An Interactive Software Tool for the Study of Event
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1. Another important reason for the interest of event based control comes from the hand of the use of the computing resources An embedded controller is typically implemented in a real time operating system The available CPU time is shared between the tasks in a manner such that it seems that each one runs independently Having occupied the CPU doing control calculations when nothing significant has happened in the process is clearly an unnecessary use of available resources IFAC Conference on Advances in PID Control PID 12 Brescia Italy March 28 30 2012 The same argument also applies to communication systems The communication bandwidth that is available in a distributed system is limited Use it to send data through a time based control scheme implies a loss of bandwidth If the number of updates of the control signal sent across the network is reduced the bandwidth will be increased This means a reduction in the number of messages that is transmitted directly and thus produces a decreasing in the average bus load Another example is a wireless sensors network where each sensor node is powered by a battery The experiences carried out by Feency and Nilsson 2001 show that comparatively wireless transmissions consume relatively more energy than required for the own internal calculations and it is therefore a limiting factor of their autonomy Therefore to reduce consumption energy it would be desirable an event based sampling method2. In essence a dynamic picture is a collection of graphical windows that are manipulated by just using the mouse If we change any active element in the graphical windows an immediate recalculation and presentation automatically begins Thus we can perceive in an immediate and coherent way how their modifications affect the result obtained The interactive tool that we present in this paper is coded in Sysquake a Matlab like language with fast execution and excellent facilities for interactive graphics and is delivered as a stand alone executable that makes it readily accessible to users Piguet 2004 The paper is organized as follows In Section 2 the basic properties of the two degree of freedom PI controller based on events are summarized The results are based on Sanchez et al 2011 where many additional details are given A summary of the tool s functionality is presented in Section 3 Finally Section 4 presents the main conclusions 2 STRUCTURE OF THE 2DOF PI CONTROLLER The block diagram of the 2DOF event based controller is shown in Figure 1 For the sake of clarity the event detection logic of both controllers is located inside one block The IFAC Conference on Advances in PID Control PID 12 Brescia Italy March 28 30 2012 purpose of this logic is similar to the clock in the computer implementation of time driven controllers i e to determine the generation of a new control action In this case the generation of the
3. P and I parts are enabled once the process is inside the dead band and they start calculating at the very moment that the process leaves the band as the result of a disturbance The event based solution consists of applying a level crossing sampling strategy to each part to trigger the computation of the control action Briefly to sample a signal x t by level crossing means to take a new sample every time that the difference in the signal with respect to the last sample is higher than a certain threshold value It can be expressed by the following logical expression x t x t gt 2 where x f is the current value of the signal and x t is the value of the signal the last time the logical condition was true The level crossing is the simplest event based sampling method Miskowicz 2006 In this particular case there will be two error based logical expressions and two different values of 6 Ap for the P part and 6 4 for the I part The logical expression of each part will depend on the error magnitude that is necessary for the two triggered counterparts to produce the control signal the error signal for P action and the integrated error IE signal for I action IFAC Conference on Advances in PID Control PID 12 Brescia Italy March 28 30 2012 Once the process is inside the deadband region defined as Y lt Vy lt yg the set point following task is over and the disturbance rejection task takes control Note
4. control actions ug and uy by the compensators Cy and Cp is triggered by state events obtained from the set point value and the control error signal The rationale of the event based feedforward compensator Cy is as follows First an open loop control action is designed to move the process towards the reference y and second a two event based proportional controller that produces a control action similar to the feedforward one is calculated off line Visioli 2004 The Cy controller is in closed loop under just two conditions when a new reference value is introduced and when the process output is crossing a certain threshold value y Based on it and on a FOPDT approximation of the original process a generic tuning formula to obtain K 1 and y is derived Once the process reaches y thanks to Cy the event based controller Cp is enabled to cope with disturbances Cy starts calculating proportional and integral actions only when the process output moves outside the dead band and it stops when the process output is again inside the band 2 1 The event based feedforward controller Cy We assume that the process to be controlled has FOPDT dynamics namely K Ls Me 1 Then without loss of generality we assume that starting from null initial conditions a process output transition from 0 to Ysp is required Fig 1 Block diagram of the 2DOF event based PI controller Figure 2 shows the open loop situation to be re
5. controller design phase e The cancellation of the P part because of a high value of Ap introduces oscillations in the loop e A good compromise between the number of events and the control performance is obtained with Ap and A ranging from 2 to 10 of yz Figure 4 shows an example of the method applied to a second order process P s 2 5 1 s 1 0 5s with a unit load disturbance step at 3 8 The PI parameters K 0 95 and 7 0 87 have been determined by applying the well known SIMC tuning rules Skogestad 2003 5 CONCLUSIONS A new interactive tool for analysis and design of a new 2DOF event based PI controller has been described The purpose is to enhance the knowledge of these kind of systems by exploiting the advantages of immediately seeing the effects of changes that can never be shown in static pictures The module has been implemented in Sysquake a Matlab like language with fast execution and excellent facilities for interactive graphics ACKNOWLEDGMENT This work was supported by the Spanish CICYT funds under Grant DPI2007 61068 REFERENCES Arz n K J 1999 A Simple event based PID controller Proceedings of 14th IFAC World Congress vol 18 Beijing China 423 428 str m K J 2007 Event based control In A Astolfi and L Marconi editors Analysis and Design of Nonlinear Control Systems Springer Verlag str m K J and B Wittenmark 1997 Computer controlled systems Theory and
6. design Third Edition Prentice Hall New Jersey Feency L M and M Nilsson 2001 Investigating the energy comsumption of a wireless network interface in an ad hoc networking environment Proceedings of IEEE Infocom 1548 1557 Heemels W P M H Sandee J and van den Bosch P 2008 Analysis of event driven controllers for linear systems Intern J of Control 81 4 571 590 Miskowicz M 2006 Send on delta concept An event based data reporting strategy Sensors 6 1 29 63 Piguet Y 2004 SysQuake 3 User Manual Calerga S arl Lausanne Switzerland Sanchez J A Visioli and S Dormido 2011 A two degree of freedom PI controller based on events Journal of Process Control 21 639 651 Skogestad S 2003 Simple analytic rules for model reduction and PID controller tuning Journal of Process Control 13 4 291 309 Visioli A 2004 A new design for a PID plus feedforward controller Journal of Process Control 14 4 455 461 Visioli A 2006 Practical PID Control Springer London UK Wittenmark B H Haglund and M Johansson 1998 Dynamic pictures and interactive learning IEEE Contr Syst Mag 18 3 26 32
7. requiring less data transmissions The event based control considered in this paper is a new event based PI controller where a two degree of freedom 2DOF structure is used to cope with the set point following and the load disturbance rejection tasks Sanchez et al 2011 As in other event based controllers a deadband around the set point value is considered Then an event based feedforward controller allows a transition of the process output to a new reference value y by just two control actions the two events that trigger the controller and the two corresponding control actions are pre calculated by a design method that requires a first order plus dead time FOPDT model Once the process is inside the deadband an event based feedback PI controller is in charge of rejecting disturbances and maintaining the process inside the band The coupling of the feedforward and feedback parts is based on an estimate of the error area to detect the presence of disturbances or on a variable dead band derived from the FOPTD model The motivation of the 2DOF event based proposal is twofold first to present an event based counterpart for the well known 2DOF PI controller by exploring new event based designs and second to improve the set point following task from an event based point of view Like any time based feedforward design the event based alternative improves the process response but it also offers another improvement a significant redu
8. IFAC Conference on Advances in PID Control PID 12 Brescia Italy March 28 30 2012 WeB2 6 An Interactive Software Tool for the Study of Event based PI Controller Sebastian Dormido Manuel Beschi Jos Sanchez Antonio Visioli 3 Departamento de Inform tica y Autom tica UNED Madrid Spain e mail sdormido jsanchez dia uned es Dipartimento di Ingegnieria dell Informazione University of Brescia Brescia Italy e mail manuel beschi antonio visioli ing unibs it Abstract The paper describes an interactive tool focused on the study of a new family of event based PI controller Most research in control engineering considers periodic or time driven control systems Event based control is particularly a very promising alternative when systems with reduced computation and communication capacities are considered For event driven controllers it is the occurrence of an event instead of the autonomous progression of the time what decides when the signal sampling should be made The tool has been developed using Sysquake a Matlab like language with fast execution and excellent facilities for interactive graphics The highly visual and strongly coupled nature of event based control system is very amenable to interactive tools The tool presented in this paper enables to discover a myriad of important properties of these systems 1 INTRODUCTION Research carried out in automatic control considers in most cases p
9. band because of disturbances The true deadband Wo E Yy Dy 5 is used to calculate the error 3 DESCRIBING THE INTERACTIVE TOOL This section describes the functionalities of the developed tool which highlights the concepts described in Section 2 The tool is freely available by contacting the authors and can be used in Windows Mac and Linux operating systems without the need for a Sysquake license One consideration that must be kept in mind is that the tool s main feature interactivity cannot be easily illustrated with written text Nonetheless some of the features and advantages of the application are shown below The reader is invited to use the tool and personally experience its interactive features When developing a tool of this kind one of the most important things that the developer needs to keep in mind is the organization of the main windows and menus to assist the user in understanding the event based PI controller described in the previous section The graphics can be manipulated directly by dragging points lines and curves or by using text edits and sliders Notice also that for all the graphics available in the tool the vertical and horizontal scales can be modified using three black triangles available on the graphics A V The tool is divided into two main parts Model identification screen and Control design screen that can be selected in the upper left hand side using two radio buttons Each part of the tool i
10. ction in the number of events during the set point task just two control actions without a significant worsening of the response one of the key issues of any event based control design This issue has not been addressed in previous works on event based PI control Automatic control ideas concepts and methods are really rich in visual contents that can be represented intuitively and geometrically These visual contents can be used for presenting tasks and handling concepts and methods and manipulated for solving problems The basic ideas of automatic control often arise from very specific and visual situations All experts know how useful it is to go to this specific origin when they want to skilfully handle the corresponding abstract objects The same occurs with other apparently more abstract parts of automatic control Using WeB2 6 visual images and intuition control specialists are able to relate constellations of facts that are frequently highly complex and the results of their theories in an extremely versatile and varied way Our feeling is primarily visual and it is thus not surprising that visual support is so present in our work Control experts very often make use of visual diagrams and other forms of imaginative processes in their work and they acquire what could be called an intuition of what is abstract Visualization thus appears to be something natural both in the origins of automatic control and the discovery of new rela
11. eriodic control systems where continuous time signals are represented by values sampled with a sampling period h These systems are designated generically as time based control systems On the contrary in an event based control system is the occurrence of an event rather than the passage of time what decides when to sample the dynamic system This means that in a time based control system is the autonomous progression of the time what triggers the execution of actions while in an event based control systems is the dynamic evolution of the system that decides when the next control action will be applied The fundamental reason for the predominance of time based control systems has been based on the existence of a theory well established and mature for sampled data control systems str m and Wittenmark 1997 There are many practical situations where it is interesting and advantageous to consider event based control systems instead of the traditional time based control system Mechanism of activation by events can vary depending on the case Arz n 1999 Some significant examples are Astr m 2007 and Heemels et al 2008 Control of internal combustion engines is an example where variable sampling intervals appears in a natural way because it is sampled with respect to the speed of the machine The nature of the event based sampling can be intrinsic to the method of measurement used or physical nature of the process that is being control
12. he sliders and text edits that are available in the Model parameters area In both cases an optimal model can also be fitted to the given process transfer function using the option called Optimization fitting in the Setting menu This option uses an optimization algorithm which tries to obtain the best model for the given data On the top right corner of the Input graphic the mean square error between the model output and the process output is shown being a reference measurement to obtain the desired model 3 2 Control design screen The second screen of the tool is shown in Figure 4 and is dedicated to design the event based PI controller using the FOPDT model obtained in the previous stage In the left part of the screen it is now included besides the Process Parameters elements the Event Based PI Controllers Parameters section These parameters are the following 2 speed of the process response f upper lower limit of the deadband region where the integral action of the Cy controller is enabled K T proportional integral action of the Cp controller Below these elements we include again the Output graphic of the Model identification screen Some guidelines on how to tune the design parameters can be outlined e yy and y must be defined according to the maximum tolerable steady state error The deadband should wrap the noise in a real implementation to avoid trains of events especially from the P part If yu a
13. led For example when using encoders sensors to measure the angular position of a motor Control systems that incorporate relays are another example that can be considered as a special case of event based sampling Event based sampling can also be a built in feature incorporated into a smart sensor device In many cases it is natural for example when used as sensors encoder or when the actuators are of on off type nature such as in satellite thrusters or in pulse width of pulse frequency modulation Event based sampling is also used in the process industry when using closed loop control of statistical process SPC concept To avoid disturbing the process a new control action is calculated only if there is a statistically significant deviation Another case of this kind is a manufacturing system where the sampling is related to the rate of production Modulators A X or the one bit A D converters normally used in mobile phones are also special cases of event based control In addition to different natural sources of triggering events and their relevance in practice there are many other reasons why the use of an event based control is of interest Event based control is much closer to the way in which human beings act as a controller In reality when an operator realizes manual control his behaviour is guided by events rather than by time No control action is taken until the measurement signal has diverged enough from the set point
14. nd y are equal to Ysp the system response oscillates around the set point value regardless the other parameters Increasing the values of Ap and A reduces the number of events and the speed and damping of the response A high value of Ap or A can cancel the P or I part respectively as events are not triggered IFAC Conference on Advances in PID Control PID 12 Brescia Italy March 28 30 2012 amp File Edit Settings Plots Figure Layout View Window Help Model identification Control design Control Events WeB2 6 Number of Events 26 PlTuning PI Manual 1F Process Parameters 0 Kp 2 5 I a 71 ontroller output 2 500 Te I 1 05 I fe mE 7 8 9 10 Identification Error 0 0991 1 000 0 500 u delay 0 0 000 Event Based PI Controller Parameters lambda 1 l 1 000 A alfa 0 1 rI beta 01 Ff 0 100 0 100 2 A dettaP 0 1 l deltalAE 0 2 l 0100 0 200 0 1 Kp 0 95 l Ti0 87 0 949 0 868 fe ontrolled output ale 6 7 8 9 Time O Event proportional action Open loop process step response Open loop model step response 1F Wiccedscedes lt d Activate integrator Desactivate integrator Upper bound Lower bound Set point 0 10 20 30 40 a 1 id 3 4 5 6 7 8 9 Time Fig 4 Interactive tool user interface for event based PI
15. peated by Cy and the two events where the control action must change The set point following task when a new set point value y is applied to the control system is given by the following algorithm 1 Determine the parameters K T and L of the model any procedure for this purpose can be applied Visioli 2006 2 Determine the proportional gain K A from e e q e v 1 0 where X KK WeB2 6 gt time Lt L t Fig 2 Open loop process response to be repeated in closed loop by the two event based controller Cy 3 Determine the value of y using r fogli KKf and y KK y l et 4 Define e Yy Y 5 If elt gt e then apply uy Kf y 6 If lelt lt Je then apply u K vy y It is important to note that in the absence of load disturbances and model mismatches during the transition from 0 to Ysp the process output will reach the y value after just two control actions 2 2 The event based feedback controller Cy To offer a complete controller the disturbance rejection task must be addressed as in any other controller but this time with an event based solution As was said from the first time that the process enters the dead band a feedback controller Cy will be in charge of compensating for any disturbance This controller is a PI controller where the activation of the proportional and integral parts is triggered by two types of asynchronous events The
16. s further divided into several sections represented in Figures 3 and 4 which show the two main screens of the interactive tool 3 1 Model identification screen The Model Identification screen is shown in Figure 3 This screen is focused on determining the K T and L parameters of a first order with a dead time model FOPDT The process transfer function to be identified can be modified depending on the option selected from the Settings menu Several examples of transfer function are given and its parameters can be modified interactively by dragging sliders or setting specific values using text edits fields However a free transfer function can be selected Interactive TF option in the Settings menu where the process poles and zeros can be inserted removed or changed from the Process Transfer Function graphic All these elements are available in the left hand area of the screen In the right hand of the screen there are different graphical elements IFAC Conference on Advances in PID Control PID 12 Brescia Italy March 28 30 2012 WeB2 6 File Edit Settings Plots Figure Layout View Window Help Model identification Control design Model transfer function e 2 000s G s 4 00s 1 Process Parameters Kp 2 5 2 500 Input delay 0 Model parameters Delay 2 000 4 000 2 000 Identification Error 230 2648 0 000 Move Poles Add oO Zeros Mode Gps O Remove oO In
17. tegrator 05 Process Transfer Function 22 24 26 28 1H J Process step response i gt Model step response A 1 2 1 0 1 0 2 4 6 8 Fig 3 Interactive tool user interface for model identification phase On the top a symbolic representation of the model shows continuously all the changes performed on the model parameters Model transfer function With this purpose some sliders and text edits are available in the same area Model parameters Below these elements there are two different graphics which represent the input signal Input and the process step response of the system Output to be identified in red colour In the second graph it is also represented the model step response in blue colour The objective of the model identification is to try that the model step response blue line coincides as much as possible with the process step response red line The user can try to fit the model in two different ways One possibility to modify in an interactive way the model parameters is by using the Output graphic In this sense it is possible to modify the static model gain using the horizontal dashed blue line in the Output graphic The model time constant and the model delay can also be changed using the vertical blue dashed lines in the Output graphic These options allow the user to find an adequate model for the given process transfer function A second alternative is using t
18. that the control action is fixed at u u p uy K 1 y until a new reference value is introduced This means that the output of Cy is constant and Cy is enabled and will start computing proportional and integral actions when the process leaves the band as a consequence of a disturbance We assume that the disturbance is a piecewise constant signal The algorithm of the Cy controller can be expressed as I K s 1 U m U mw IE current 0 gt Yu BY sp gt Yui pa PY y gt 2 If y t 2 Yu then E current Yu 5 y t else if y S Yu then E current Yu m y t gt 0 last else e current T last IE IE h If current last If ZE 2 4 then w u K T IE IE 0 nom E current 2 2 A then uy K e p current gt Clast e current a Cn AA Ug Up tg 5 Go to 2 NYA na A U Note that Anom corresponds to the sampling period of the sensor not of the controller This parameter allows us to simulate the fast sampling of the sensor with a digital DAQ In a real implementation it should be fixed as short as possible to detect accurate crossings The main problem with the previous algorithm is the possible unnecessary activation of the controller Ca during the set point following task without disturbances An alternative solution is to extend the triggering of Cp always from t 0 when the process output is outside the deadband One way to do that is
19. tions between mathematical objects Traditionally the design of the systems is carried out following an iterative process Specifications of the problem are not normally used to calculate the value of the system parameters because there is not an explicit formula that relates them directly This is the reason to split each iteration in two phases The first one often called synthesis consists of calculating the unknown parameters of the system taking as a basis a group of design variables that are related to the specifications During the second phase called analysis the performance of the system is evaluated and compared to the specifications If they do not agree the design variables are modified and a new iteration is performed It is possible however to merge both phases into one and the resulting modification in the parameters produces an immediate effect In this way the design procedure becomes really dynamic and the users perceive the gradient of change in the performance criteria This interactive capacity allows us to identify much more easily the compromises that can be achieved in a control design problem In control education many tools have been developed over the years with these aims Many interesting ideas and concepts were implemented by Prof Astr m and col at Lund In this context we should highlight the concepts of dynamic pictures and virtual interactive systems introduced by Wittenmark Wittenmark et al 1998
20. to modify the deadband by enclosing the process output trajectory during the set point following task that is from 0 The point is to consider a false lower band just to produce the triggering of Ca while maintaining at the same time the constant original lower limit to calculate the proportional and integral actions It is worth studying how to modify the lower band by analysing the impact of the disturbances on the process response During the transition positive disturbances push the process output towards the dead band by themselves so these disturbances are not a problem because they contribute to the earlier activation of the controller Cy Thus the upper limit of the dead band should not be changed However negative disturbances avoid the activation of the controller because they make the process output fail to attain the lower limit The false lower limit should then be designed in such a way that it follows the process response in the absence of negative disturbances We exploit the FOPDT model to adapt the lower limit The new false lower limit during the transition will be derived from the step response of the FOPDT model as WeB2 6 y t uK I ey 3 using as input u qay K Therefore the false deadband is redefined as ay e s y lt By 4 from 0 Now the coupling of the two control tasks is natural because Cy is always enabled but starts working only when the process output leaves the false dead
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