1 end examplel O The top level concept of PAL is the module Several blocks may be grouped together in a module In the example above the block block1 is declared within the module examplel The first section of the block defines the interface In this example it consists of one input signal n one output signal out one parameter p and one state variable i After the interface section comes the algorithm section The two procedures calculate and update define the periodic algorithm of the block 3 Block Variables Variables declared in the block scope are global at the block level They are visible for all procedures and functions in the block Global variables are also visible from outside the block i e it is possible to monitor and log those variables Local variables are declared before the begin statement in procedures and functions They are only visible inside the scope of the function or the procedure and may not be monitored or logged The syntax for defining variables is name value inter
142. hout dramatic consequences Ifthe word processor or email software crashes it is usually not a big problem it is simple to reboot and carry on On the other hand if the maneuvering systems in an airplane malfunctions it is unlikely that the pilot will save the situation by pressing Ctrl Alt Delete The development of embedded systems requires special tools This paper introduces the PALSJO framework Eker 1997 and the PAL lan guage Blomdell 1997 P LSJ is an experimental rapid prototyping tool developed with an emphasis on code reuse and interactivity in embed ded systems PAL PALSJO Algorithm Language is a dedicated controller description language used for implementing controllers that will run in PALSJO When developing real time systems it is highly desirable to reuse com ponents and modules from one program version to another or from one software project to another The mixture of timing statements and logical statements in languages such as ADA and C C makes it cumbersome to reuse code Even if two applications share the implementation struc ture code reuse is hindered by differences in timing requirements There fore to better support code reuse timing specifications are kept separate from the control algorithm in PALSJO and PAL It is common to generate ADA or C C code for controllers directly from a simulation environment such as Simulink MathWorks 1997 or SystemBuild Integrated Systems 1996a Integrated Systems 19
143. ich is a commercial offspring from the work of the J Consortium supports deterministic real time tasking and real time garbage collection NewMonics 1999 SUN Microsystems together with the Real Time Expert Group quite recently announced the Real Time Specification for Java The specification extends the Java platform to support deterministic real time behavior The Simplex group at SEI CMU has developed a framework Simplex that supports safe on line upgrades of real time systems in particular safety critical real time control systems Seto et al 1998a Sha 1998 The basic building block of Simplex is the replacement unit and a typical example of a replacement unit is a controller Replacement units are or ganized into application units that also contain communication and task management functions A special safety unit is responsible for basic re liable operation and operation monitoring A common set up is that the system contains two units a safety controller and a baseline controller The baseline controller provides the nominal control performance and it is assumed that it is executing when a new upgraded version of this controller is to be installed If the new controller which is added on line does not work correctly Simplex switches in the safety controller When the controlled process is eventually back in a safe state Simplex switches the baseline controller back in Summary PALSJO is a software environment for
144. ignals the states and the parameters and these calculations must always be implemented in calculate and update The block PI implements two interfaces one for communicating with the process and one for retrieving controller parameters negotiator B active block implements io MISO fulfills myContract C2 QoS active QoS sampling interval WCET max myBlocks WCET V active V arbitrates myBlocks algorithm that fulfills C2 every myContract sampling interval Vi myBlocks i io io active find_min myBlocks i V active calculate io active io active update 113 Paper 3 A Contract Based Language for Embedded Control Systems Negotiator B accepts child blocks that fulfill the contract of type C2 At the beginning of every sampling interval the interfaces of all the child blocks are updated with new input values via the interface of B The active sub controller is then selected as the child block with the smallest value of V the function find_min is assumed to be available The new output signal of B is given as the output signal from the active sub controller algorithm C extends PI a parameter real implements io2 MISO i02 u io u lo y 102 y io yref io2 yref fulfills myContract C2 i02 io QoS a sampling interval V i02 y1 102 y ef i02 y2 10 Y ef WCET Block C extends the PI block by adding a contract This is an example
145. imulation of real time systems for ex ample STRESS Audsley et al 1994 and DRTSS Storch and Liu 1996 Very little effort has however been put into mixed simulations where both the continuous dynamics of the process the discrete algorithm of the con troller and the behavior of the control task running on a computer are simulated One noticeable exception is Liu 1998 where a control task and a continuous process are simulated using Ptolemy II Davis II et al 1999 The Toolbox To get the full picture of the performance of an embedded control system it may be necessary to consider the real time behavior of the controller task The well known and much used simulation environment Simulink was chosen as the platform for a toolbox designed to support simulations of embedded systems at task level Using the toolbox the control engi neer may first simulate and design the controller without any real time considerations and then at a later stage with only minor modifications simulate it as if running on a virtual computer The toolbox is imple mented as a set of Simulink blocks and MATLAB functions A kernel block is the core of the virtual computer block It samples continuous signals and writes discrete signals Figure 14 shows a view from a simulation The model consists of two dynamic processes which are controlled by two 47 Introduction 0 02 D AS E Time offset 0 0 02 0 04 Time offset 0
146. ing while a function that re turns the absolute deadline of a task implements earliest deadline first scheduling There currently exist predefined priority functions for rate monotonic RM deadline monotonic DM arbitrary fixed priority FP and earliest deadline first EDF scheduling The user may also write his own priority function that implements an arbitrary scheduling policy The execution model used is similar to the live task model described in Storch and Liu 1996 During a simulation the kernel executes user defined code i e Matlab functions that have been associated with the different tasks A code function returns an execution time estimate and the task is not allowed to resume execution until the same amount of time has been consumed by the task in the virtual CPU The Task Each task in the kernel has a set of basic attributes A name a list of code segments to execute a period a release time a relative deadline and the remaining execution time to be consumed in the virtual CPU Some of the attributes such as the release time and the remaining execution time are constantly updated by the kernel during a simulation The other attributes such as the period and the relative deadline remain constant unless they are explicitly changed by kernel function calls from the user code The Code The local memory of a task is represented by two local user defined data structures states and parameters The states may be
147. input real v r2 output real I 0 0 e 0 0 real K 0 5 Ti 10 0 parameter real Tr 10 0 parameter real h sampling interval bi K x h Ti br h Tr calculate begin e r y end calculate update begin r2 Limiter minRef maxRef r I I bixe br u vu end update function Limiter max real min real value real real begin end Limiter end PI end MyPl O The top level concept of PAL is the module Several blocks may be grouped together in a module In the example above the block Pl is declared within the module MyPI The first section in the block defines the interface There are a set of input signals output signals and parameters There are 76 4 PAL P lsj Algorithm Language also two state variables and e and two indirect parameters bi and br After the interface section comes the algorithm section The two sections calculate and update define the periodic algorithm of the block Data Types PAL has a set of predefined data types Among these are regular scalar ones e g real integer boolean as well as aggregate types such as ar rays matrices and polynomials The availability of arithmetic operations for polynomials and matrices makes it straightforward to express control algorithms Below is an example of scalar data types r real i integer bool true boolean The type dimension is an integer variable used to specify the dimension
148. inst uncertainties in exe cution times and workload When a control task performs a mode change and this leads to a change in its execution time the feedback scheduler adjusts the sampling frequencies so that the system remains schedulable 124 2 Integrated Control and Scheduling Deadlines may be missed if a change in execution time causes the system to overload In such a situation the feedback scheduler adjusts the sampling rates to regain schedulability but deadlines may however still be missed If the feedback scheduler instead is aware of a forthcoming mode change it could avoid an overload by changing the sampling rates in advance This can be dealt with by establishing a communication channel between the feedback scheduler and the control tasks The control tasks notify the feedback scheduler by sending a request prior to a mode change and may not proceed with the mode change until given permission to do so The module that handles this is called the admission controller It is also responsible for handling the arrival of new tasks and the termination of old tasks Figure 2 shows a block diagram of the feedback scheduler with the admission controller Outline An overview of related work is given in Section 2 Section 3 defines the problem and the LQ based cost function calculation are presented in Sec tion 4 Section 5 describes the design of the feedback scheduler 2 Integrated Control and Scheduling In order to achi
149. ints on the switching curves could be stored in a table instead of using 185 Paper 6 Design and Implementation of a Hybrid Control Strategy the analytical expressions If the switch is too early or too late because of the nonlinearities this information could be used to update the switching curve table 9 Summary Hybrid controllers for a double tank system and a heating ventilation process have been designed and implemented Both simulations and real experiments were presented It was shown that a hybrid controller con sisting of a time optimal controller combined with a PID controller gives very good performance The controller is easy to implement It gives in one of its forms a guaranteed closed loop stability The proposed controller solves a practical and frequent problem Many operators switch to manual control when handling start up and set point changes It is fairly easy to combine this method with a tuning exper iment that gives a second order model of the system From the tuning experiments it is easy to automatically generate a PID controller and an approximate time optimal controller The model mismatch was not seri ous The nonlinearity led to some additional min max switches The simple hybrid controller was tested on a fast set point problem on a school Simulations indicated that the theoretically derived switching curves could be approximated with simple functions without too much performance deterioration Meas
150. ired temperature the tank is emptied and a new batch can be started Grafcet Grafcet David and Alla 1992 is a convenient and powerful way of im plementing sequential algorithms There exist constructs in PAL for ex pressing Grafcet algorithms These constructs are steps actions and tran sitions Grafcet statements are expressed in PAL with a textual represen tation that is based on Sequential Function Charts in IEC 1131 Lewis 1995 Each state in a sequential algorithm is defined as a step in Grafcet A state may be active or inactive Several states may be active at the same time A Grafcet must have an initial step The PAL syntax for parts of the Grafcet in Figure 2 is presented below A step is defined as follows initial step Init pulse activate CloseV2 end Init step StartHeating activate Heat end StartHeating step StopHeating pulse activate NoHeat end StopHeating To each step an action can be attached The action contains the statements 197 Appendix A PAL P lsj Algorithm Language Init Start StartFilling CloseV2 Openv1 not L1 Figure 2 Grafcet for the controller of the boiler process see Figure 1 This figure is generated by the PAL compiler using th
151. irplanes are more and more relying on computers and it is unlikely that the pilot can save the situation by pressing Ctrl Alt Delete when an unrecoverable application error occurs By making embedded systems more adaptive to changes in the environment they would be less likely to fail Having a more flexible set up would also allow the support for on line software upgrades Being able to change embedded software without shutting down the plant is highly desirable as it would save both time and money An upgrade must however be done in a safe and well defined way The implementation of advanced control systems require good interactive environments which are nontrivial to design because of the real time aspects 11 Introduction Many applications for embedded systems are control systems In this thesis some software issues for embedded control systems are investi gated An interactive development tool is presented together with two languages for controller implementation There is rarely any interaction between the control loops and the un derlying real time kernel or operating system From a control engineering perspective the system executes in open loop In this thesis the possibil ity of using feedback in the scheduling of real time tasks is explored This is called feedback scheduling An algorithm for selecting sampling rates based on the quality of the control performance is presented By viewing the control task the underlying
152. is proposed as a way to allow graceful degradation in cases of overload failures or violation of pre run time violations The mechanism permits clients to ex press in their service requests a range of QoS levels they can accept from the provider and the perceived utility of receiving service at each of these levels Using this the application designer e g the control engineer is able to express acceptable tradeoffs in QoS and their relative cost benefit The approach is demonstrated on an automated flight control system Sampling Rate Adjustments In Buttazzo et al 1998 an elastic task model for periodic tasks is pre sented Each task is characterized by five parameters computation time Ci a nominal period T a minimum period T a maximum period T and an elasticity coefficient e gt 0 A task may change its period within max 40 5 Feedback Scheduling its bounds When this happens the periods of the other tasks are adjusted so that the overall system is kept schedulable An analogy with a linear spring is used where the utilization of a task is viewed as the length of a spring that has a given rigidity coefficient 1 e and length constraints The elasticity coefficient is used to denote how easy or difficult it is to adjust the period of a given task compress or decompress the spring A task with e 0 can arbitrarily vary its period within its range The approach can be used under fixed or dynamic priority sch
153. is started in the downward position In both the simulation and the real case the observer was initiated to start in the downward position In the simulations measurement noise is approximated with a high frequency sinusoid Notice the good agreement between experiment and simulation and the good performance of the nonlinear observer The Pendulum on the Robot The controller used on the robot is the same as the one previously de scribed In that case the input signal to the process was the acceleration of the pivot In the robot set up the input signal to the process is the acceleration of the pivot point i e the point where the pendulum is at tached to the robot While the pivot of the pendulum on the cart moves along a straight line the pivot of the pendulum on the robot moves along a circular path This fact is not considered in the implementation but as long as the speed of the robot arm is low the influence from Corioli forces may be neglected The output from the control block is the desired acceleration for the pivot Control Signal T T Figure 8 Plots from the swing up and stabilization of a real pendulum process The pendulum starts in the downward position 29 Introduction The results from the experiments with the robot are presented in Fig ures 9 and 10 Initially the pendulum is in the downward position The robot uses joint 1 to swing up and stabilize the pendulum Control Si
154. itable nominal sampling interval ho and using J ho J ho Jn ho Jr ho the coefficients are given as P Jn ho 2ho a J ho Bho 135 Paper 4 A Feedback Scheduler for Real time Controller Tasks The following approximate cost function and derivate are then obtained Vf ai Bi f Vf 21B1 F8 Ball Vis 6 diag B1 f4 Ba Using these approximate functions instead of the exact ones will give a much less computation intense problem The optimal solution is obtained from Equation 5 and by inserting the approximative expression for Vp we get 2B f AC gt f 28 4C P gt U gt Cif DD C 2B 40 t 1 1 Now an explicit expression for the optimal solution is given by A 1 UN C P 26 1 fi 2B 40 14 EXAMPLE 2 continued Again consider the system with three pendulum controllers From the explicit analytical expressions in Equation 7 the following frequencies are calculated f 4 866 4 347 5 29 Note that these frequencies are very close to those from Example 2 This example shows that the approximative cost functions are sufficient to achieve good optimization results for some processes O 6 Conclusion In this paper a novel feedback scheduler has been proposed For a class of control systems with convex cost functions the feedback scheduler cal culates the optimal resource allocation pattern The calculation of cost functions and their dependence on samplin
155. ity of service functions are associated with each process and are used by the run time system to optimize the global performance Related work is found in Andersson 1999 where a framework for an adaptive multiprocessor system is suggested The Rialto operating system Jones et al 1995 from Microsoft Research negotiates with its applications and distributes resources to maximize the performance of the entire system The ALTAS testbed Jehuda and Berry 1995 implements a top layer approach for handling dynamic job loads The FARA framework Rosu et al 1998 is designed for adaptive resource allocation There are software components that represents the resources or the tasks and they negotiate in order 106 3 Friendly Concepts to distribute the available resources In Krasner and Bernard 1997 the design of the NASA deep space mission software is described Depending on the phase of the mission the goals change and software modules are added or removed The ideas behind contracts have been adopted from Helm et al 1990 and Meyer 1992 A related architectural software pattern is the Broker pattern see Buschman et al 1996 The Broker pattern is used for de signing software with loosely coupled components which may be added or removed during run time A C D F G Figure 2 The hierarchical structure of a real time c
156. ize cannot be changed from within the PAL code It may however be parameterized using dimension variables n dimension inl input array 1 n of real m dimension in2 array 0 m of input real Accessing elements in1 1 3 14 tmp in1 2 matrix A matrix is a fixed size two dimensional array of real valued elements The size of the matrix is given as the upper and the lower limits when declaring the matrix instance Dimension parameters may be used to parameterize the size of a matrix instance out input matrix 1 n 1 m of real Accessing elements out 2 2 3 14 tmp out 3 3 Operators applied to matrix operands applied to a scalar real and a matrix The matrix data type maps down onto the Newmat matrix class Davis 1997 The Newmat function library may thus be used for matrix manipulation 7 Expressions and Statements e polynomial A polynomial is a fixed one dimensional array of real valued elements The degree of the polynomial is given when declar ing the polynomial instance The degree of a polynomial may be pa rameterized using dimension parameters A polynomial with degree n has n 1 coefficients starting with index 0 par parameter polynomial n of real Accessing elements par 2 3 14 tmp par 3 Operators div mod applied to polynomial operands x applied to a scalar real and a polynomial The polynomial
157. k that calculates new output signals given new input signals The actual controller code is divided into two block methods calculate and update An algorithm block may consist of a set of sub blocks of algorithm type e The Negotiator A Negotiator is a block that consumes and dis tributes resources A negotiator may consist of a set of sub blocks which may be either algorithm blocks or negotiator blocks e The Contract A contract specifies how a block depends on available resources A possible parent block may require that a block fulfills a specified contract before it adopts it e The Interface An interface specifies how a block interacts with other blocks i e the format of the input and output signals and of the parameters The two types of blocks algorithm and negotiator have the same abstract superblock see Figure 5 The relation between the FRIEND components are shown in Figure 6 The labels on the arcs are the keywords used for connecting the components For example a negotiator may arbitrate con tracts belonging to its child blocks but also fulfill contracts with its parent block A contract may require that the block that fulfills the contract has a certain interface The FRIEND language is demonstrated below by two examples A Hybrid Controller A hybrid controller consists of a combination of several different control strategies Figure 7 shows an example of a hybrid control system The 110 4 The FRIEND Language
158. k was designed The most important ones were e Rapid prototyping The framework should reduce the develop ment time for prototype controllers e Code reuse and algorithm libraries The framework must have a structure that allows algorithms to be stored and reused Expandable It should be possible to add new features for example new data types to an existing system e On line configurable Changes in running setups should be al lowed without stops e Efficient execution Neither the code size nor the execution speed of an application built using the framework should differ from an application built from scratch 2 PAL P lsj Algorithm Language PAL is a block based imperative language for implementation of embed ded controllers It is designed to support and simplify the coding of control algorithms Control algorithms can often be described as a combination of periodic tasks and finite state machines PAL supports those types of algo rithms the finite state machine in form of Grafcet David and Alla 1992 Furthermore the language supports data types such as polynomials and matrices which are extensively used in control theory In this section a brief introduction will be given to the PAL language For a more in depth description see Blomdell 1997 87 Paper 2 A Flexible Interactive Environment for Embedded Controllers Blocks and Modules Algorithms are described as input output blocks New values for the out
159. lation System The hybrid controller was implemented in FORTH on a Diana ADP 2000 system and tested against a process simulation using real time SIMNON see Elmqvist et al 1990 The control system Diana ADP 2000 manufactured by Diana Control AB is mainly used in heating ventilation applications The system is flex ible modular and well suited for testing of new software It is possible to install new controller code without having to rebuild the whole system for input output handling logging etc The controller hardware Diana ADP 2000 is modular One unit can itself have several control loops and on large installations several Diana ADP 2000 can be interconnected in a network In the network configura tion one of the control units is a master and the others are slaves This master unit could be reached over a modem connection and from the mas ter it is possible to communicate with all the others Over the telephone line and via a user interface it is possible to log data change parameters and down load new code for every controller The programming of both the real time operating system and the ap plication programs is done in FORTH Amongst its good properties are that 183 Paper 6 Design and Implementation of a Hybrid Control Strategy it is both interactive and compiled Structure can be built with the no tion of words Words are executable functions or procedures that can be arranged in a hierarchical structure Dian
160. lso straightforward to find examples of controllers that be cast on sieve function form For example in an indirect adaptive controller the updating of the adapted parameters can be skipped when time con straints are hard or in a LQG controller the updating of the observer can be skipped when time constraints are hard Similarly in a PID controller the updating of the integral part may be skipped if needed The extreme case is of course to skip the entire execution of the controller for a cer tain sample Scheduling of systems that allow skips is treated in Koren and Shasha 1995 and Ramanathan 1997 The latter paper considers scheduling that guarantees that at least k out of n instantiations will execute 42 5 Feedback Scheduling Finally it is also possible to find examples of multiple version methods in control e g situations with one nominal control algorithm and one backup algorithm However in most cases the motivation for having the backup algorithm is control performance rather then timing issues Mode changes Mode changes for priority based preemptive scheduling is an issue that has received some interest In the basic model the system consists of a number of tasks with task attributes Depending on which modes the system and the tasks are in the task attributes have different values During a mode change the system should switch the task attributes for a task and or introduce or remove tasks in such a way that the
161. mated A nonlinear observer is proposed The need for a nonlinear observer becomes evident when considering the swing up strategy which requires both the angle and the angular velocity at all positions A linear observer will only give accurate estimates values around some linearization point The proposed nonlinear observer has the same structure as a linear observer but with the linear model replaced by a nonlinear model dx W0ko ki x1 or oX2 k1 x1 1 d a SL n la o sin u g o cos 1 ka x1 1 Note that the observer has a very simple structure It combines a model for the nonlinear dynamics with a simple feedback from the measured angle Conditions for stability and design based on linearized analysis are presented in Paper 5 Before applying the observer to the robot system it is Control signal 0 0 2 4 6 8 10 Angle estimate 4 o T T T T 1 0 2 4 6 8 10 Estimated angular velocity 104 T T T T 1 0 2 4 6 8 10 Figure 7 A simulation of swinging up and stabilizing the pendulum using the non linear observer The simulation starts with the pendulum in the downward position The observer is initiated to start in this position 28 4 The Robot Pendulum tested in simulation see Figure 7 The next step is to test the observer on a stand alone pendulum This experiment is shown in Figure 8 Both the simulation and the experiments show a swing up followed by stabilization The pendulum
162. meters can only be set from outside the block by the user or by the system The value of a parameter cannot be changed internally in the block A set of states S which describe the internal states of the block A state can only be assigned internally A set of events E which the block responds to An event can be either synchronous or asynchronous Synchronous events are executed at the next sampling instance Asynchronous events are executed im mediately when they arrive A synchronous event could for example be a request for a mode change in the controller An emergency stop event should typically be asynchronous Sequential logic L which is described by one or several Grafcets An algorithm A that describes the periodic behavior of the block If a block contains periodic algorithms it must be executed periodically To support the reuse of algorithms the design decision was made to separate temporal and functional specifications in the design The basic idea is to view PAL blocks as input output blocks which only need to know at what frequency they are executed A PAL block cannot contain any temporal constraints and neither can it demand synchronization All temporal functionality is taken care of by designated system blocks which handle the actual execution of the PAL blocks Using this approach the 91 Paper 2 A Flexible Interactive Environment for Embedded Controllers
163. ming requirements than those that can sometimes be found in closed loop control systems Missing a deadline may decrease the QoS level but without causing any critical system faults Depending on the requested QoS tasks may adjust their attributes to accommodate the requirements of other concurrent activities On line admission control has been used to guarantee predictability of services where request patterns are not known in advance This concept has also been applied to resource reservation for dynamically arriving real time tasks e g in the Spring kernel Stankovic and Ramamritham 1991 A main concern of this approach is predictability Run time guar antees given to admitted tasks are never revoked even if they result in rejecting subsequently arriving more important requests competing for the same resources In soft real time systems services are more con cerned with maximizing overall utility by serving the most important re quests first than guaranteeing reserved resources for individual requests Priority driven services can be categorized this way and are supported in real time kernels such as Mach Tokuda et al 1990 Under overload con ditions lower priority tasks are denied service in favor of more important tasks In the Rialto operating system Jones and Leach 1995 a resource planner attempts to dynamically maximize user perceived utility of the entire system In Abdelzaher et al 1997 a QoS renegotiation scheme
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165. ms PhD thesis Department of Computer Science Lund Institute of Technolgy Lund Sweden Integrated Systems 1996a AutoCode User s Guide Integrated Systems Inc 3260 Jay Street Santa Clara CA 95054 3309 USA Integrated Systems 1996b SystemBuild User s Guide Integrated Sys tems Inc 3260 Jay Street Santa Clara CA 95054 3309 USA J Consortium 1999 International J Consortium specification http www j consortium org Johannesson G 1994 Object oriented Process Automation with Satt Line Chartwell Bratt Ltd ISBN 0 86238 259 5 Jones M and P Leach 1995 Modular real time resource management in the Rialto operating system In Proceedings of the of the Fifth Workshop on Hot Topics in Operating Systems Kligerman E and A D Stoyenko 1986 Real Time Euclid A language for reliable real time systems IEEE Trans on Software Eng SE 12 9 pp 941 949 Koren G and D Shasha 1995 Skip over Algorithms and complexity for overloaded systems that allow skips In Proceedings of the IEEE Real Time Systems Symposium Kosugi N A Mitsuzawa and M Tokoro 1996 Importance based scheduling for predictable real time systems using MART In Proceed ings of the 4th Int Workshop on Parallel and Distributed Systems pp 95 100 IEEE Computer Society Kosugi N and S Moriai 1997 Dynamic scheduling for real time threads by period adjustment In Proceedings of the World Co
166. mulations more realistic the scheduler itself could also be modeled as a task that consumes CPU time This would also enhance the possibilities for the user to implement new scheduling strategies for control tasks 162 8 Acknowledgments 8 Acknowledgments This work was sponsored by the Swedish national board of technical de velopment NUTEK and by the Swedish network for real time research and education ARTES 9 References Abdelzaher T E Atkins and K Shin 1997 QoS negotiation in real time systems and its application to flight control In Proceedings of the IEEE Real Time Systems Symposium Ancilotti P G Buttazzo M D Natale and M Spuri 1998 Design and programming tools for time critical applications Real Time Systems 14 3 pp 251 269 Audsley N A Burns M Richardson and A Wellings 1994 STRESS A simulator for hard real time systems Software Practice and Experience 24 6 pp 543 564 Cervin A 1999 Improved scheduling of control tasks In Proceedings of the 11th Euromicro Conference on Real Time Systems pp 4 10 Liu J 1998 Continuous time and mixed signal simulation in Ptolemy II Technical Report UCB ERL Memorandum M98 74 Department of Electrical Engineering and Computer Science University of California Berkeley Ryu M S Hong and M Saksena 1997 Streamlining real time con troller design From performance specifications to end t
167. n AC k Feedback f k 1 Uk scheduler Figure 5 The feedback scheduler calculates new sampling frequencies to acco modate for changes in the execution times C or in the desired workload level time vector C k be time varying We want to design a control loop that adjusts the sampling frequencies so that the control performance cost is kept at the optimum see Figure 5 Let f k 1 f k AF R A k 1 A k AA R C k 1 C k AC R We assume that 4 gt 0 i e that the CPU constraint is active Linearization of Equation 5 around the optimum gives Ve t VppAf A AA C AC 0 c7 ACT f Af Uref If the quadratic delta terms are disregarded we get pe o la B m AAC CT OJ LAA LU CTf ACT Now the increments in f and are given as Ria T V AC aaj e 0 Urep CT f ACTF A solution exists if Vpr is positive or negative definite and C 4 0 Note that the matrix V is diagonal 6 av av Ver diag oF Thus there is a solution to Equation 6 if oF gt 0 Vi 1 133 Paper 4 A Feedback Scheduler for Real time Controller Tasks REMARK 1 It can be shown that this optimization routine corresponds to constrained Newton optimization see for example Gill et al 1981 EXAMPLE 2 A single CPU system is used to control three inverted pendulums of differ ent lengths Every pendulum is controlled by one controller Each control loop has an executi
168. n the input stream may lead to changes in the execution order of the processes and a new run time scenario is created Implementation of concurrent tasks and task communication re quires firm programming discipline Incorrect implementation of real time tasks may cause errors that are very difficult to trace Embedded systems must be efficient because the execution is con strained by deadlines that should not be missed Many large and complex systems need to be implemented using low level techniques in order to get the desired performance Many control applications are implemented in assembly language or low level languages such as Forth or C due to the requirements for fast execution and small program sizes Other common languages are Modula 2 or Ada which have built in support for concur rency They provide a higher abstraction level but will give larger and slower programs No matter which approach is used the implementation of real time controllers becomes time consuming and error prone The pop ular language C has no built in support for concurrency and the weak typing the pointer arithmetics and the memory management are constant sources to problems The more appealing object oriented language Java is currently emerging as an alternative not only for desktop applications but also for real time systems Usually there is a trade off between perfor mance and high abstraction levels the more support the language gives for structured
169. nctions which are called by the 72 2 The PALSJO System Periodic Synchronous timing spec N y Event Driven Figure 2 In order to execute the block diagram in a real time application more information needs to be added Such information could be which blocks that should be mapped to which processes timing constraints and what kind of connections synchronous or asynchronous Operator Communication User Task 1 User Task 2 Plant IO Figure 3 A schematic view of the P LSJ system There are a set of predefined modules managing operator communication for example Furthermore there is a set of user defined processes which is the actual controller process in order to execute the block Connections between blocks residing in the same process is synchronous while connections between different processes are asynchronous 73 Paper 1 A Tool for Interactive Development of Embedded Control Systems User Task 1 Inputs Calculate Outputs Update Parameters States Figure 4 A PAL block has a set of methods that are executed by the owner process 3 Configuring the System PAL blocks are instantiated and connected on line using PCL PCL is a simple language for administrating blocks and assigning variables While PAL is used to describe the algorithm of a block it cannot be used to specify how the block shall be executed All information that de fines real time behavior is ent
170. ne on mixed simulations of both process dynamics control tasks and the underlying real time kernel An exception is Liu 1998 where a single control task and a continuous plant was simulated within the Ptolemy II framework The simulator proposed in this paper is designed for simultaneous simulation of continuous plant dynamics real time tasks and network traffic in order to study the effects of the task interaction on the control performance 2 The Basic Idea The interaction between control tasks executing on the same CPU is usu ally neglected by the control engineer It is however the case that having a set of control tasks competing for the computing resources will lead to various amounts of delay and jitter for different tasks Figure 2 shows an example where three control tasks with the same execution times but different periods are scheduled using rate monotonic priorities In this case the schedule does not tell the whole story In the example the actual control delay the delay from reading the input signal until writing a new output signal for the low priority task varies from one to three times the execution time Intuitively this delay will affect the control performance 148 2 The Basic Idea Activation Graph T high medium low Figure 2 The activation graph for three control tasks with fixed prioritie
171. ngress on Systems Simulation pp 402 406 Kosugi N K Takashio and M Tokoro 1994 Modification and adjust ment of real time tasks with rate monotonic scheduling algorithm In Proceedings of the 2nd Workshop on Parallel and Distributed Systems pp 98 103 Kuo T W and A Mok 1991 Load adjustment in adaptive real time systems In Proceedings of the 12th IEEE Real Time Systems Symposium 65 Introduction Le Lann G 1996 The ariane flight 501 failure a case study in sys tem engineering for computing systems In Hand Out European Ed ucational Forum School on Embedded System European Educational Forum Lee C R Rajkumar and C Mercer 1996 Experiences with processor reservation and dynamic QoS in real time Mach In Proceedings of Multimedia Japan 96 Lewis R 1995 Programming industrial control systems using IEC 1131 3 The Institution of Electrical Engineers London U K Liu J 1998 Continuous time and mixed signal simulation in Ptolemy II Technical Report UCB ERL Memorandum M98 74 Department of Electrical Engineering and Computer Science University of California Berkeley Liu J K J Lin and S Natarajan 1987 Scheduling real time periodic jobs using imprecise results In Proceedings of the IEEE Real Time System Symposium pp 252 260 Liu J K J Lin W K Shih A Yu J Y Chung and W Zhao 1991 Algorithms for scheduling imprecise
172. nput signal to the pendulum system is the acceleration of joint 1 The model for the joint is a second order system where the input signal 7 is the applied torque and the output signal is the angle of the joint k FD 25 Introduction fo gd Figure 5 The pendulum on a cart The damping is denoted D The input to the pendulum model is the ac celeration of the pivot i e u which is given by D krt For the purpose of this experiment the damping was neglected and hence xRkt gt uxlkt The linearized model for the robot and the pendulum in the upright posi tion may now be written as 0 0 0 sl 0 Wo 0 0 0 kl o g x x T 0 0 0 1 0 0 0 0 0 k The Controller The controller is designed to swing up the pendulum and stabilize it in the upright position This is done using a hybrid controller consisting of three sub controllers one for swinging up the pendulum one for catching the pendulum and one for stabilizing the pendulum The switching logic for this hybrid controller is shown as a Grafcet in Figure 6 To swing up the pendulum an energy approach is used The idea is to control the energy of the pendulum and move it to its upward position The energy is calculated as ml E mg cos 0 1 l 26 4 The Robot Pendulum Y Stepl Off aa Step2 Swing Up
173. nsion parameter dimA and dimB respectively The dimension pa rameter dimA determines the size of the output signal out and dimB de termines the size of the input signal in The output signal from BlockA is connected to the input signal from BlockB A global dimension variable DIM is defined and it is is connected to the dimension variables in the blocks Finally a value is given to the dimension variable EXAMPLE 2 pel gt pcl gt s new Periodic pcl gt s BlockA new BlockTypeA pcl gt s BlockB new BlockTypeB pc1 gt s BlockA out gt s BlockB in pel gt dim DIM pcl gt s BlockA dimA DIM pcl gt s BlockB dimB DIM pcl gt DIM 5 pcl gt O When a dimension variable is changed all dimension parameters and all variables that in turn are connected to them are changed The change of variable sizes is synchronized throughout the whole system so that problems with incompatible variables are avoided show P lsj provides a text interface for entering PCL commands There is no built in facility for presenting data in graphical form Instead it is possible to export data to other programs via the network The command show is used to make data visible on the net The syntax is shown below pcl gt show lt block gt lt block gt lt signal gt Before the signal of a block can be exported the Periodic block that owns the block must be connected over the network to a plot or data log utility This is done by s
174. nt Contracts are suitable for expressing the demand and performance of a control algorithm The negotiator allo cates and distributes resources The top negotiator contains all platform and hardware specific information The run time system is responsible for checking and evaluating contracts It is assumed that there are underly ing mechanisms that support dynamic linking of block code in real time There are currently no FRIEND compiler available and it is most likely that the language will evolve during the implementation This paper only discusses the contract aspects of FRIEND The rest of the language is very similar to PAL and FRIEND may be viewed as PAL with contracts FRIEND is not intended as a general real time language but instead as a tool that will support the incorporation of adaptive behavior in embedded control systems 6 References Abdelzaher T E Atkins and K Shin 1997 QoS negotiation in real time systems and its application to flight control In Proceedings of 117 Paper 3 A Contract Based Language for Embedded Control Systems the IEEE Real Time Systems Symposium Andersson B 1999 Adaption of time sensitive tasks on shared mem ory multiprocessors A framework suggestion Master s thesis 777 Department of Computer Engineering Chalmers University of Tech nology Blomdell A 1997 PAL the P LSJ algorithm language Report ISRN LUTFD2 TFRT 7558 SE Departme
175. nt of Automatic Control Lund Institute of Technology Lund Sweden Branicky M S V S Borkar and S K Mitter 1998 A unified framework for hybrid control Model and optimal control theory IEEE Trans Automatic Control 43 1 p 31 Buschman F R Meunier P Rohnert H Sommerlad and M Stal 1996 A System of Patterns Pattern Oriented Software Architechture Wiley Chichester West Sussex Eker J 1997 A Framework for Dynamically Configurable Embedded Controllers Lic Tech thesis ISRN LUTFD2 TFRT 3218 SE Depart ment of Automatic Control Lund Institute of Technology Lund Swe den Helm R I M Holland and D Gangopadhyay 1990 Contracts Specifying Behavioral Compositions in Object Oriented Systems In Proceedings of the OOPSLA ECOOP 90 Conference on Object oriented Programming Systems Languages and Applications pp 169 180 Published as ACM SIGPLAN Notices volume 25 number 10 Jehuda J and D Berry 1995 A top layer design approach for adaptive real time software In IFAC Real Time Programming IFAC Fort Lauderdale Jones M B P J Leach R P Davis and J S Barerra III 1995 Mod ular real time resouce management in the rialto operationg system Technical Report MSR TR 95 16 Microsoft Research Advanced Tech nology Division Microsoft Corpration One Microsoft Way Redmond WA 98052 Krasner S M and D E Bernard 1997 Integrating autonomy technolo
176. ntrollers are minimized The result is a smaller accumulated loss and thus better control performance 158 6 Simulation Features saat Accumulated Loss 6 E cost 4 L normal 2 L improved 7 0 20 40 60 80 100 time Figure 12 The accumulated loss see Equation 1 for the low priority controller using normal and improved scheduling The cost is substantially reduced under the improved scheduling l y l Hn ia i i i i o 0 05 0 1 0 15 0 2 0 25 0 3 0 35 0 4 Figure 13 The activation graph when the improved scheduling strategy is used Note that the control delay for the low priority task is approximately the same as for the other tasks 6 Simulation Features Further features of the toolbox are the support for common real time prim itives like mutual exclusion locks events also known as condition vari ables and network communication blocks 159 Paper 5 A Matlab Toolbox for Real Time and Control Systems Co Design Locks and Events The control tasks do not only interact with each through the use of same CPU but also due to sharing other user defined resources The kernel allows the user to define monitors and events for implementing complex dependencies between the task The syntax and semantics of the mutex and event primitives are demonstrated by a small e
177. o determine the value to the system of running a given task at a given period In Buttazzo et al 1998 an elastic task model for periodic tasks is presented A task may change its period within certain bounds When this happens the periods of the other tasks are adjusted so that the overall system is kept schedulable An analogy with a linear spring is used where the utilization of a task is viewed as the length of a spring that has a given spring coefficient and length constraints The MART scheduling algorithm Kosugi et al 1994 Kosugi et al 1996 Kosugi and Moriai 1997 also supports task period adjustments MART has been extended to also handle task execution time adjustments The system handles changes both in the number of periodic tasks and in the task timing attributes Before accepting a change request the system analyzes the schedulability of all tasks If needed it adjusts the period and or execution time of the tasks to keep them schedulable with the rate monotonic algorithm Feedback scheduling An on line scheduler that dynamically adjusts task attributes can be viewed as a controller Important issues that must be decided are what 126 2 Integrated Control and Scheduling the right control signals measurement signals and set points are what the correct control structure should be and which process model that may be used So far very little has been done in the area of real time feedback scheduling A notable ex
178. o end timing constraints In Proceedings of the IEEE Real Time Technology and Applications Symposium Seto D J Lehoczky L Sha and K Shin 1996 On task schedulability in real time control systems In Proceedings of the IEEE Real Time Systems Symposium Stankovic J C Lu and S Son 1999 The case for feedback control real time scheduling In Proceedings of the 11th Euromicro Conference on Real Time Systems pp 11 20 Storch M F and J W S Liu 1996 DRTSS A simulation framework for complex real time systems In Proceedings of the 2nd IEEE Real Time Technology and Applications Symposium pp 160 169 163 Paper 5 A Matlab Toolbox for Real Time and Control Systems Co Design 164 Paper 6 Design and Implementation of a Hybrid Control Strategy Johan Eker and J rgen Malmborg Abstract A hybrid controller for set point changes is presented The strategy com bines a time optimal controller with a PID controller to achieve both good set point response and steady state behavior The control strategy is de signed and implemented both for a double tank lab process and a real life heating ventilation system Both simulations and experiments are pre sented 165 Paper 6 Design and Implementation of a Hybrid Control Strategy 166 1 Introduction 1 Introduction Traditionally there is a trade off in design objectives when choosing con troller parameters It is usually hard to achieve
179. oS i 1 and still keep the system schedulable The outline of the FRIEND code for this system is presented in Example 2 below EXAMPLE 2 contract C3 extends C1 negotiates dQoS real sampling interval gt dQos requires interface io SISO The contract C1 is extended with a new relation which specifies how the sampling interval affects dQoS which is the derivative of the QoS with respect to the sampling interval negotiator E implements io SISO fulfills myContract C1 QoS gt myBlocks QoS WCET 115 Paper 3 A Contract Based Language for Embedded Control Systems arbitrates myBlocks algorithm that fulfills C3 on resourceChange n length myBlocks calculate H myBlocks sampling interval H on new Blocks algorithm calculate H Blocks i sampling interval H Blocks i io io i schedule Blocks on delete Blocks algorithm Negotiator E implements an array of interfaces The actual size is de termined at run time and depends on available resources It accepts blocks that fulfill contracts of type C3 The main difference between block B and E is that the child blocks of E execute concurrently The task of block E is to distribute available computing resources It deter mines the sampling intervals for its child blocks through inspection of their contracts By using the relations between the sampling interval and the quality of servi
180. offers a wide set of advanced control techniques as well as powerful analysis tools and a user friendly graphical interface The PAL 44 6 Simulation of Embedded Control Systems compiler produces C code that fits both SIMART and the P LSJ run time system For an algorithm whose code has been validated in sim ulation no further compilation is needed for real time implementation This constitutes the main advantage of the proposed environment over the mentioned commercial packages SIMART SIMART is a general purpose CACSD package designed to support all lev els of controller development from design to implementation It contains a set of built in toolboxes such as LQG and GPC for design support Fur thermore it has tools for performance and robustness analysis such as Bode diagrams and sensitivity functions The user interface is graphical and menu driven SIMART has a range of predefined realistic nonlinear models for a number of processes In addition the user may enter lin ear model descriptions interactively SIMART is currently available on PCs for MS Windows and in an X 11 version for UNIX workstations and Linux PCs Operator Fie Identification Control Analysis Tools Windows PAL Regulator O Input Disturbance parameters O Output Disturbance sie im ro sem o Figure 12 PAL inside SIMART 45 Introduction start PAL coded controller PAL compiler A A i E C coded controller controll
181. ology Lund Sweden Blomdell A 1999 Linux in control http www control lth se Boussinot F and R de Simone 1991 The ESTEREL language In Proceedings of the IEEE vol 79 Buttazzo G G Lipari and L Abeni 1998 Elastic task model for adaptive rate control In Proceedings of the IEEE Real Time Systems Symposium Chung J Y J Liu and K J Lin 1990 Scheduling periodic jobs that allow imprecise results JEEE Trans on Computers 39 9 Dahl O 1990 SIM2DDC User s manual Report TFRT 7443 Depart ment of Automatic Control Lund Institute of Technology Lund Swe den 63 Introduction David R and H Alla 1992 Petri Nets and Grafcet Tools for modelling discrete events systems Prentice Hall Davis II J M Goel C Hylands B Kienhuis E A Lee J Liu X Liu L Muliadi S Neuendorffer J Reekie N Smyth J Tsay and Y Xiong 1999 Overview of the Ptolemy project Technical Report ERL Technical Report UCB ERL No M99 37 University of California Berkeley EECS CA USA 94720 Eker J 1997 A Framework for Dynamically Configurable Embedded Controllers Lic Tech thesis ISRN LUTFD2 TFRT 3218 SE Depart ment of Automatic Control Lund Institute of Technology Lund Swe den Elmqvist H 1973 SIMNON User s guide Technical Report TFRT 3106 Department of Automatic Control Lund Institute of Technology Lund Sweden Elmqvist
182. on the diagonal x x2 The full lines show the switching curves for the nonlinear system while the dashed lines show the linearized approximate switching curves Above the switching line the minimum control signal is applied and below it the maximum control signal is used It is not necessary to use the exact nonlinear switching curves since the time optimal controller is only used to bring the system close to the new set point When sufficiently close the PID controller takes over The heating ventilation system is a linear second order system with real poles and a time optimal controller for such a system is known to be of bang bang type The switching curves for the heating ventilation system were derived through simulation and a simple linear function was fitted to the simulated curves The approximate linear function is simply a function of the steady state coordinate Both the simulated switching curves and the linear approximations are shown in Figure 8 6 Simulations In this section some different switching methods are evaluated In all simulations a switching surface for the time optimal controller based on the linearized equations is used All simulations have been made in the Omola Omsim environment Andersson 1994 which supports hybrid systems 178 6 Simulations x2 Switch Curves for the Ventilation Process x1 Figure 8 The switching curves for the heating ventilation system The figure shows bo
183. on time C and a sampling frequency f Let the initial sampling frequencies be f One of the tasks operates in two modes with very different execution times The feedback scheduler adjusts the sam pling frequencies for the tasks so that the total control performance is optimized given the current execution times and the workload reference The workload reference is given by the admission controller Figure 6 shows some plots from a simulation where execution times sampling frequencies and load are plotted as functions of the iteration steps From the initial frequencies f 4 4 5 5 an optimal solution is found after 7 8 iterations At step 15 Task 2 sends a request to the admission controller for more execution time due to a forthcoming mode change The admission controller must first lower the workload reference before any task is allowed to increase its execution time in order to avoid overload At step 15 the request for more CPU time from Task 2 results in the workload reference changing from 1 to 0 7 At step 20 the actual workload is sufficiently near the reference and the admission controller grants the request from Task 2 which then immediately performs a mode change At the same time the admission controller changes the workload reference back to 1 The final frequencies are f 4 822 4 378 5 276 O An approximate version The feedback scheduling algorithm proposed above includes solving both Riccati and Lyapunov e
184. ontrol system designed in FRIEND The blocks C D F and G are control tasks and blocks A B and E are supervisors 3 Friendly Concepts Flexible control systems may in FRIEND be designed in a hierarchical fashion where the resources are distributed in a top down manner A block has one parent block and possibly several child blocks It requests resources from its parent blocks and distributes them among its child blocks Each block has one or more contracts with its parents block that it must fulfill This hierarchical structure is illustrated in Figure 2 The top level block A is assigned all available system resources and divides them between blocks B and E by inspection of their contracts Blocks B and C will then themselves distribute their alloted resources among their child blocks The contracts allow the parent blocks to reason about how resources are best distributed The blocks A B and E are negotiator blocks They allocate resources from their parent block and divide them among their child blocks In Figure 2 only the blocks at the bottom level are actual control tasks they are so called algorithm blocks All blocks have an interface which defines how the block communicates with the world i e the format of its input and output signals A block 107 Paper 3 A Contract Based Language for Embedded Control Systems may have none or several interfaces The blocks C and D in Figure 3 may communicate with each other or with
185. or th lt minTh and th gt maxTh transition from step3 to step4 when th gt minTh and th lt minTh transition from step4 to step1 when not on function sat max input real value input real real begin if value gt max then result max elsif value lt max then result max else result value end if end sat function sign r input real real begin if r lt 0 0 then result 1 0 33 Introduction else result 1 0 end if end sat procedure start begin on true end start procedure stop begin on false u 0 0 end stop end PendulumController end Pendel The PCL script The controller is configured by the PCL script in Example 2 A number of PAL modules are made available through the use statement Blocks are allocated using new statements The top level block is of type Periodic which is a system block designated for executing other blocks All blocks belonging to a Periodic block are periodically executed in sequence ac cording to the data flow The input and output signals of the blocks are connected using the gt operator Some signals are made available for export over the network using the show command Figure 11 shows the resulting block diagram The PCL language is presented in Appendix B EXAMPLE 2 use StandardBlocks use Robot use Gripper use Pendel s new Periodic with s gr new EndEffector gref new GripperR
186. orkload from the kernel This infor mation is then used to calculate how CPU resources should be allocated in an optimal fashion Let the number of tasks on the system be n and let each task execute with a sampling interval h task period and have the execution time C Each task is associated with a cost function J h which gives the con trol cost as a function of sampling interval h The following optimization problem may now be formulated minimize J gt Ji hi 1 i l subject to the constraint gt _ Ci hi lt Urer where U ef is the desired utilization level 4 Cost Functions In this section the LQ cost function and its derivatives with respect to the sampling interval are calculated These functions will be used in the feedback scheduler algorithm as described in Section 5 Let the system be given by the linear stochastic differential equation dx Axdt Budt dve 2 128 4 Cost Functions where A and B are matrices and v is a Wiener process with the incre mental covariance R dt The sampled system is then given by x kh h 9x kh Tu kh v kh where e T i e4SdsB and v kh is noise with the following property h Eu kh v kh Ri h eye dr 0 The cost function for the controller is chosen as x t SE f T 010 dt t Qie Q2 Q7 Qs f Note that only the cost in stationarity is regarded and that the cost is scaled by the time horizon i e the sampling interval
187. ost based on measurements 62 9 References 9 References Abdelzaher T E Atkins and K Shin 1997 QoS negotiation in real time systems and its application to flight control In Proceedings of the IEEE Real Time Systems Symposium Andersson M 1994 Object Oriented Modeling and Simulation of Hy brid Systems PhD thesis ISRN LUTFD2 TFRT 1043 SE Depart ment of Automatic Control Lund Institute of Technology Lund Swe den Armstrong J R Wirding and M Williams 1993 Concurrent Program ming in Erlang Prentice Hall Arz n K E B Bernhardsson J Eker A Cervin K Nilsson P Persson and L Sha 1999 Integrated control and scheduling Report ISRN LUTFD2 TFRT 7586 SE Department of Automatic Control Lund Institute of Technology Lund Sweden str m K J and K Furuta 1996 Swinging up a pendulum by energy control In IFAC 96 Preprints 13th World Congress of IFAC vol E pp 37 42 San Francisco California Audsley N A Burns M Richardson and A Wellings 1994 STRESS A simulator for hard real time systems Software Practice and Experience 24 6 pp 543 564 Benveniste A and G Berry 1991 The synchronous approach to reactive and real time systems In Proceedings of the IEEE vol 79 Blomdell A 1997 PAL the PALSJ6 algorithm language Report ISRN LUTFD2 TFRT 7558 SE Department of Automatic Control Lund Institute of Techn
188. put signals are calculated based on the values of the inputs the internals states and the parameters The top level concept of PAL is the module Several blocks may be grouped together in a module In Example 1 the block SimplePI is declared within the module MyBlocks The first section is the block interface which here consists of two input signals y and yref one output signal u and two parameters K and Ti The variable a is an indirect parameters i e a function of other parameters There are also two state variables e and I The algorithm section comes after the interface section The two methods calculate and update define the periodic algorithm of the block EXAMPLE 1 module MyBlocks block SimplePI y ref input real u output real I 0 0 e real K Ti parameter real h sampling interval a K h Ti calculate begin e ref y u i Kxe l end calculate update begin I I axe end update end SimplePI end MyBlocks O The calculate section is used to calculate output signals from input sig nals and the update section is used to update the internal states The algorithm is divided into two parts to minimize the sampling delay i e the delay from the reading of the input signal to the writing of the output signal and to enable the states to be correctly updated in case of signal limitations Eker 1997 Typically the control signal is sent to the plant after calculate is executed but before updat
189. quation 1 and the parameters are assigned heuristically The feedback scheduling in this case is very much simplified since the same cost functions are used independently of which mode the controller executes in A better approach would be to derive the cost function parameters analytically and have one cost function for each controller mode However in this example this simple approach works very well The desired utilization is set to 80 and actual utilization in simu lation is 79 3 Furthermore there are no missed deadlines The output from the system controlled by Controller 1 is shown in Figure 22 bot tom The feedback scheduler gives much better control performance for Controller 1 and slightly worse for Controllers 2 amp 3 The results for all three double tank systems from all three simula tions are presented in Table 1 Summary This simple example shows how the control performance may be improved by adjusting the sampling frequencies so that high CPU utilization is ob tained and at the same time few deadlines are missed This example also demonstrates the type of simulation that can be made with the real time kernel toolbox The double tank system is quite robust towards missed deadlines and if the simulations were made using a more time critical process the results would probably have been different A possible ex tension to the feedback scheduler would be to introduce performance ob servers that give the estimated c
190. quations on line This is expensive and a compu tationally cheaper algorithm is desirable From Figure 3 it seems that the cost functions could be approximated as quadratic functions of the sam pling interval h The relation between performance and sampling rates for LQG controllers was also discussed in str m 1963 where it was shown that the cost is indeed quadratic for small sampling intervals Let the approximative cost J h be defined as J h 0 Bh 134 5 A Feedback Scheduler Execution Times 0 1t l a EET ee ee eee ee eee 0 05 ES ey E A sl 0 i L L L L L 5 10 15 20 25 30 35 Sampling Frequencies 8 EF O E EEE E a pe o 4 Z pe Y 5 10 15 20 25 30 35 Load 1 1 T T T T T T tt 0 9 l J 0 8F J 0 7 1 1 ie 1 1 1 5 10 15 20 25 30 35 Cost 6000 T T T T r r 4000F RE i EA oe ie sie 34 RA i J 5 10 15 20 25 30 35 Figure 6 Plots from Example 2 The top plot shows how the execution time for task 2 doubles at step 20 The second plot from the top shows how the sampling rates are adjusted by the feedback scheduler Task 1 full Task 2 dash dotted Task 3 dashed The load plot shows how the workload reference dash dotted goes from 100 to 70 at step 15 and back to 100 at step 20 The full line is the actual workload The bottom plot shows the sum of the cost functions i e the optimization criterion By choosing a su
191. r 4 combined with standard rate monotonic scheduling would form such an solution In the following some non feedback and feedback scheduling solutions to the problem are described and evaluated by simulations It is shown that a more flexible scheduling approach can give better control performance The Set Up The number of double tank systems to control is assumed to be constant and equal to three The systems are identical except for the tank cross sections which are different for the different double tanks This causes the processes to have different time constants T 60 s Tz 45 s and Tg 30 s Setpoint changes for the levels of the lower tanks are assumed to occur with different frequencies for the different systems f 0 0067 s7 fo 0 0094 s71 and f3 0 0133 s The differences between the processes make the scheduling problem more interesting The control algorithm executes in either one of the modes Ref for setpoint changes Opt for optimal control or PID for PID control The setpoint change frequencies described above will cause each controller to spend about half of its time in the Opt mode and the other half in the PID mode The Ref mode is only active for a single sample at a time and only when a setpoint change has been detected by the controller In this example the behavior of the controller is typically the following It executes in the Ref mode for one sample then in the Opt mode for several samples th
192. r generates the reference value to the second Pl controller In order to handle actuator limitations cor rectly the integral states must be updated with care The PI controller in Example 2 has an extra output signal r2 The r2 signal is calculated in the update procedure and is used to propagate actuator limitations back wards against the data flow The input signal r is the desired reference signal and r2 is the reference signal modified with respect to actuator limitations This execution order of the blocks is illustrated in Figure 7 80 6 On Line Configurations 6 On Line Configurations PALSJO allows the block configuration to be edited without having to stop and restart the system This is managed by using two identical sets of blocks called running and shadow The running configuration is the set of blocks that are executing and the shadow configuration is used for editing All commands that deal with creating blocks moving blocks con necting blocks etc are executed on the shadow configuration When the edit session is completed the shadow configuration becomes the running configuration The values of all internal states are copied to the shadow configuration before it is switched in The new shadow configuration is now updated and turned into an identical copy of the current running configuration 7 Summary The PALSJO system consists of two main parts a compiler and a frame work The compiler translates PAL code into C
193. r is heated The output of the system is the air temperature T after the fan which blows the air into the classrooms The final temperatures in the classrooms are controlled with radiators on a separate control system While the double tank system was well known there was no model available for the heating ventilation system A system model was iden tified The identification data was logged running the system in manual control mode and then uploaded over a modem connection System iden tification data was collected by exciting the system with the input pro file sketched in Figure 6 The identification software used is described in Wall n 1999 The only measurable state of the system is the outlet air temperature During normal use the reference temperature varies be tween 17 and 22 degrees centigrade The goal of the experiment was to also be able to handle the start up phase from considerably lower tem peratures Therefore the transfer function was estimated at a much lower 173 Paper 6 Design and Implementation of a Hybrid Control Strategy valve 4 opening Figure 6 Input profile for the system identification The figure shows valve open ing in percent of full opening as a function of time temperature as well The actual modeling was done by fitting step responses of low order to match the input output data The identification data was separated into several sets each covering different working points In fact ther
194. real time kernel and the controller processes as an interconnected system it is possible to study how the interaction between the real time tasks influences the control performance A toolbox which supports simulation of such systems is pre sented in the thesis This more holistic view on embedded control systems enhances the possibilities for designing systems with predictable behavior 2 Outline and Summary of Contributions The thesis consists of this introduction and six papers Below the contents and major contributions of each paper are summarized References to related publications are also given Paper 1 and Paper 2 The PALSJO environment for embedded control systems is presented in two papers Eker J A Tool for Interactive Development of Embedded Control Sys tems In Proceedings of the 14th IFAC World Congress 1999 Beijing China Eker J and A Blomdell A Flexible Interactive Environment for Em bedded Controllers To appear in Control Engineering Practice Contributions Design and implementation of a software environment for dynamically configurable embedded systems and design of the controller description language PAL Related publications Tona P J Eker and M M Saad PALSIMART A New Framework for Computer Aided Rapid Prototyping of Advanced Control Systems 12 2 Outline and Summary of Contributions In Proceedings of the European Control Conference 1999 Karlsruhe Germany
195. rem and a more detailed description of the strategy see Malmborg 1998 The case where several Lyapunov functions achieve the minimum is discussed in Malmborg 1998 Lyapunov function modifications From a control designer s point of view the design of a hybrid control scheme using the min switching strategy can be reduced to separate de signs of n different control laws and their corresponding Lyapunov func tions To improve performance it is often convenient to change the location of the switching surfaces This can to some degree be achieved by differ ent transformations of the Lyapunov functions One example is transfor mations of the form V g V where g are monotonously increasing functions In some cases there can be very fast switching known as chattering between two or more controllers having the same value of their respective Lyapunov function The hybrid controller is still stabilizing but it may not lead to the desired behavior in a practical implementation One way to avoid chattering is to add a constant A to the Lyapunov functions that are switched out and subtract A from the Lyapunov functions that are switched in This works as a hysteresis function For two controllers with Lyapunov functions V and Va the equations are V V A and V2 Va if controller two is in use and V V and V V A if controller one is controlling the process This guarantees that a controller is used for a time period gt
196. replace an old block Does it for example have the desired interface towards other blocks 18 3 Implementation of Control Systems A C D F G Figure 1 The hierarchical structure of a real time control system designed in FRIEND Resources are distributed from the top down The parent blocks control the execution of its child blocks e If a new block executes correctly The contract may contain ways to verify the functionality of a block Blocks are organized in a hierarchical fashion as shown in Figure 1 There are two block types in FRIEND algorithm and negotiator blocks An algo rithm is an input output block that calculates new output signals based on the values of the inputs signals the internal states and the parame ters A negotiator is a block that allocates resources and distributes them among its child blocks The negotiator is a sort of resource broker The interface specifies how a block interacts with other blocks The interface is useful for on line decisions about whether or not a new block can replace an old block Figure 2 shows an example of a FRIEND block diagram At at the top level it consists of three blocks Block B has three child blocks inside block D E and F These blocks may either execute concurrently or exclusively depending on the application If yet another block should be added to B it is necessary th
197. ret_s Lo Level 29 12_3 u u Fast Computer y Slow Computer y y2 y2 Double Tank 3 Double Tank 3 oz 1 Her m P xP lt 1 Show Results Show Results Show Results Setpoint 1 Plot Tank 1 Plot Tank 2 Plot Tank 3 oca pat Tipe rere 3 x bl 2 Setpoint 2 122 s mm Or f 3 rera T2 3 gt Ri 7 Ga Setpoint 3 D A Figure 19 A screen shot of the Simulink model of the control system To the left the tanks are controlled by a fast ideal computer To the right the tanks are controlled by a slow real computer The behavior of the left system is used as a reference when evaluating the performance of the right system cution times for this hybrid controller is found in Persson 1998 Simulation The toolbox described in Paper 5 is used to evaluate different scheduling strategies The hybrid control algorithm is very easily rewritten into a MATLAB function states exectime hybridController flag states params which is the control algorithm format prescribed by the toolbox The func tion is executed periodically during simulation It returns the new con troller states including the controller mode and the simulated execution time of the algorithm To isolate the effects of scheduling on control performance two com plete control systems are simulated in parallel see the screen shot shown in Figure 19 To the left the three double tanks are controlled by an ideal very fast
198. riod and the input output latency A heuristic iterative algorithm is proposed for the optimization of these parameters subject to schedulability constraints The algorithm is based on using the period calibration method Gerber et al 1995 for determining the task attributes The tasks are scheduled using EDF and a cyclic executive is used for run time dispatching On line Task Attribute Adjustments A key issue in any system that allows dynamic feedback between the control algorithms and the on line scheduler is the ability to dynamically adjust task parameters Reasons for the adjustments could for example be to improve the performance in overload situations and to dynamically optimize control performance Examples of task parameters that could be modified are periods and deadlines One could also allow the maximum allowed worst case execution time for a task to be adjusted In order for this to be realistic the controllers must support dynamically changing 39 Introduction execution times Changes in the task period and in the execution time both have the effect of changing the utilization that the task requires Quality of service resource allocation Much of the work on dynamic task adaptation during recent years is mo tivated by the requirements of multimedia applications Activities such as voice sampling image acquisition sound generation data compres sion and video playing are performed periodically but with less rigid ti
199. rocess The second process is a heating ventilation system in a public school in Klippan Sweden The process see Figure 5 is a combined heating and ventilation system where pre heated air is blown into the classrooms The control problem here is to design a controller that has both the desired steady state behavior and transient behavior The participating company was interested in new ways of improving start up and reference change performances Specifically the control problem is that they want to have two different settings for the ventilation air temperature one during the day and one during the night Another related problem is that when the system has been shut down for some reason it is necessary to start from considerably lower temperatures The air is heated in a heat exchanger and the incom ing air has outdoor temperature which can be very low in Sweden during 172 4 The Processes Figure 5 The control valve for the heating ventilation system the winter The variation in outdoor temperature will cause considerable variation in the process parameters The existing PID controller was tuned very conservatively to be able to handle these cold starts without too large overshoots This was exactly the problem type that the fast set point hybrid controller previously discussed was designed for The control signal u is the set point for the opening of the valve Hot water flows through the valve to a heat exchanger and the ai
200. ry a lot and this makes the scheduling difficult The Problem How should the tasks be scheduled in order to get the best performance from the system If the computing resources were unlimited the con trollers could be designed to execute at very high rates and with very good control performance But with limited computing resources the con trollers must execute at much lower rates in order to avoid overload When the utilization of the CPU is close to 100 percent the interaction between the control tasks also becomes noticeable Preemption and blocking causes jitter and delays and the control performance deteriorates even further 55 Introduction During a transient overload some controllers might shut down completely depending on the scheduling policy used The general problem is extremely complicated because of the different modes that the hybrid controllers might switch between A hypothetical optimal solution would continuously redistribute the computing resources between the tasks depending on the current and possible future combi nations of the controller states the controller modes and the execution history Even if the optimal solution was obtainable it would never be implementable in a system with limited computing power Instead one should aim for a simple heuristic solution that can be applied on line and without too much detailed knowledge about the system An approximate version of the feedback scheduler from Pape
201. s The possibility to adjust the allowed maximum execution time for a task necessitates an approach for handling tasks with imprecise execution times particularly the case when the tasks can be described as any time algorithms i e algorithms that always generate a result but where the quality of the result the QoS level increases with the execution time of the algorithm The group of Liu has worked on scheduling of imprecise calculations for a long time Liu et al 1987 Chung et al 1990 Liu et al 1994 In Liu et al 1991 imprecise calculation methods are categorized into milestone methods sieve function methods and multiple version methods Milestone methods use monotone algorithms that gradually refine the re sult and each intermediate result can be returned as an imprecise result Sieve function methods can skip certain computation steps to tradeoff computation quality for time Multiple version methods have different implementations with different cost and precision for a task Examples of all three types of imprecise algorithms can be found in control Algorithms that are based on on line numerical solution to an optimization problem every sample can be viewed as milestone or any time methods The result generated from the control algorithm is grad ually refined for each iteration in the optimization up to a certain bound Examples of this type of control algorithms are found in model predictive control It is a
202. s high medium low running in a pre emptive kernel The execution times are the same for all three processes F i Read sample Write control ds u 4 AE N 4 oe Activation graph 4 A A lo y ly y Figure 3 This is how the low priority task from Figure 2 interacts with its plant u is the control signal y is the measurement signal but how much and how can we investigate this To study how the execution of tasks affects the control performance we must simulate the whole system i e both the continuous dynamics of the controlled plant and the execution of the controllers in the CPU 149 Paper 5 A Matlab Toolbox for Real Time and Control Systems Co Design Kernel Model Control Controller 1 E Controller 2 Controller 3 Blocked e Plant 3 gt gt Plant 1 A Plant 2 Figure 4 Schematic view of the simulation setup The controllers are tasks ex ecuting in a simulated pre emptive kernel The controllers and the control signals are discrete while the plant dynamics and the plant output are continuous The continuous signals from the plants are sampled by the control tasks Process Outputs We need not simulate the execution of the controller code on instruction level In fact it is enough to model the timely aspects of the code that are of relevance to other tasks and to
203. s must be stopped before exiting pc1 gt quit use User defined PAL modules are not by default visible to the run time shell They must be imported to make the block types in the modules visible To import a module the use command is used The syntax is pcl gt use lt module name gt After this command has been issued all blocks in the module are visible to the run time shell and may be accessed by the user When there exists several blocks with the same name but in different modules these mod ules may not be in use at the same time A solution to this problem is to use the module name when instantiating the block as shown below s control new MyBlocks PI enduse When a PAL module is no longer needed it is possible to remove it from the list of available modules This is done using the command enduse as shown below pcl gt enduse lt module name gt dim Complex variables such as string arrays polynomials and matrices may in PAL be created with dynamical sizes The sizes of block variables such as arrays etc may be linked to a dimension parameter Several variables in the same block can be linked to the same dimension parameter Dimen sion variables in different blocks can be connected via global dimension variables in the workspace which are defined as follows pcl gt dim A 205 Appendix B PCL P lsj Configuration Language In Example 2 there are two blocks BlockA and BlockB which both have a dime
204. simulation The real time systems engineer is given a control algorithm to implement and configures the real time system by assigning priorities deadlines etc The real time systems engineer usually regards control systems as hard real time systems i e deadlines should never be missed The control engineer on the other hand expects the computing platform to be predic tive and support equidistant sampling In reality none of the assumptions are necessarily true This is even more obvious in the case where several control loops are running on the same hardware unit The controllers will interact with each other since they are sharing resources such as CPU network analog digital converters etc see Figure 1 A new interdisciplinary approach is currently emerging where control and real time issues are discussed at all design levels One of the first pa pers that dealt with co design of control and real time systems was Seto et al 1996 where the sampling rates for a set of controllers sharing the same CPU are calculated using standard control performance met rics Control and scheduling co design is also found in Ryu et al 1997 where the control performance is specified in terms of steady state error overshoot rise time and settling time These performance parameters are expressed as functions of the sampling period and the input output 147 Paper 5 A Matlab Toolbox for Real Time and Control Systems Co Design latency A heuris
205. sis is based upon a vision of a dynamic flexible and interactive integrated control and scheduling environment with the following features 37 Introduction The control design methodology should take the availability of com puting resources into account e The requirement of known worst case execution times should be re laxed Instead the system should be able to guarantee stability and a certain level of control performance based only on knowledge of nominal execution times e The system should be able to adapt task parameters in overload situations in such a way that stability and an acceptable level of control performance are maintained e The system should be able to dynamically trade off control perfor mance and computing resource utilization e The system should support on line information exchange between the on line scheduler and the control tasks The information could for example consist of mode change requests from the control tasks execution time allotments from the on line scheduler etc e The system should be able to measure the actual execution time spent by the different tasks and take appropriate actions in case of over runs e The system should admit on line experiments Controller code should be allowed to be added tested and replaced on a running system un der safe condition as suggested in Seto et al 1998a In order to make the above visions possible a lot of information needs to be provided Th
206. stead it is much more time consuming and sometimes even dangerous The control engineer may add new types of blocks to Simulink and use them later for code generation but must write them C In P LSJ algorithms are written in PAL which offers strong typing high level data types and well defined real time semantics It is easy to translate PAL code to MATLAB S functions for use in simulation To go in the other direction is much more complicated since PAL is more strongly typed than MATLAB The code generated from Simulink and SystemBuild is static It is not possible to replace blocks or components at run time The whole system must be recompiled with each change The P LSJ environment has a much higher level of interactivity It allows system reconfiguration and updates without having to restart the system This offers the potential of replacing algorithms while the system is operating The authors believe that an interactive development environment enhances the development process and speeds up controller implementation substantially Updating control software is a related issue The software in embedded systems needs to be upgraded periodically Since the cost for shutting down a manufacturing cell is high upgrading the control algorithms might not be feasible even if it would give better performance and cost reduction There is a definite need of embedded control system software that allows on line updates and reconfigurations It should
207. system Scheduling Three different scheduling approaches are compared worst case schedul ing average case scheduling and feedback scheduling All approaches are based on rate monotonic scheduling 58 8 A Unifying Example Worst Case Scheduling Worst case scheduling is probably the most common scheduling approach in real time control systems today Tasks are assigned periods off line and schedulability analysis is carried out assuming worst case conditions during execution In our case the worst case condition occurs when all controllers happen to execute in the Ref mode at the same time It is however unnecessarily pessimistic to use the worst case execution time of Cree 1800 ms in the scheduling analysis We know that in our example the controller only spends a single sample in the Ref mode and then switches to the Opt mode in the next sample Average Case Scheduling The drawback with worst case scheduling is that the average resource utilization becomes low with poor control performance as a result An alternative would be to use average case scheduling where tasks are as signed periods to give a higher average utilization of the CPU Of course tasks may now miss their deadlines If rate monotonic scheduling is the underlying scheduling principle the lower priority tasks may miss a lot of deadlines while the higher priority tasks do not need to miss a single deadline This unfair distribution of computing resources
208. t to parameter special care must be taken In P LSJ a special process the Parameter Server process is used to handle this is possible to define parameters as functions of other parameters When the output signals of the source block change the parameters in the target blocks must be updated However before the new parameters can be used by the target block all indirect parameters must be calculated This may be a time consuming operation and cannot be performed by the block itself since the extra computation time could cause deadlines to be missed In PALSJO when a parameter receives a new value from an output signal it sends a request to the parameter server which then becomes responsible for calculating the indirect parameters see Fig 7 The param eter server runs at a lower priority than the Periodic Sporadic tasks and signals going via the parameter server will be delayed This is usu ally not a problem since this type of connection is designed for adaptive systems where the adaptation loop is allowed to be much slower than the feedback loop see str m and Wittenmark 1995 The third type of connection is dimension to dimension The dimen sion parameters of one or more PAL blocks may be connected to a global dimension variable When the global dimension variable changes all local 97 Paper 2 A Flexible Interactive Environment for Embedded Controllers PID PID 1 a E
209. teger of real d output array 0 n of real 1 output matrix 0 n 0 n of real phi array 0 n of real lambda input real i j integer e w real begin d 0 lambda e phi 0 for i 1tondo e e theta i phili w philil for j i 1 to n do w w phily l i j end for 1 0 i 0 0 l i 0 w end for for i n downto 1 do RowAsRealArray l 0 tmp1 RowAskRealArray l i tmp2 DyadicReduction tmpl1 tmp2 d 0 di 0 7 n Real ArrayAsRow tmpl 0 1 Real ArrayAsRow tmp2 i 1 end for for i 1 to n do thetal i thetali L 0 i e d i d i lambda end for end LDFilter The variables tmp1 and tmp2 are global variables declared in the block scope The value of the integer variable n is dynamically bound to the size of the input vector theta O A function is a subprogram which consists of a sequence of statements A value is returned after finishing execution The head defines the name of 195 Appendix A PAL P lsj Algorithm Language the function the interface used for calling the function and the type of the return data Parameters are passed as inputs or outputs in the same fashion as for procedures The return value is stored in the predefined variable result function Limiter max real min real value real real begin if value lt min then result min elsif value gt max then result max else result
210. th the actual simulated switching curves dashed and the approximate linear ones full The Double Tank System A natural simple switching strategy would be to pick the best parts from both PID control and time optimal control One way to accomplish this is to use the time optimal controller when far away from the equilibrium point and the PID controller when coming closer As a measure of closeness the function V lose is used R T R Xi X1 Xi X1 Velos P 0 gt i Fa l Ma where nie cos 9 ysin 98 1 y sin 0 cos 0 g Pan sin 9 y cos 6 The switching strategy here is to start with the time optimal controller and then switch to the PID controller when V jose lt p The size and shape of the catching region may be changed with the y and 0 parameters The P matrix above gives ellipsoidal catching curves In this simulation switching back to the time optimal controller is not allowed until there is a new reference value See Figure 3 for a graphical description of the algorithm The simulation results in Figure 9 show how the best parts from the sub controllers are combined to give very good performance In this second simulation set the min switching strategy that guaran tees stability for the linearized system is used The two Lyapunov func 179 Paper 6 Design and Implementation of a Hybrid Control Strategy R X2 Xa X 0 2 0 2 0 15 4 F 0 15 4 E 0 1 Ve Ne 0 1 L 0 05
211. the desired step change response and at the same time get the wanted steady state behavior An example of contradictory design criteria is tuning a PID controller to achieve both fast response to set point changes fast disturbance rejec tion and no or little overshoot In process control it is common practice to use PI control for steady state regulation and to use manual control for large set point changes Figure 1 shows a system that is controlled left by a PID controller and right with manual control combined with a PID controller The simulations show a step response at time zero and a load disturbance rejection at time 80 This paper describes a hybrid control structure which combines a steady state PID controller with a minimum time controller for the set point changes Both good response to set point changes and good disturbance rejection are achieved jo Mb A aa I T 1 y T 1 0 50 100 150 0 50 100 150 0 T T 1 0 T T 1 0 50 100 150 0 50 100 150 0 5 Figure 1 In the design of a PID control system there is often a choice between a fast controller giving a large overshoot or a slow controller without overshoot In the left figure this is illustrated by two examples of PID control The right figure shows a PID controller combined with manual control The top figures shows the set point ysp and the measured variable y The bottom figures shows the control signal u Design and implementation of such a hybri
212. the stability of the closed loop 79 Paper 1 A Tool for Interactive Development of Embedded Control Systems Calculate 1 2 3 4 5 6 7 D Reference E v Po Limiter gt AnalogOut e AnalogIn AnalogIn Update 7 6 5 4 3 2 1 Figure 7 First the calculate method is executed for each block starting with block number one Then the update method is executed for each block in the reverse order system depends on the time it takes for a process measurement to show up in the actuator signals to the process If there are multiple blocks between the input and output special care has to be taken to ensure that no unnecessary delays are introduced due to improper ordering of calculations The algorithm for the PI controller in Example 2 is divided into two parts one for calculating the output signal and one for updating the in tegral state It is important to finish the calculation of the new control signal as fast as possible in order to minimize the sampling delay The update of the internal state is on the other hand allowed to be more time consuming It can be shown that by treating a control block as two sep arate blocks calculate and update and scheduling them separately the control performance is improved see Cervin 1999 Handling Limiters Consider the implementation of a cascade PI controller Two PI blocks are connected in series The first PI controlle
213. the switching rules are implemented using automata all transitions must be altered If instead each controller is associated with a contract describing how well the controller operates at a certain point in the state space the task of the supervisor would be to evaluate the contracts and select the best suited controller If a new controller is added on line its contract is sim ply handed to the supervisor which may now include it in the selection process The contract approach to switching rules is well suited for in 108 4 The FRIEND Language a 197 F b bo E R R EN R R R Figure 4 The switching rules for a hybrid controller are expressed as sectors in the states space To the left the state space is divided between two controllers Ry Ra and to the right two more sub controllers have been added cremental changes Figure 4 b shows how the state space is partitioned after two more sub controllers are added System Resources The only block in the hierarchy in Figure 2 that has any hardware specific information is block A All the other blocks see the world through the eyes of block A This means that it may be possible to write controller code that is parameterized in terms of the hardware Instead of giving the execution times directly in seconds a more measure could be used The task scheduling and resource allocation of the underlying real time kernel are hidden from the user through the specifications of
214. the world but then only through the interface of block B The interface of B may be viewed as the gateway to the rest of the system for the blocks in B In Figure 3 block B is assigned some Analog IO and network ports and may divide them among its child blocks The two child blocks of B can be either algorithm or negotiator blocks depending what type of controller block B is implementing All Available All AnaloglO ports System Resources All Network ports Ex CPU Network bandwidth TAE Signals A g ae aor B A Some AnaloglO ports m Some Network ports Some CPU Share Some Network Bandwidth C D Figure 3 The resources of the system are distributed in a top down fashion The top block A contains all hardware specific information An Example Consider a second order system controlled by a hybrid controller with two sub controllers Which sub controller to use depends on the current position in the state space Figure 4 a shows how the state space is par titioned into two sectors each corresponding to a controller mode R or Ry Assume that the controller is doing well in the first and the third quadrants but not so well in the second and fourth The control engineer wants to improve the performance by adding two more controllers one for the second quadrant and one for the fourth How can this refinement pro cess be made as simple and straightforward as possible If
215. tic iterative algorithm is proposed for the optimization of these parameters subject to schedulability constraints Good interaction between control theory and real time systems theory opens up for a unified approach and more integrated algorithms Schedul ing parameters could for example be adjusted automatically on line by a kernel supervisor Such a setup would allow much more flexible real time control systems than those available today Ideas on adaption of schedul ing parameters are for example found in Abdelzaher et al 1997 and Stankovic et al 1999 The development of algorithms for co design of control and real time systems requires new theory and new tools This paper presents a novel simulation environment for co design of control systems and real time sys tems within the Matlab Simulink environment The advantages of using Matlab for this purpose are many Matlab Simulink is commonly used by control engineers to model physical plants to design control systems and to evaluate their performance by simulations A missing piece in the sim ulations however has been the actual execution of the controllers when implemented as tasks in a real time system On the other hand most of the existing tools for task simulations for instance STRESS Audsley et al 1994 DRTSS Storch and Liu 1996 and the simulator in Ancilotti et al 1998 give no support for the simulation of continuous dynamics Not much work has previously been do
216. tion of PAL blocks at run time The inheritance structure is known as the composite pattern Gamma et al 1995 Using Container blocks the system supports a hierarchical structure A block derived from Algorithm must have a Container block as a parent in order to be executed Creating Blocks and Signals In PALSJO blocks and data types are loosely coupled to the rest of the framework through the use of an abstract factory pattern see Gamma 92 3 The PALSJO framework PID Analog Filter gt Switch Analog In Out Le LOG Figure 3 The block diagram created by the PCL commands in Example 3 et al 1995 The run time system calls the block factory upon initializa tion and registers each available block type by giving a name tag and a constructor function The block factory keeps a table over all registered block types When a client wants to create a new block it simply calls the block factory It is possible to register new block types and delete old ones during execution Hence it is possible to extend the system with out shutting it down A similar factory is also used for dealing with data types Block Execution While PAL is used to describe the algorithm of a block it cannot be used to specify how the block shall be executed All information that defines real time behavior is entered during run time using the PALSJO Configuration L
217. tomatic Control Lund Ramanathan P 1997 Graceful degradation in real time control appli cation using m k firm guarantee In Proceedings of the IEEE Real Time Systems Symposium RealTimelnnovations 1995 ControlShell Object Oriented Framework fro Real Time System Software Real Time Innovations Inc 155A Moffet Park Drive Suite 111 Sunnyvale CA 94089 USA Ryu M and S Hong 1998 Toward automatic synthesis of schedulable real time controllers Integrated Computer Aided Engineering 5 3 pp 261 277 Ryu M S Hong and M Saksena 1997 Streamlining real time con troller design From performance specifications to end to end timing constraints In Proceedings of the IKEE Real Time Technology and Applications Symposium Seto D B Krogh L Sha and A Chutinan 1998a Dynamic control system upgrade using the Simplex architecture IEEE Control Sys tems August Seto D J Lehoczky and L Sha 1998b Task period selection and schedulability in real time systems In Proceedings of the IEEE Real Time Systems Symposium Seto D J Lehoczky L Sha and K Shin 1996 On task schedulability in real time control systems In Proceedings of the IEEE Real Time Systems Symposium Sha L 1998 Dependable system upgrade In Proceedings of IEEE Real Time Systems Symposium Sha L R Rajkumar and J Lehoczky 1989 Mode change protocols for priority driven pre e
218. tting the desired utilization to 80 Results The choice of sampling intervals for control loops is a research area in it self In this case the choice of sampling intervals can be motivated by the process dynamics and the setpoint change frequencies The fastest pro cess with the most frequent setpoint changes obviously requires the most frequent actions from its controller The sampling intervals are chosen so that the ratio h T is the same for all tree tanks The whole system i e the three control tasks the kernel and the three double tank systems was simulated for 1500 seconds using three different scheduling approaches Rate monotonic priority assignments were used in all cases Table 1 also presents some results from the simulations Worst Case Scheduling In the worst case scheduling scenario the sampling intervals are chosen so that no deadlines are missed The sampling intervals are through sim ulation found to be h 7 s ha 4 9 s and h3 3 5 s These are the shortest sampling intervals that will not cause missed deadlines The uti lization will however be very poor and is in the simulation found to be only 33 1 The slow sampling rates result in poor performance for all three controllers The output of the system controlled by Controller 1 is shown in Figure 22 top 60 8 A Unifying Example 0 25 Figure 22 The output from the tank controlled by the controller with lowest priority for the
219. ublications The nonlinear observer used in the robot and pendulum example later in this introduction is presented in Eker J and K J str m A Nonlinear Observer for the Inverted Pendu lum In Proceedings of the IEEE Conference on Control Applications 1996 Dearborn Michigan The work on a feedback scheduler for a set of double tank processes pre sented in Section 8 will appear in Cervin A J Eker and L Sha Improving Control Performance by Feed back Scheduling Manuscript in preparation Chapter Outline The P LSJ environment and the PAL language are introduced in Sec tion 3 The continuation of this work the proposed FRIEND language is discussed in the same section The use of PALSJO PAL is demonstrated by an example in Section 4 A brief overview of the state of the art in integrated control and scheduling is given in Section 5 The presenta tion is based on rz n et al 1999 Section 6 discusses tools for sim ulation of embedded controllers The PALSIMART environment and a MATLAB Simulink toolbox are presented Section 7 discusses the imple mentation of the controller from Paper 6 Finally in Section 8 a unifying example is given where tools and ideas from the different papers are com bined 3 Implementation of Control Systems Many real time control systems are components embedded in a larger en gineering system They are often implemented on small microcontroller systems Examples of em
220. uling delays have on the stability and performance of the plant under control From a historical perspective the separate development of control and scheduling theories for computer based control systems has produced many useful results and served its purpose 36 5 Feedback Scheduling However upon closer inspection it is quite clear that neither of the three above assumptions need necessarily to be true Many control algo rithms are not periodic or they may switch between a number of different fixed sampling periods Control algorithm deadlines are not always hard On the contrary many controllers are quite robust towards variations in sampling period and response time It is also in many cases possible to compensate on line for the variations by e g recomputing the controller parameters It is also possible to consider control systems that are able to do a trade off between the available computation time i e how long time the controller may spend calculating the new control signal and the control loop performance By integrating control design and scheduling it is possible to go beyond the simple fixed sample period and known WCET model and to develop theory that also addresses the dynamic interaction between control and scheduling The optimality of computer control is subject to the limitations of available computing resources especially in advanced applications with fast plant dynamics and sophisticated state estimation and
221. unnyvale CA 94089 USA Seto D B H Krogh L Sha and A Chutinan 1998 Dynamic con trol system upgrade using the simplex architechture IEEE Control Systems 18 4 pp 72 80 101 Paper 2 A Flexible Interactive Environment for Embedded Controllers 102 Paper 3 A Contract Based Language for Embedded Control Systems Johan Eker and Anders Blomdell Abstract The paper presents a new proposed block oriented language called Friend designed for the implementation of flexible and adaptive embedded con trol systems Requirements on a controller block and its performance as a function of available resources are specified using contracts A Friend con trol system is arranged in a hierarchical structure where a parent block is responsible for distributing resources to its child blocks The use of contracts simplifies the design and implementation of embedded systems that can adapt to altered operating conditions The contracts allow the sys tem to negotiate about resources and redistribute them when necessary Friend addresses the implementation of systems with adjustable quality of service levels and the implementation of hybrid controllers Friend is illustrated in the paper by two examples 103 Paper 3 A Contract Based Language for Embedded Control Systems 104 1 Introduction 1 Introduction Embedded control systems of today are generally not very flexible They are often designed in an ad hoc fashion and th
222. urements at the school showed that the process variations were not significant and the variation in steady state gain could be estimated from input output data before or during a set point change A fairly crude model of the system together with approximative switch ing curves gave significant improvements for set point changes The speed was doubled without large overshoots At this first test no attempts were made to smooth the control signal The extra min max switches could have been avoided with a hysteresis function 10 References Andersson M 1994 Object Oriented Modeling and Simulation of Hy brid Systems PhD thesis ISRN LUTFD2 TFRT 1043 SE Depart ment of Automatic Control Lund Institute of Technology Lund Swe den Antsaklis P J W Kohn A Nerode and S Sastry Eds 1998 Hybrid Systems V Springer Verlag 186 10 References Antsaklis P J and A Nerode 1998 Hybrid control systems An introductory discussion to the special issue IEEE Trans Automatic Control 43 4 p 497 Blomdell A 1997 PAL the PALSJ6 algorithm language Report ISRN LUTFD2 TFRT 7558 SE Department of Automatic Control Lund Institute of Technology Lund Sweden Branicky M 1995 Studies in Hybrid Systems Modeling Analysis and Control PhD thesis LIDS Massachusetts Institute of Technology Branicky M S V S Borkar and S K Mitter 1998 A unified framework for hybrid control
223. uts signals Output signals Figure 1 An adaptive real time systems is formed by introducing a feedback loop between the real time kernel and the tasks distributes system resources among the controllers based on informa tion given by the controllers The inputs to the feedback scheduler from the control tasks are for example performance measurements which in dicate how well the tasks are working and resource requirements for example CPU utilization The output signals from the scheduler are the sampling frequencies of the control loops By adjusting the sampling rates the feedback scheduler can protect the system from overload An example of a feedback scheduler is found in Stankovic et al 1999 A related language is FLEX see Natarajan and Lin 1988 which supports the implementation of flexible real time systems by introducing imprecise computations and constraint blocks The body of a constraint block is executed only if the constraint is fulfilled otherwise an excep tion is raised A constraint may specify resource or timing requirements FLEX allows the user to specify imprecise computations within a con straint block and the run time system then decides on a suitable precision level that will not violate the constraint There are several existing software systems that are adaptive in one way or another For example RTPOOL Abdelzaher et al 1997 allows the real time processes to negotiate about system resources Qual
224. value end if end Limiter A PAL block may have a set of events that it responds to An event itself is a text string When a block receives an event it executes the proce dure with the same if there is any All procedures in PAL are registered as events when executed in the P LSJ run time environment Let for example the procedure Reset be defined in the block RST procedure Reset i integer begin for i 0 to m do Uli 0 0 Y 1 0 0 Uc i 0 0 end for end Reset The Reset procedure may then be called from the PCL command line by the following command pcl gt process block new RST pcl gt process block Reset There are two predefined block procedures calculate and update They are used to implement periodic algorithms The calculate procedure cal culates an output signal while update updates the state variables The reason for dividing the algorithm like this is discussed in detail in Eker 1997 196 8 Procedures Functions and Events Control Signals Controller Vi L2 A Sensor Information GA Eu v2 A Process Control Signal Figure 1 The reactor is used for mixing and heating fluids When batch is started the valve is opened and the tank starts filling When the tank level reaches L1 the heater and the mixer start The valve stays open until the upper level L2 is reached When the tank is filled and the content has reached the des
225. x library in C http nz com webnz robert Eker J 1997 A Framework for Dynamically Configurable Embedded Controllers Lic Tech thesis ISRN LUTFD2 TFRT 3218 SE Depart ment of Automatic Control Lund Institute of Technology Lund Swe den Eker J and K J str m 1995 A C class for polynomial operation Report ISRN LUTFD2 TFRT 7541 SE Department of Automatic Control Lund Institute of Technology Lund Sweden Lewis R 1995 Programming industrial control systems using IEC 1131 8 The Institution of Electrical Engineers London U K 201 Appendix A PAL P lsj Algorithm Language 202 Appendix B PCL Palsj Configuration Language 1 Introduction User defined blocks for the P LSJ environment are programmed in PAL and instantiated and connected on line using PCL the PALSJO Config uration Language PCL is a simple language for administrating blocks and assigning variables In this chapter all keywords and operators in PCL will be presented Examples are given to illustrate the use of every command 2 Keywords The predefined keywords in PCL are the following new delete with help reset quit use enduse dim show hide break endwith new An instance of a specified block type is created using the new statement The following syntax is used pcl gt lt block name gt new lt block type name gt The lt block name gt must contain the full block name Blocks in P LSJ
226. xample Two tasks Regul and OpCom are sharing a variable called data To ensure mutual exclusion the variable is protected by the mutex variable M1 Associated with M1 is a monitor event called E1 The Regul task consists of two code segments called rsegi and rseg2 that are shown in Example 5 Each time the Regul task is released it tries to lock the monitor variable M1 Once the monitor is locked it may access the shared data If the value of the data variable is less than two it waits for the event E1 to occur EXAMPLE 5 function exectime states rsegl flag states params switch flag case 1 enterCode if lock M1 data readData M1 if data lt 2 await E1 exectime 0 else exectime 0 003 end else exectime 0 end case 2 exitCode unlock M1 end function exectime states rseg2 flag states params switch flag case 1 enterCode y analogIn params inChan states u 50x y exectime 0 003 case 2 exitCode analogOut params outChan states u end 160 6 Simulation Features Outputs Inputs Controller Sensor Computer Computer Receiver ID 1 Receiver ID2 1 Y Y N Network a 5 5 O O Sender ID 1 Sender 2 u y1 y2 Double Tank Figure 14 A distributed control system where the sensor and the CPU are dislo cated The controller and the sensor are implemented as periodic
227. y is to be able to make an integrated design of control algorithms and scheduling algorithms off line Such a design process should allow an in corporation of the availability of computing resources into the control de sign by utilizing the results of scheduling theory This is an area where so far relatively little work has been performed One of the first references that addressed this problem was Seto et al 1996 An algorithm was pro posed which translates a control performance index into task sampling periods considering schedulability among tasks running with pre emptive priority scheduling The sampling periods were considered as variables and the algorithm determined their values so that the overall perfor mance was optimized subject to the schedulability constraints Both rate monotonic scheduling RM and earliest deadline first scheduling EDF were considered The performance index was approximated by an expo nential function only and the approach did not take input output latency into account The approach was further extended in Seto et al 1998b An approach to optimization of sampling period and input output la tency subject to performance specifications and schedulability constraints is presented in Ryu et al 1997 Ryu and Hong 1998 The control per formance is specified in terms of steady state error overshoot rise time and settling time These performance parameters are expressed as func tions of the sampling pe
228. ystem is implemented on top of Real Time Mach In Shin and Meissner 1999 the approach in Seto et al 1996 is ex tended making on line use of the proposed off line method for processor utilization allocation The approach allows task period changes in multi processor systems A performance index for the control tasks is used to determine the value to the system of running a given task at a given pe riod The index is weighted for the importance of the task to the overall system The paper discusses the issue of task reallocation from one pro cessor to another and the need to consider the transient effects of task reallocations Two algorithms are given for task reallocation and period adjustments In Stankovic et al 1999 a PID controller is proposed as an on line scheduler under the notion of Feedback Control EDF FC EDF The mea 41 Introduction surement signal the controlled variable is the deadline miss ratio for the tasks and the control signal is the requested CPU utilization Changes in the requested CPU utilization are effectuated by two mechanisms An ad mission controller is used to control the flow of workload into the system and a service level controller is used to adjust the workload inside the system The latter is done by changing between different versions of the tasks which have different execution times A simple liquid tank model is used as an approximation of the scheduling system Imprecise calculation
229. zed subject to the schedulability con straints Both fixed priority rate monotonic and dynamic priority Earliest Deadline First EDF scheduling were considered The loop cost function was heuristically approximated by an exponential function The approach was further extended in Seto et al 1998 A heuristic approach to optimization of sampling period and input output latency subject to performance specifications and schedulability constraints was also presented in Ryu et al 1997 Ryu and Hong 1998 The control performance was specified in terms of steady state error over shoot rise time and settling time These performance parameters were expressed as functions of the sampling period and the input output la tency An iterative algorithm was proposed for the optimization of these parameters subject to schedulability constraints Task attribute adjustments A key issue in any system allowing dynamic feedback between the control algorithms and the on line scheduler is the ability to dynamically adjust task parameters Examples of task parameters that could be modified are period and deadline In Shin and Meissner 1999 the approach in Seto et al 1996 is extended making on line use of the proposed off line method for processor utilization allocation The approach allows task period changes in multi processor systems A performance index for the control tasks is used weighting the importance of the task to the overall system t

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