MULTITANK SYSTEM - Alpha Control Lab
Contents
1. 0 2 0 15 0 1 0 05 0 0 05 0 1 0 15 0 2 0 2 0 15 0 1 0 05 0 0 05 0 1 0 15 0 2 m dH2 m Degree of membership Mini 1 o imum Minimum Medium Maximum 1k 1 o E EISE RENE Degree of membership 1 1 1 1 1 Pump Control m3 s 5 Fig 6 46 Membership function for dH dH and pump control signals Table 6 1 Rules for fuzzy controller No Rule 1 is Maximum and 4 2 is Maximum and dH3 is Maximum then Pump Control is Minimum 2 4 is Maximum and 4 2 is Maximum and dH3 is Medium then Pump Control is Minimum 3 If dHl is Maximum and dH2 is Maximum and dH3 is Minimum then Pump Control is Minimum 4 If dH is Medium and dH2 is Medium and dH3 is Maximum then Pump Control is Medium 5 f dHl is Medium and dH2 is Medium and is Medium then Pump Control is Medium 6 If dHl is Medium dH2 is Medium and dH3 is Minimum then Pump Control is Maximum 7 If dHl is Minimum and 4 2 is Minimum and dH3 is Maximum then Pump Control is Maximum 8 dH7 is Minimum and dH2 is Minimum and dH3 is Medium then Pump Control is Maximum 9 Jf dHl is Minimum and dH2 is Minimum and dH3 is Minimum then Pump Control is Maximum 10 If is Maximu2. 8 1 1 1 1 1 1 1 1 1 1 1 1 Life ib ie ee ee ee ee Jg 1 1 1 1 D 1 1 1 1 1 1 1 1 o 1 1 1 1 Bote ik gt ES 1 1 1 1 1 1 1 1 T p La esee AEE E 9 1 1 1 1 1 1 1 1 2 0 TENET EE Side i E on Pe 1 1 1 1 1 1 1 1 1 4 27 Laa u 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 o o a T T Ti gt Time s Fig 6 49 Pump control signal Time s Time s Fig 6 52 H level Fig 6 51 level Real time Experiment The fuzzy control experiment can be performed from the Multitank Control Window by invoking Fuzzy from the Demo Controllers group In the model of the control system Fig 6 53 the Tank Model block was replaced by the driver block Before running experiment the FIS matrix must be loaded using following command in MATLAB Workspace Tank3_Fis readfis Tank3_Fis Tank 3 Fuzzy Controller Control P Level 1 DC Pump 0 Characteristic1 Level 2 Valve1 0 _ gt y Level 3 Valve2 pr Valve3 Saturation1 Fuzzy Logic Controller Saturatio Saturatio H3
3. NEN IPIE 3 o M 1 M CR RES o B o 4 ess supere ee ea a a rere c Se o uda 07 707 7707777 177777 o 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 gt 1 1 1 1 1 L L 1 L oO L e Ite N i re o E i i QN i i o o N T E o ex T e H en ui ZH uw on Pe 0 2256 80 5 5800e 005 Alfa2 Time s Fig 5 32 The middle tank identification C2 C3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 t je reme 1 1 1 1 1 1 1 1 t 1 1 1 oo 1 1 0 gp a 1 1 1 1 1 1 1 1 poo sigs Fillies oc clt c c s ge den etel 1 1 1 1 fda pg X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 L 1 1 wo e wo N wo lo e e ui H 80 70 5 0 2487 7 4102e 005 1 Fig 5 33 The lower tank identification C3 6 REAL TIME CONTROL EXPERIMENTS In the following section a number of control experiments is described Each experiment consists of the simulation phase and real time phase QD The con
4. BA get TankObj BaseAddress 000 000 000 000 306 297 000 000 000 000 306 294 8 2 BIAS Purpose The bias level of the liquid level measurements The bias values are equal to the levels read from the A D converters when the tanks are empty When a new value of this property is set the new biases are stored in a file for future use Synopsis B get TankObj Bias set TankObj Bias NewBias Description The bias value is subtracted from value obtained from the A D converter to obtain the bias less level value See ScaleCoeff Examples see Section 3 2 8 3 BITSTREAMVERSION Purpose Read the version of the logic design for the RT DAC PCI board Synopsis Version get TankObj BitstreamVersion Description This property determines the version of the logic design of the RT DAC PCI board The tank systems may be different and the detection of the logic design version makes it possible to check if the logic design is compatible with the physical model 8 4 PWM Purpose Set and get the duty cycle of the PWM waves Synopsis PWM get TankObj PWM set TankObj PWM NewPWM Description The property determines the duty cycle of the PWM waves for the valves and for the pump The first PWM channel is responsible for the pump control The remaining five channels are applied to control the valves The NewPWM variable is a 1x6 vec
5. development of the mathematical model based on physics of the process simplification of the model and or its transformation into a standard form development of a simulation model tuning of the model parameters identification practical verification of the model Fig 4 20 Configuration of the multitank system In the next sections we will execute the steps given above for the multitank system Liqiud levels H H5 H in the tanks are the state variables of the system Fig 4 20 For the tank system there are four controlled inputs liquid inflow 7 and valves settings Therefore several models of tanks system can be analysed Fig 4 21 classified as pump controlled system valve controlled system and pump valve controlled system a Tank system parameters Tank system c 4 H Cj Tank system gt Fig 4 21 Models of the tank system as pump controlled system b valve controlled system c pump valve controlled system Several issues have been recognised as potential impediments to high accuracy control of level or flow in the tanks nonlinearities smooth and nonsmooth caused by shapes of tanks saturation type nonlinearities introduced by maximum or minimum level allowed in tanks nonlinearities introduced by valve geometry and flow dynamics nonlinearities introduced by pump and valves input output characteristic curve
6. MULTITANK SYSTEM MATLAB R2008a b R2009a b R2010a b R2011a b PCI version User s Manual Y Y www inteco com pl AAA www inteco com pl NOTES Multitank System User s Manual 2 www inteco com pl SAFETY OF THE EQUIPMENT The equipment when used in accordance with the supplied instructions within the parameter set for its mechanical and electrical performance should not cause any danger to health or safety if normal engineering applications are observed If in specific cases circumstances exist in which a potential hazard may be brought about by careless or improper use these will be pointed out and the necessary precautions emphasised Some National Directives require to indicate on our equipment certain warnings that require attention by the user These have been indicated in the specified way by labels The meaning of any labels that may be fixed to the equipment instrument are explained in this manual Risk of electric shock PRODUCT IMPROVEMENTS The Producer reserves a right to improve design and performance of the product without prior notice major changes are incorporated into up dated editions of manuals and this manual is believed to be correct at the time of printing However some product changes which do not affect the capability of the equipment may not be included until it is necessary to incorporate other significant
7. 4 1 LAMINAR OUTFLOW OF THE IDEAL FLUID The laminar outflow rate of an ideal fluid from a tank Fig 4 22 is governed by the Bernoulli law This equation is obtained by a simple calculation of the potential and kinetic energy of the fluid 5 Q uSA2 gH 4 1 where S is the output area of the orifice _ is the orifice outflow coefficient inflow qo const Ho level 0 S p q Fig 4 22 Outflow of ideal fluid 4 2 MODEL OF A CASCADE OF N TANKS Assuming the laminar outflow of an ideal fluid for a cascade of n tanks the model describing dynamics of the process can be obtained by means of mass balance dV q C JH dt dV 4 2 C a H 1 dt where Vi Va fluid volumes in the tanks C5 resistance of the output orifice Hi fluid levels in the tanks q inflow to the upper tank From equations 5 2 we obtain _ syag JH a dV dH x dH dp 4 3 H CHE dH di As mentioned above for the laminar flows the outflow rate from a tank is governed by the Bernoulli law In this case 1 2 For the real configuration of tanks tubes and valves if turbulence and acceleration of the liquid in the tube can not be neglected a more general coefficients are applied 4 3 NONLINEAR MODEL OF THE THREE TANK SYSTEM PUMP CO
8. while other must be identify and introduced according to the current setting of the valves Block Parameters Tank3 Model i Subsystem mask r Parameters Initial Conditions H10 H20 H30 0 001 0 001 0 001 1 2 t 11 08 8 43 8 28 TE 5 Alfal Alfa2 Alfa3 05 0505 Upper Tank a w 0 25 0 035 Middle Tank b c 2 0 348 0 1 0 35 Lower Tank H3max 0 365 0 35 _ Cancel Apply Fig 3 11 Parameters of the model of tank system An example of the step response of the tank system simulation model is given in Fig 3 12 3 5 0 08 3 0 07 2 5 Pu 0 06 mp co 2 0 05 H1 m 1 5 m 3 s 0 04 1 0 03 0 5 0 02 0 0 01 05 300 400 500 600 0 0 100 200 300 400 500 Times Time s 0 14 0 12 T 0 1 0 1 0 08 H3 0 08 m m 0 06 0 06 0 04 0 04 0 02 0 02 0 0 0 300 400 500 600 0 100 200 300 400 500 Time s Time s Fig 3 12 Example of the step response simulation 3 3 RTWT DEVICE DRIVER The main driver is located in the RTWT Device Driver group The driver integrates MATLAB Simulink environment and RT DAC PCI board transforming and transmitting measurement and control signals from to the tanks
9. 5 Street R L Watters 7 Vennard J K Elementary Fluid Mechanics John Wiley amp Sons Inc 1996 6 Grega W Heterogeneous Control Laws in Open Architecture Enviroment Third International Symposium on Methods and Models in Automation and Robotics Miedzyzdroje Poland September 1996 pp 1097 1102 7 Rosol M Control of Nonlinear Liquid Flow Process PhD Thesis in Polish Grega W supervisor AGH University of Science and Technology Department of Control Krakow 2001
10. After clicking on the block the following window opens Fig 6 40 The Tank Model block is replaced by the drivers block see description in Section 3 The inverted characteristic curve of the pump is represented by it Look_Up Table Tank 3 LQR Controller Control Control DC Pump 3 Characteristic 1 Valve2 MT Level 3 Tu Terminator lt Saturation Cohtrol 4 H10 K lt _ Hio H30 H30 H20 H20 Fig 6 40 LQR real time controller The results of experiments are given in Fig 6 41 Fig 6 42 Fig 6 43 and Fig 6 44 T T T T T T T T cs i E ET pe us aa Tau TT ERE 4 4 1 1 0125 52 Ee eg CUENTEN tci m See et METRE NR NN PAF E MEN 0 21 e T js eee TASER jc ERSS AE z 1 eR m Here om on eene AER ety Ines eR 55 4 Red icm Booed z 0 08 5 1 1 1 1 Nee al hee Acum de DE 0 06 4 Disce eee ces ee eed 5 s a
11. Gain 2 0 00014471780029 and Bias 2 2449 5 Gain 3 0 00014913908601 and Bias 3 2409 56077554064 To store permanently the identified parameters the following commands must be executed TankScaleCoeff Gain 1 Gain 2 Gain 3 1 1 TankBias Bias 1 Bias 2 Bias 3 0 0 save matlabroot toolbox Multitank m TankV2PU Coeff m4 TankBias TankScale Coeff V4 5 2 IDENTIFICATION OF VALVES The bottom outflow of each tank is equipped with the controlled valve The valves are adjusted using the PWM signal from the power interface Fig 5 27 shows characteristic curve of one of the valves Fig 5 28 demonstrates how the outflow depends on the level for a given control signals PT 10 Valve characteristic Measured outflow m3 s 5 4 5 4 3 5 3 2 5 2 1 5 1 0 65 0 7 0 75 0 8 0 85 0 9 0 95 1 PWM control signal Fig 5 27 Controlled valve characteristic 0 25 o o zs Fluid level m 100 PWM control signal Outflow time s Fig 5 28 Time characteristic curve of the valve 5 3 IDENTIFICATION OF PUMP The system is equipped with DC pump providing liquid transportation from the lowest tank to the upper tank The goal of the DC pump is to adjust the inflow to the upper tank according to the control signals The DC pump is supplied from the power interface by an appropriate PWM control signal The frequency a
12. Rx uam du pete 004 peeeeqeeeAem Peete hr piis E 3 5 0 100 200 300 400 500 600 0 time 0 100 200 400 500 600 Fig 6 41 Pump control signal Fig 6 42 level 6 1 04 0 16 onal lint s D 0 09 cerros EE EE DW Pac PS Ins oa Odd poc pev Meo 4 ra at 008 fr 4 jov tee qc cA CES CE e Q12L ic y 2 Loss poer more ome rte mca pos 7 0207 deed peto eas e spat gt ts Leet tot finora 1 1 1 1 1 1 1 01 qo ee epe cese crees et fc cte eee ee E Sese ght d T ER ENS ny m tese resi e E fi i rum UNES nc E S Teese qs ee 0 06 rea eb jeter de jj m JE S ASS e i 1 004 m a ieee MW je ge ves vu ry Padi Gar Vil f oo2W etes push 002 4 RU i 0 01 0 0 100 200 300 400 500 600 0 100 200 300 400 500 600 time m tim
13. assigned to the board by the computer system and may differ from computer to computer The base address is given in the decimal and hexadecimal forms Logic version Displays the number of the configuration logic of the on board FPGA chip A logic version corresponds to the configuration of the RT DAC PCI board defined by this logic and depends on the version of the tank model Application The name of the application taken from the on board FPGA chip A name of the application corresponds to the configuration of the RT DAC PCI board I O driver status Shows the status of the driver that allows the access to the I O address space of the microprocessor The status has to be OK string In other case the Multi Tank software HAS TO BE REINSTALLED Control The frame allows to set the control signals of three valves and to set the control signal for the pump Valve I Valve 2 Valve 3 Pump The control signals of the valves and the pump may be set by entering a new value into the corresponding edit fields or by moving the corresponding slider The control values may vary from 0 0 to 1 0 The value of 0 0 and 1 mean respectively the zero control and the maximum control If the valves are considered the zero control means that the valve is closed however the maximum control fully opens the corresponding valve For the pump the flow increases when the control value changes from 0 0 to 1 0 If a new control value is entered into the edit f
14. changes Multitank System User s Manual 3 www inteco com pl ELECTROMAGNETIC COMPABILITY This equipment when operated in accordance with the supplied documentation does not cause electromagnetic disturbance outside its immediate electromagnetic environment COPYRIGHT NOTICE Inteco Sp zo o rights reserved No part of this manual may be reproduced stored in a retrieval system or transmitted in any form or by any means electronic mechanical photocopying recording or otherwise without the prior permission of Inteco Ltd ACKNOWLEDGEMENTS Inteco Sp z o o acknowledges all trademarks IBM IBM PC are registered trademarks of International Business Machines MICROSOFT WINDOWS are registered trademarks of Microsoft Corporation MATLAB and Simulink are registered trademarks of Mathworks Inc Multitank System User s Manual 4 www inteco com pl CONTENTS 1 INTRODUCTION AND 2 asses e eese ee 7 SYSTEM OVERVIEW ecc ieteeeseeesxeseee duce cds 8 122 HARDWARE INSTALEATION con 10 1 3 SOFTWARE INSTALLA
15. in continuous bloom casting Mould level oscillations tend to stir foreign particles and flux powder into molten metal resulting in surface defects in the final product 1 The goal of the Multitank System design is to study and verify in practice linear and nonlinear control methods The general objective of the control is to reach and stabilise the level in the tanks by an adjustment of the pump operation or and valves settings This control problem can be solved by a number of level control strategies ranging from PID to adaptive and fuzzy logic controls 2 3 4 The Multitank System has been designed to operate with an external PC based digital controller The control computer communicates with the level sensors valves and pump by a dedicated I O board and the power interface The I O board 15 controlled by the real time software which operates in MATLAB Simulink RTW RTWT rapid prototyping environment This manual describes the system the installation of the multitank software the mathematical models and theory related to control experiments the identification procedures how to use the library of ready to use real time controllers 9 9 9 9 step by step how to design and apply ones own controller in the MATLAB Simulink RTWT environment This is assumed that a user has an experience with MATLAB and Simulink from MathWorks Inc 1 1 SYSTEM OVERVIEW The tank system consists of a number of tanks placed abo
16. properly and if level in the tank 1 is measured correctly After clicking Test Pump and Tank 1 Level button the pump starts and works 20 seconds Then the pump is stopped and the liquid level in the tank 1 is plotted Fig 2 5 In the Step 4 the valve in the tank 1 opens and the levels in the tanks 1 and 2 are measured The measurements are plotted Fig 2 6 Figure No 1 Fig 2 5 The proper operation of the sensors level in the tank 1 the pump works and valve 1 is closed Figure No 1 Fig 2 6 Levels in the tanks 1 and 2 valve 1 is opened e In the Step 5 the valve 2 is opened and the levels in the tanks 2 and 3 are measured Results are shown in Fig 2 7 LT ulnis File Edit Insert Tools Window Help 2 2 Test results of the tank 2 valve and level measurements in tank 2 red and tank 3 blue 0 14 Level e c e ceo N 2 m EY Az 0 02 0 5 10 15 20 25 Time sec Fig 2 7 Levels in the tank2 and 3 valve 2 is opened In the Step 6 the valve 3 is opened and the level in the tank 3 is measured The results are shown in Fig 2 8 File Edit Insert Tools Window Help osmalar pez Test results of the tank 3 valve and level measurements in tank 3 0 1 Level m e m Time sec Fig 2 8 Level in tank 3 valve 3 is opened In the step 7 the logical limit switches built into the FP
17. system If a user wants to build his own application he must copy this driver to a new model After clicking the Tank System Device Drivers button the window shown in Fig 3 13 opens File Edit View Simulation Format Tools Help 5 amp Bs m 100 Fig 3 13 Tanks system Device Drivers The driver has four PWM inputs The first input Pump controls the DC pump The inputs Valvel Valve2 and Valve3 control the valves of the upper middle and lover tanks There are three analog outputs of the driver Levell Level2 Level3 and one digital output Alert Each analog output represents the liquid level in the tank displayed in metric units The frequency signal of the level sensor is prescaled to the metric units inside the device driver block Fig 3 14 Each level sensor is described by two parameters Gain and Bias see Section 5 1 These parameters should not be changed inside the device driver To modify a parameter of the level sensor characteristic curve the following commands should be type in MATLAB command window gt gt aux tank Creating object aux of the tank class gt gt set aux ScaleCoeff 0 0380 0 0380 0 0380 0 0 0 0 Changing the Gain parameters The first value of the vector corresponds to the Gain parameter of the upper level sensor characteristic etc see section 5 gt gt set aux 10 0020 0 0020 0 0020 0 0 0 01 Changin
18. the computer No of detected boards Presents the number of detected RT DAC PCI boards If the number is equal to zero it means that the software has not detect any RT DAC PCI board When more then one board is detected the pull down board list must be used to select the board connected with the program Board Contains the list applied for selection of the board currently used by the program The list contains a single entry for each RT DAC PCI board installed in the computer A new selection executed at the list automatically changes values of the remaining parameters within the frame If more then one RT DAC PCI board is detected the selection at the list must point to the board applied to control the multitank system Otherwise the program is not able to operate in a proper way Bus number Shows the number of the PCI bus where the current RT DAC PCI board is plugged in The parameter may be useful to distinguish boards when more then one board is used and the computer system contains more then single PCI bus Slot number It is the number of the PCI slot where the current RT DAC PCI board is plugged in The parameter may be useful to distinguish boards when more then one board is used Base address Contains the base address of the current RT DAC PCI board The RT DAC PCI board occupies 256 bytes of the I O address space of the microprocessor The base address is equal to the beginning of the occupied I O range The I O space is
19. the same way as other blocks from the Simulink library The only difference consists in applying the Real Time Windows Target RTWT to create the executable library which runs in the real time mode The only goal of the control is to stabilize the liquid level in the upper tank by the relay controller The valves control signals for the upper middle and lower tanks are set to 0 6 1 0 1 0 respectively The mask of the Relay block is given in Fig 3 16 The characteristic corresponding to the relay controller is presented in Fig 3 17 Block Parameters Relay Relay Dutput the specified on or off value by comparing the input to the specified thresholds The on off state of the relay is not affected by input between the upper and lower limits m Parameters Switch on point 015 Switch off point 0 14 Dutput when on o Dutput when off 1 o Show additional parameters Cancel Apply Fig 3 17 Relay controller characteristic Fig 3 16 Relay controller parameters curve PWM control signal 0 14 0 15 Level m Notice that the control generated by the controller takes two values 0 and 1 The switching limits are 0 15 m and 0 14 m It means that the liquid level will be changed between these limits except beginning of experiment relative to initial conditions with the speed corresponding to the operation of DC pump and Valve fixed settings equal
20. to be selected In our example the fifth order integration method ode5 is chosen The Stop time field defines the length of the experiment This value may be set to a large number Each experiment can be terminated by pressing the Stop real time code button The Fixed step solver is obligatory for real time applications If you use an arbitrary block from the discrete Simulink library or a block from the drivers library remember that different sampling periods must have a common divider Third party compiler is not requested The built in Open Watcom compiler is used to create real time executable code for RTWT The RTW tag is shown in Fig 7 60 The system target file name is rtwin tlc It manages the code generation process Notice that rtwin tmf template makefile is used This file is default one for RTWT building process Configuration Parameters Tank3 Relay Configuration x m Target selection Select n Solver System target file Browse Data Import Export Optimization Language G Diagnostics Description Real Time Windows Target Sample Time Data Integrity Documentation Conversion Generate HTML report Connectivity Compatibility Model Referencing Hardware Implementation m Build process i Model Referencing TLC options E o o C Real Time Worksh Make command rtw Comments Symbols Templ
21. 0 p Fig 6 53 Tank system fuzzy controller The results of experiments are given below Fig 6 54 seu jorjuoo 250 300 350 400 Time s 200 100 150 200 250 300 350 400 450 500 Time s 50 Hi level Pump control signal 250 300 350 400 Time s 200 300 350 400 250 Time s level 200 level Fig 6 54 Results of fuzzy control experiment 7 PROTOTYPING AN OWN CONTROLLER IN RTWT ENVIRONMENT In this section the method of building your own controller is described The Real Time Windows Target RTWT toolbox is used Section 9 shows how to use the Tank software Here we introduce the reader how to proceed in the RTWT environment Before start test your MATLAB configuration by building and running an example of real time application Real time Windows Target Toolbox includes the rtvdp mdl model Running this model will test the installation by running Real Time Workshop Real Time Windows Target and the Real Time Windows Target kernel In the MATLAB window type rtvdp Next build and run the real time model To build the system that operates in the real time mode the user has to create a Simulink model of the control system which consists of the Tank Device Driver and other blocks chosen from the Simulink library build the executable file under RTWT see the pop up menus in Fig 7 5
22. 2 bit operating mode this frequency corresponds to the prescaler value 31 and should not be changed PWM PWMMode To set the prescaler value equal to 31 for all the PWM channels execute the command set TankObj PWMPrescaler 31313131311 8 6 PWMMODE Purpose Determines the 8 bit or 12 bit PWM mode Synopsis Mode get TankObj PWMMode set TankObj PWMMode NewMode Description PWM blocks can operate in two modes 8 bit resolution and 12 bit resolution The 12 bit mode is selected as the default one In the 12 bit mode a single PWM period contains 4095 impulses The time of logic output 1 is set by a number from 0 to 4095 In the 8 bit mode a PWM period contains 255 impulses The time of logic 1 is set by a number from 0 to 255 The 8 bit mode is used for high speed The 12 bit mode gives a high accuracy and is selected as the default mode for all the tank experiments The NewMode variable is a 1x6 vector Each element of these vectors determines the operating mode of the single PWM wave The value of 0 selects the 8 bit mode and the value of 1 selects the 12 bit mode See PWM PWMPrescaler Example To set the 12 bit PWM generation mode execute the command set TankObj PWMMode 11111 8 7 VALVE Purpose Set and get the control value for the valves Synopsis PWM get TankObj Valve set TankObj Valve NewValveControl Description The property determ
23. 30 4 2 MODEL OF CASCADE OF N TANKS inse ense ense sese nene ener ene n 30 4 3 NONLINEAR MODEL OF THE THREE TANK SYSTEM PUMP CONTROLLED SYSTEM eene 31 4 4 LINEAR MODEL OF THE TANK SYSTEM ccccccecececececececececececececececececececececeeeceeseeeseeescececececececeeeceeeseeseeeseeeecess 33 4 5 DEFINITIONS OF CONTROL TASKS cccccecececececececececececececececececseecececececeeecececececeeeseeececeeeeecececeeecececeeeeeeseeeeess 35 5 IDENTIFICATION it cete vessoect ves dee ee oleo 37 5 1 SENSOR CHARACTERISTIC 4 nnne isso oE nennen ERAN S ER arona n nennen nennen 37 5 2 IDENTIFICATION OF VALVES ER Dd 39 5 3 IDENTIFICATION OE PUMP corriente Ure esee ee a ce epe Renee err E eS 40 5 4 IDENTIFICATION OF PARAMETERS OF THE TANKS eene 41 6 REAL TIME CONTROL EXPERIMENTS 1 1 111331111 ette en sn asses e eese sese 44 6 1 DESIGN OF LINEAR CONTROLLER ssssesesssesesesescsesesesesesesescsessesesecesesesesesesesesesereseseeeseceeeseseeeseeereeeresereee
24. 5 Relay File Edit View Simulation Format Tools Help ux amp X Data explorer Simulink debugger Look up table editor Data class designer Model discretizer Real Time Workshop Build Model Build Subsystem Generate S Function External mode control panel Fixed Point settings Linear analysis Report generator Requirements management interface Pump Control Tank Filter2 Tank3 Generate RTW code 10095 4 5 2 Fig 7 55 Creating the executable under e start the real time code to run from the Simulation Connect to target and the Simulation Start real time code pull down menus 7 1 CREATING A MODEL The simplest way to create a Simulink model for the tank system is to use one of the models included in the Multitank Control Window as a template For example the Relay be saved as the MySystem mdl Simulink diagram The MySystem Simulink model is shown in Fig 7 56 LI MySystem 4 A ioj xj File Edit View Simulation Format Tools Help Da S gt b 579 Heo aes Ready 1100 lode 2 Fig 7 56 The MySystem Simulink model Now you can modify the model You have absolute freedom to develop your own controller Remember not to delete the Tank3 driver model This is necessary to support the data communicati
25. F H q Jy Jg 0 4 A H Hy The n x n matrix Jg takes the following general form for the cascade of n tanks Far 0 0 O0 aH OF L2 0 0 Jn 9 25 F 0 0 0 OH For n tank system the Jacobian matrices are in the following form B G4 BH C m C 0 T Ja Ho 0 0 2 1 Hina BIOL GL The linear model can be used for the local stability analysis and for the design of local controllers of the pump controlled system 4 5 DEFINITIONS OF CONTROL TASKS Under the Assumptions 1 the following example control problems can be formulated Pump controlled system open loop control For a defined objective function find a control q t transferring the system from a given initial state H to a given target state H in a minimum time while satisfying 0 q t S 4 0 H t amp H Example time optimal control 6 Close loop control of pump controlled system Fig 4 24 For a defined objective function find feedback control linear nonlinear q H H H stabilizing the system at the given desired state H while satisfying 0 lt 4 1 lt 4 0 lt 1 lt Controller Tank system Ci 2 C H Fig 4 24 Pump controlled system closed loop Valve c
26. GA chip structure RT DAC 4 I O board are tested The task of these emergency switches is to turn off the pump if the overflow in any of the tanks occurs When the pump is turned off and the level in the tank falls down under the emergency limit the pump starts again Close the manual valve in the tank 1 and click Overflow limits button The pump starts and works until the level in tank becomes equal to the value pre set in the FPGA chip To finish the tests click the Pump off button in the MultiTank Main Window to set the pump control to zero 2 3 TROUBLESHOOTING Problem Solution System does not work Check if the RTDAC PCI board is properly installed Check if the power interface is on Check if hardware stop button is released Pump does not work Check the cable connection between the pump and the power interface Overflow alert empty the water out of tank Valve does not open Check the cable connection between the valve and the power interface Overflow alert empty the water out of tank Level measurements are not correct Check the cable connection between the level sensors and the power interface Check if the rubber pipe is connected to the sensor and to the metal pipe in the tank 2 4 STOPPING PROCEDURE The system is equipped with the hardware stop pushbutton It cuts off the transfer of control signals to the tanks The pushbutton does not terminate the real ti
27. MAX edet UID eeu e UR 70 SIS SAFETY MUNG A eR ENERO 70 514 SAFETY ALERT IU MERE NINE 70 8 15 THE TANK CLASS QUICK REFERENCE 2 4 0 0 01 0 000000000000000000000000000000000000 72 nno 73 1 INTRODUCTION AND DESCRIPTION nk ag e controlled valves manual valves pump Fig 1 1 Multitank system The Multitank System Fig 1 1 comprises a number of separate tanks fitted with drain valves The separate tank mounted in the base of the set up acts as a water reservoir for the system Some of the tanks have a constant cross section while others are spherical or conical so having variable cross section This creates main nonlinearities of the system A variable speed pump is used to fill the upper tank The liquid outflows the tanks due to gravity The tank valves act as flow resistors The area ratio of the valves is controlled and can be used to vary the outflow characteristic Each tank is equipped with a level sensor based on hydraulic pressure measurement The Multitank System relates to liquid level control problems commonly occurring in industrial storage tanks For example steel producing companies around the world have repeatedly confirmed that substantial benefits are gained from accurate mould level control
28. NTROLLED SYSTEM Using the equations 4 3 for 3 the nonlinear model of tank system from Fig 4 21 is obtained dH 1 1 2 1 d 1 4 o 2 4 4 dt 1 1 where BH gt BH fluid level in the i tank i 1 2 3 cross sectional area of i tank at the level H defined as B H constant cross sectional area of the upper tank H B H cw bw variable cross sectional area for the middle tank 2max 5 ew4R R 3 J variable cross sectional area of the lower tank C resistance of the output orifice of i tank flow coefficient for i tank Geometrical parameters cm of the tanks are given in Fig 4 23 Himax 35 35 N 25 pz34 5 gt MEET gt 10 36 4 lt 3 gt 35 Fig 4 23 Geometrical parameters of the tanks Let us assume that pump control system is considered Rewrite the right sides of equations 4 4 in the form F x q F where 1 1 F 4 H q UT aO AGO 1 1 F H H C Hp C H5 gt 2 BH iHa BH 2 4 5 1 1 F H H C H5 C H 3 H H BH 213 BH 3 The model 5 4 for given initial conditions and control describes the dynamics of th
29. TION 6 con secet eoe tee a e tee eoe Ta 10 2 STARTING AND TESTING 8 5 1 estesa sas assa esee e teen asses eee 11 2 ER 11 2 2 BASIC WES RENTUR 12 2 3 TROUBLESHOOTING 55 15 2 4 STOPPING PROCBDUBRE 15 3 MULTITANK CONTROL WINDOW 16 SN M M 16 3 2 SIMULATION 20 3 3 RTWT DEVICE nnn nnn n n n n n nn en pasan pn sp pn p n p 22 3A DEMO CONTROLLBBS erret eter re e peter Peres ee 25 4 MATHEMATICAL MODEL OF THE TANK 65 8 4 4440 1 sese 28 4 1 LAMINAR OUTFLOW OF THE IDEAL FLUID
30. TLAB version R2008a b R2009a b R2010a b or R201 1a b with Simulink and RTW RTWT toolboxes not included RT DAC PCI programmable Input Output board to be installed in the PC included e CD ROM including the multitank software and the e manuals Manuals e Installation Manual e User s Manual The experiments and corresponding to them measurements have been conducted by the use of the standard INTECO systems Every new system manufactured and developed by INTECO can be slightly different to those gt standard devices It explains why a user can obtain results that are not identical to these given in the manual 1 2 HARDWARE INSTALLATION Hardware installation 15 described in the nstallation Manual 1 3 SOFTWARE INSTALLATION Insert the installation CD and proceed step by step the displayed commands 2 STARTING AND TESTING PROCEDURES 2 1 STARTING PROCEDURE Invoke MATLAB by double clicking on the MATLAB icon The MATLAB command window opens Then simply type Tank3 MATLAB brings up the Multitank Control Window see Fig 2 2 The user has a rapid access to all basic functions of the Multitank control and simulation systems from the Multitank Control Window It includes tests drivers models and application examples Tank3 File Edit View Simulation Format Tools Help Open Loop Tank System Device Drivers Fig 2 2 Multitank Control Window of the tanks system The Servo Control Window c
31. and the measurements of the multitank system as well as status signals and flags may be shown Moreover the control signals of three valves and the pump may be set manually Fig 3 9 The application contains four frames RT DAC PCI board Control Levels e Safety levels and flags The RT DAC PCI board frame presents the main parameters of the PCI board The Control frame allows to change the control signals The current liquid levels are given in the Levels frame The Safety levels and flags frame contains the maximum and minimum liquid levels the state of the safety flag and the state of the overflow alert The Display I O pushbutton activates the window that presents the contents of all RT DAC APCI input registers the data presented by the Tank Manual Setup program are updated 10 times per second ia Tank3 Manual Setup RT DACA PCI board No of detected boards Board Board 1 Bus number 2 Slot number 10 Base address 54272 0 0400 Logic version 105 Application Tank 1 0 driver status OK ee 11 Levels cm Safety levels cm and flags Current level Min level Activity flag Overflow alert Tank 1 0 02 28 81 27 67 v Safe Tank 2 0 12 29 26 28 00 Tank 3 17 04 28 91 27 66 Display 1 0 Help Fig 3 9 Manual Setup window RT DAC4 PCI board The frame contains the parameters of the RT DAC PCI boards detected by
32. ate makefile rtwin tmt Custom Code f Debug E t PAM Launch report after code generation completes Fig 7 60 Configuration parameters page for MATLAB If all the parameters are set properly you can start the real time executable building process For this purpose press the Build push button at the Real Time Workshop tag Fig 7 59 or simply CRTL B Successful compilation and linking processes generate the following message Model MyModel rtd successfully created Successful completion of Real Time Workshop build procedure for model MyModel Otherwise an error message is displayed in the MATLAB Command Window In this case check again your MATLAB configuration and simulation parameters 8 DESCRIPTION OF THE TANK CLASS PROPERTIES The Tank is MATLAB class which gives the access to all the features of the RT DAC PCI board equipped with the logic for the tank model The RT DAC PCI board is an interface between the control software executed by a PC computer and the power interface of the multitank system The board contains the following blocks PWM generation block the FPGA logic generates up to six signals The PWM prescaler for each PWM block determines the frequency of the corresponding PWM wave The PWM waves control up to five valves and the pump The default prescaler value is 31 which is equivalent to the PWM wave frequency equal to 305Hz This frequency is recom
33. e SC get TankObj ScaleCoeff set TankObj ScaleCoeff NewScaleCoeff The values obtained from the A D converter are multiplied by the scale coefficients to obtain the levels expressed in meters See Example Bias See Section 3 2 8 10 TIME Purpose Synopsis Description Return time information T get TankObj Time The Tank object contains the time counter When a Tank object is created the time counter is set to zero Each reference to the Time property updates their value The value is equal to the number of milliseconds past since the object was created 8 11 SAFETYFLAG Purpose Synopsis Description See Return the safety level flags SLF get TankObj SafetyFlag The I O board applied to control the multi tank system processes the liquid level measurements to avoid the overflow For each tank maximum and minimum liquid level is defined that turns on and off the safety alert flag If a safety flag is active the level in the appropriate tank influences the safety alert When the level in a safety active tank exceeds the maximum level the pump and the automatic valves are turned off The control is set by the I O board to zero regardless of the control value sent out from the MATLAB Simulink environment The system returns to the normal operating mode if all levels in safety active tanks fall under the minimum level Such a safety algorithm allows to a
34. e m Fig 6 43 H level Fig 6 44 H level 6 2 FUZZY CONTROLLER In this section we demonstrate how to develop and edit fuzzy inference systems by hand using Fuzzy Toolbox from Mathworks The following steps are essential in the design of a fuzzy controller e selection of input output variables e scaling the variables if necessary e definition of membership functions for all variables fuzzification development of the inference mechanism fuzzy rules e selection of the defuzzification strategy e re scaling the variables if necessary There are two methods of building a fuzzy controller interactive using the graphical tool and automatic using the clustering and adaptive neuro fuzzy mechanism There are also two types of fuzzy inference system Mamdani and Sugeno In this section we focus on the Mamdani inference system edited interactively This approach makes possible to understand in a direct way consequences of modifications being introduced into the inference mechanism and membership functions The proposed fuzzy controller for the tank system has three inputs and one output control The input variables are the following dH H Hi dH H4 H dH H Hi where H o H H desired levels H H current value of levels Hy H The presented fuzzy controller uses Mamdami inference system The Control Surface Fig 6 45 is generated with three membership function for dH
35. e process on the set of model admissible states 1H 0H S0 2 0 i 1 2 3 while process admissible states of the process are usually determined as X H SH eH 12123 imax Remark 1 The shapes of the tanks are such regular that the functions Fi F F are continuous and differentiable on X The admissible set of the control is given in the form 4 0 lt 4 lt Remark 2 In the most cases the set of process admissible states can be obtained as a closure of the set of admissible states of the model Nj For the model 5 4 for fixed 4 do we can define an equilibrium state steady state points given by H H H 0 F H H 0 2 3 q Q H X The equilibrium states can be calculated from the equations qo C H C Hg 4 6 or E A An 9 Il foes ON Als Assumption 1 Any admissible the corresponding is state admissible In the laboratory practice this assumption can be achieved by a proper setting of parameters 4 4 LINEAR MODEL OF THE TANK SYSTEM Taking into account the Remark 2 the linearized model is obtained by the Taylor expansion of 4 5 around the assumed equilibrium state dh where is the modified state vector deviation from the equilibrium state 4 qois deviation of the control relative to J are Jacobians of the function 4 5 Eu O
36. ed as 0 1983e 3 0 0765e 3 0 0496 31 Simulation The LQR simulation can be performed from the Tank System Multitank Control Window by invoking LOR from the group Simulation Models After clicking the LOR block the following window opens Fig 6 34 Tank 3 LQR Controller Control gt Saturation Control Levels Fig 6 34 The Simulink model for the LOR controller Notice that the control signal is q QO The steady state desired value H20 and QO were introduced into constant blocks 10 H20 H30 00 respectively see equation 5 6 as well as the optimal gain vector gain blocks K2 The identified parameters of the model as well as the starting point initial conditions can be set by double clicking the Tank Model block Fig 6 35 Function Block Parameters Tank3 Model Fig 6 35 Mask of the Tank Model block The simulation results are given in Fig 6 36 Fig 6 37 Fig 6 38 and Fig 6 39 The levels have achieved the desired value after 520 seconds approximately T r r r duc eu E EE CC CC FM eae Ce d cue poesia etiem eet E 1 sese petuum lg asinine ll ec Sanh ete ell be eon T E RE g agen eee ax CE SEL M Leen
37. eee SERRE HERE rig 5 5 RETI EM MESE 9 T 1 1 WT T eee n hh all UM S P ate eae ate viz T T T 300 400 500 600 300 400 500 600 time m time m Fig 6 36 Pump control signal simulation Fig 6 37 Level simulation pis T 0 16 T T T T T i ia je 1 1 1 1 b Y 3 T Rs ES EE jenen a i _ am 6 ero CH LEUR oe F 1 1 i i 1 1 1 1 1 pr EN cree EET CC D PEE 54040 MM 0024 loses I mes S Ico 1 1 1 1 1 j 100 200 200 600 100 200 300 400 500 600 time m time m Fig 6 38 Level simulation Fig 6 39 Level simulation Real time experiment LQ experiment can be performed from the Multitank Control Window invoking LOR Experiment from the Demo Controllers group
38. ers General Data history Tip try right clicking on axes Axes Number of axes 5 floating scope Time range 30 Tick labels bottom axis only Sampling Decimation 1 Fig 7 57 Setting the parameters of the Scope block Tank parameters o General Data history Tip try right clicking on axes Limit data points to last 12000 Save data to workspace Variable name TankDat4 Format Structure with time When the Simulink model is ready click the Tools External Mode Control Panel option and click the Signal Triggering button The window given in Fig 7 58 opens Select XT Scope set Source as manual set Duration equal to the number of samples you intend to collect and finally close the window Tank3_Relay External Signal amp Triggering Signal selection Block Path Trigger Source manual 7 EXE Trigger signal Pump Control Duration 12000 Delay fo Atm when connect to target Di ris iso 21 v Iv Select all Clear all on Trigger signal ha Go to block Port 1 Element any zi Hold off n Level os Revert Help Apply Close Fig 7 58 External Signal amp Triggering window 7 2 CODE GENERATION AND BUILD PROCESS Once a model of the system has been created the code for the real time mode can be generated compiled linked and downloaded into the target proc
39. essor The code is generated by the use of Target Language Compiler TLC see description of the Simulink Target Language The makefile is used to build and download object files to the target hardware automatically First you have to specify the simulation parameters of your Simulink model in the Simulation parameters dialog box Fig 7 59 The Real Time Workshop and Solver tabs contain critical parameters 5 Configuration Parameters Tank3_OpenLoop Configuration Active Simulation time Start time 0 0 Stop time 9999 Data Import E port i Optimization Diagnostics i Sample Time Data Validity Type Conversion Connectivity Compatibility Model Referencing Hardware Implementation Solver options Type Fixed step Solver ode5 D ormand Prince Periodic sample time constraint Unconstramed Fixed step size fundamental sample time 01 Tasking mode for periodic sample times SingleT asking Higher priority value indicates higher task priority Automatically handle data transfers between tasks t Model Referencing Real Time Workshop i Comments Fig 7 59 Solver tag The Solver tab allows you to set the simulation parameters Several parameters and options are available in the window The Fixed step size editable text box is set to 0 01 this is the sampling period in seconds The Start time has to be set to 0 Fig 7 59 The solver method has
40. f V4 sp 299 Level 1 Tank1 Scale Level 2 Bias 2 Scale 3 RT DAC Tanks Bias Tank3 Scale Frequencies Level 4 Bias Tank4 Scale repo gt g Tank5 Scale Level 5 Tank5 Bias Fig 3 14 The level sensor characteristic curve built into the device driver Tank4 and Tank5 are not used Do not make any changes inside the original driver They should be made only inside its copy The C source code of the all components of the driver is included in the DevDriv directory 3 4 DEMO CONTROLLERS In this group the preprogrammed examples of the tank control systems are given These demos can be used to familiarize the user with the tank system operation and help to create the user defined control algorithms Before starting an experiment real time executable file must be created by pressing Tools Real Time Workshop Build Model item in the Tools pull down menu Due to similarity of the examples we focus our attention on one of them After clicking on the Relay button the model of simple relay controlled tank system appears Fig 3 15 File Edit view Simulation Format Tools Help 22 w Etenad mE Tank 1 Relay Controller Fig 3 15 Control system with relay controllers Notice that this model looks like a typical Simulink model The device driver given in Fig 3 15 is applied in
41. g the Bias parameters The first value of the vector corresponds to the Bias parameter of the upper level sensor characteristic etc Example Change Gain parameter of the upper level sensor characteristic to 0 034 and Bias parameter of the lower level sensor characteristic to 0 0021 gt gt aux lt tank gt gt OldGain get aux ScaleCoeff Reading the old Gain parameters gt gt OldGain 1 0 034 Modifying the first Gain gt gt set aux ScaleCoeff OldGain Writing the new parameters gt gt OldBias get aux Bias Reading the old Bias parameters gt gt OldBias 3 0 0021 Modifying the third Bias gt gt set aux Bias OldBias Writing the new parameters This way can change parameters only temporary To change them permanent the parameters must be saved in the 2 Coeffm4 file This file is located in the matlabroot toolbox Multitank m directory The parameters are read from this file To see the variables stored in this file type the commands gt gt load mat TankV2PU_Coeff m4 gt gt who Your variables are TankBias TankScaleCoeff gt gt size TankBias ans 1 5 Length of the TankBias and TankScaleCoeff variables is 5 Only three elements are used but five must be stored the two last elements are prepared for future using The command to store permanently new parameters is as follows save matlabroot toolbox Multitank m TankV2PU Coeff m4 TankBias TankScaleCoef
42. i dH for input signals three membership function for control signal Fig 6 46 and 27 rules presented in Table 6 1 Pump Control m3 s dH1 m dH m Fig 6 45 Pump control surface versus dH and input signals j T F T T j F F Minimum Maximum Minimum Medium Maximum ME upper J SaN N D x 1 P Lo Ww 1 d 08 Na 1 t 1 08 Na Ls 1 Ls c te tie s d E MOS 2 N 1 JA N 1 A 2 1 JS 1 N 4 A 5 LX 1 B 1 1 5 FN 1 1 ft bee Mou ered SB gcc UE ule oed 1 1 1 1 E 1 13 1 1 1 9 1 NC 1 1 Y 1 9 1 1 1 b d A 1 1 1 1 1 A 1 1 E W 1 1 1 fin eq RN ie ic RS I ge NES N Vy 1 el ie N I 9 Ly 1 NI F 1 yl NU y N B 1 N v N ek ET 1 1 1 1 1 1 1 S i 1 LEON DT 1 1 1 1 1 DOW dew 1 1 Y N LZ N OMNIS P CIN a ES 1 1 1 1 1 1 1 1 1 1 1 1 1 1
43. ield the corresponding slider changes respectively its value If a slider is moved the value in the corresponding edit field changes as well STOP The pushbutton is applied to switch off all the control signals When pressed all the control values are set to zero Levels The frame presents the levels of liquid in three tanks The levels are scaled in centimeters Within this frame the safety system parameters are given as well Safety levels and flags There are maximum and minimum liquid levels associated with each tank If in any tank the liquid level is higher then the maximum level the RT DAC PCI board automatically activates the overflow alert If the overflow alert is active the RT DAC PCI board switches off all the control signals During the overflow alert the valves are closed and the pump is off regardless of the control signals The overflow alert is disabled if the levels in all tanks are lower then the minimum levels As during the overflow alert the automatic valves remain closed it is required to open manual valves to lower the liquid level below the minimum level Max level Min level The maximum and minimum levels of the liquid in the tanks The levels are given in centimeters Activity flag The state of the flags that enable the safety system for the respective tank Overflow alert The state of the overflow alert It displays the SAFE message if the overflow flag is inactive The ALERT message indicates that
44. ines the control value for the valves The NewValveControl variable is a 1x5 vector Each element of these vectors determines the control for a single valve starting from the upper tank The values of the elements of this vector can vary from 0 0 to 1 0 The value of 0 0 means the zero control and the vale of 1 0 means the maximum control If the control is equal to 0 0 the valve is closed If it is equal to 1 0 the valve is fully opened See Example 8 8 PUMP Purpose Synopsis Description See Example Pump PWM To open only the upright valve execute the following command set TankObj Valve 10000 Set and get the control value for the pump PWM get TankObj Pump set TankObj Valve NewPumpControl The property determines the control value for the pump The NewPumpControl variable is a scalar Its value can vary from 0 0 to 1 0 The 0 0 value means the zero control and the 1 0 value means the maximum control If the control is equal to 0 0 the pump is stopped If it is equal to 1 0 the outflow from the pump is the maximum Valve PWM To establish the 0 5 value control to the pump execute the following command set TankObj Pump 0 5 8 9 SCALECOEFF Purpose Synopsis Description Return and set the scaling coefficient of the liquid level measurements When a new value of this property is set the new scaling coefficients are stored in a file for future us
45. ive definite matrix R gt 0 R R in our case R is a scalar The pair is controllable The weighting matrices Q and R are selected by the designer but they must satisfy the above conditions This is most easily accomplished by choosing Q to be diagonal with all diagonal elements positive or zero The LQR optimal scalar control u is given then by 6 3 where is the optimal state feedback matrix The optimal control problem is now defined as follows find the gain K such that the feedback law 7 3 minimizes the cost function 6 2 subject to the state equation 6 1 The optimal feedback gain can be obtained by iterative solution of the associated matrix Riccati equation SA A S SBR B S4Q 20 To solve the LQ controller problem the gry function can be used from the Matlab Control System Toolbox The synopsis of is K S E Iqry A B C D Q R The LQ control simulations and experiments were performed for the following parameters e 1 0057e 004 C2 1 1963e 004 9 8008 005 These values reffers to fully open manual valves e Desired levels and control values 9 0 1425 m H5o 0 1007 m 0 1500 m and the corresponding steady state in flow QO 3 7958e 005 m s The starting point 0 H5 0 H3 0 2 0 m or c 1 0 The weighting matrices and R 0 0 0 15000000 0 1 The optimal gain matrix for considered parameters was calculat
46. low coefficient for i tank 1 2 3 For each tank the outflow experiment has been performed the data are collected and the characteristic curves has been fitted to the data Fig 5 30 For this purpose FMINS procedure from MATLAB Optimization Toolbox was applied for the objective function given as N ee DA Hz i k 1 i l J where H i the measurements for k tank at i time point i are the simulation results for k tank is a weighting coefficient for k tank 0 Co 00 Initial value Fig 5 30 Principle of tank parameters identification Finally the parameters given in Fig 5 31 Fig 5 32 and Fig 5 33 were found example C1 0 35 ON I S 1 1 1 1 1 1 1 1 1 1 1 1 1 1 m lt B 1 1 A Po 4 5 S eo uv M 65 aa a ae ea ee cC t CO S oo 1 c 4 o ES LIE etel 1 1 1 8 1 28 ir di I que Stn mA Lh v 1 1 1 ll 1 1 1 ere Strahl Da 1 e 8 we sees 1 o
47. m and 4 2 is Medium and dH3 is Maximum then Pump Control is Minimum 11 If dH is Medium and dH2 is Maximum and dH3 is Maximum then Pump Control is Minimum 12 4 is Maximum and dH2 is Medium and dH3 is Medium then Pump Control is Minimum 13 f dHl is Medium and dH2 is Maximum and dH3 is Medium then Pump Control is Medium 14 is Maximum and dH2 is Medium and dH3 is Minimum then Pump Control is Medium 15 4 is Medium and dH2 is Maximum and dH3 is Minimum then Pump Control is Medium 16 is Minimum and 4 2 is Medium and dH3 is Maximum then Pump Control is Maximum 17 If 4 is Medium and dH2 is Minimum and dH3 is Maximum then Pump Control is Medium 18 If 4 is Minimum and 4 2 is Medium and dH3 is Medium then Pump Control is Maximum 19 is Medium and dH2 is Minimum and dH3 is Medium then Pump Control is Maximum 20 If dHl is Minimum and 4 2 is Medium and dH3 is Minimum then Pump Control is Maximum 21 f dHl is Medium and dH2 is Minimum and dH3 is Minimum then Pump Control is Maximum 22 JIf dHl is Minimum and 4 2 is Maximum and dH3 is Minimum then Pump Control is Medium 23 f dHl is Maximum and dH2 is Minimum and dH3 is Minimum then Pump Control is Medium 24 Jf dHl is Minimum and 4 2 is Maximum and dH3 is Medium then Pump Control is Medium 25 dH1 is Maximum and dH2 is Minimum and dH3 is Medium
48. me process running in the background on PC Therefore to stop the task you have to use Simulation Stop real time code pushbutton from the pull down menus in the model window 3 MULTITANK CONTROL WINDOW The user has a quick access to all basic functions of the multitank system from the Multitank Control Window It includes tests drivers models and application examples Type at Matlab prompt Tank3 command and Multitank Control Window presented in Fig 2 2 opens The Multitank Control Window contains menu items divided into four groups Tools Basic tests and Manual Setup Simulation Models e RTWT Device Driver Demo Controllers 3 1 TOOLS The respective buttons in the TOOLS column perform the following tasks Basic Tests checks the fluid levels measurements DC pump operation and controlled valves operation The Basic Tests tool is described in details in section 3 2 Valve 1 ON fully opens the valve of the first upper tank Valve OFF fully closes the valve of the first upper tank Valve 2 ON fully opens the valve of the second middle tank Valve 2 OFF fully closes the valve of the second middle tank Valve 3 ON fully opens the valve of the third lower tank Valve 3 OFF fully closes the valve of the third lower tank Manual Setup opens the window giving access to the basic parameters of the laboratory 3 tank setup The most important data transferred from the RT DAC PCI board
49. mended for the valves and for the pump The PWM blocks can operate in two modes 8 bit resolution and 12 bit resolution The 12 bit mode is selected as the default one In the 12 bit mode a single PWM period contains 4095 impulses of the output prescaler frequency The time of logic output 1 is set by a number from 0 to 4095 In the 8 bit mode a PWM period contains 255 impulses of the output prescaler frequency The time of logic 17 is set by a number from to 255 The 8 bit mode is used for high speed The 12 bit mode gives a high accuracy Digital inputs are responsible for reading the signals from frequency sensors of a liquid levels The input is proportional to the liquid level The Tank class converts the value read from the D input to the level expressed in meters the parameters and measured variables from the RT DAC PCI board are accessible by the appropriate methods of the Tank class The object of the Tank class is created by the command object name tank The get method is called to read a value of the property of the object property value get object name The set method is called to set new value of the given property set object name property new property value The display method is applied to display the property values when the object name is entered in the MATLAB command window This section describes all the properties of the Tank class The de
50. nd pulse width of the PWM signal can be set using the PWM function from the Tank Class in MATLAB see section 9 or by setting parameters of the DC driver in Simulink The DC pump experimental characteristic curve Fig 5 29 represents dependence between outflow and in m s and the pulse width value of the PWM control signal The inverse averaged experimental DC pump characteristic curve can be applied in the control loop look up table of LQR real time controller example Section 7 x 107 Pump characteristic 1 8 Sid eed e SE pon ces A n M EU d d 5 0 8 pe E pix c o E gs dag cies pueden 7 0 4 See RE Z i fo xS D PME 7 0 4 0 5 0 6 0 7 0 8 0 9 1 PWM control Fig 5 29 DC pump characteristic curves measured for PWM frequency 4 8 kHz PWMPrescalerz1 and 12 bit mode 5 4 IDENTIFICATION OF PARAMETERS OF THE TANKS For fixed valves settings the following parameters of the mathematical models of the tank system Section 4 have to be identified experimentally Ci resistance of the output orifice of i tank f
51. ns 44 Simula E 46 Real time xperi Ment m T 48 6 2 FUZZY 255 49 Simulation ci COTON 52 Real time Experiment eee o I e 54 7 PROTOTYPING AN OWN CONTROLLER IN RTWT ENVIRONMENT eese eese 1 56 T T GREATING A MODED iiti reium i D E 57 7 2 CODE GENERATION AND BUILD 55 h 7 59 8 DESCRIPTION OF THE TANK CLASS PROPERTIES eee eee enne eese etn 62 58 2 ede dorf secedere ES 64 S BIAS 65 8 3 BITSTREAMVERSION i 65 ngu 65 REPRE 66 67 67 He 68 5 9 TR 68 IM 69 Multitank System User s Manual 5 S NC Nn IUD dB CAR C ME 69 8 12 SAFETY
52. on with the PCI I O board Though it is not obligatory we recommend you to leave the scope Tank block in Fig 7 56 You need a scope to watch how the system runs Other blocks in the window are not necessary for a new project Creating your own model on the basis of the old example ensures that all internal options of the model are set properly These options are required to proceed with compiling and linking in a proper way To put the Tank Device Driver into the real time code a special makefile is required This file is included to the Tank software You can use the most of the blocks from the Simulink library However some of them can not be used see MathWorks references manual for details The scope block properties are important for appropriate data acquisition and watching how the system runs The Scope block properties are defined in the Scope property window see Fig 7 57 This window opens after the selection of the Scope Properties tab You can gather measurement data to the Matlab Workspace marking the Save data to workspace checkbox The data is placed under Variable name The variable format can be set as structure or matrix The default Sampling Decimation parameter value is set to 1 This means that each measured point is plotted and saved Often we choose the Decimation parameter value equal to 5 or 10 It is a good choice to get enough points to describe the signal behaviour and to save the computer memory Tanke paramet
53. ontains testing tools drivers models and demo applications See section 4 for detailed description 2 2 BASIC TESTS This section explains how to perform the basic tests checking if mechanical assembling and wiring has been done correctly The tests have to be performed obligatorily after assembling of the system They are also necessary if any incorrect operation of the system was detected The tests have been designed to validate the existence and sequence of measurements and controls They do not relate to accuracy of the signals Tank3 BasicTest Edit View Simulation Format Tools Help Tank Basic Test Step 1 mi If all tanks are empty go to step 2 else Open all manual valves starting from the lowest one wait until the controlled tanks are empty and go to step 2 Tank Basic Test Step 2 lei Close all the manual valves and go to step 3 EN Fig 2 4 Message windows for Stepl and Step 2 Fig 2 3 The Basic Tests window Seven testing steps are applied The procedures allow user to check the pump operation three controlled valves three level sensors and overflow limits Double click the Basic Tests button The window given in Fig 2 3 appears The Step 1 and Step 2 prepare system for testing You must start tests with empty tanks and closed valves After clicking on Step 1 and Step 2 buttons the messages shown in Fig 2 4 are displayed In the Step 3 you can check if the pump works
54. ontrolled system Fig 4 25 Controller 7 Tank system Fig 4 25 Valve controlled system closed loop For a defined objective function find a feedback control C H stabilizing the system at the given desired state H while satisfying 0 lt C t lt C imax 0 lt 1 lt The target desired state is usually selected as the steady state equilibrium point of the process 5 IDENTIFICATION The identification of the triple tank system consist of the following steps e level sensors characteristic curves DC pump characteristic curve proportional valves characteristic curves e identification of parameters of the mathematical model The identified parameters and characteristic curves are used in simulation and real time experiments see Section 7 Parameters and characteristic curves given below and introduced into Simulink demo models are only examples Therefore it is recommended to identify the current system parameters before starting experiments 5 1 SENSOR CHARACTERISTIC CURVE three tanks are equipped with piezo resistive pressure transducer and the appropriate electronic interface for measuring the level of the liquid The pressure sensors provide a very accurate and linear frequency output proportional to the applied pressure of liquid The characteristic curve of the level sensor which describe liquid level
55. scription consists of the following fields Purpose Provides short description of the property Synopsis Shows the format of the method calls Description Describes what the property does Arguments Describes arguments of the set method See Refers to other related properties Examples Provides examples how the property can be used 8 1 BASEADDRESS Purpose Synopsis Description Read the base address of the RT DAC PCI board BaseAddress get TankObj BaseAddress The base address of RT DAC PCI board is determined by operating system Each Tank object has to know the base address of the board When a Tank object is created the base address is detected automatically The detection procedure detects the base address of the first RT DAC PCI board plugged into the PCI slots Example Create the Tank object TankObj tank Display its properties by typing the command TankObj Type BaseAddress Bitstream ver PWM PWMPrescaler PWMMode Valve Pump Scaling coeff Zero level Frequency Level Safety max min ag ert Safety Safety fl Safety al Read the base address bias Tank Object 54272 D400Hex x202 4095 0 4095 4095 31 31 31 31 31 1 1 4 1 0 0 0 1 0 0001 0 0001 0 0002 1 0 002 0 002 0 002 0 2430 4746 3143 0 0 029 0 238 0 171 0 0 306 0 306 0 306 0 0 297 0 297 0 297 0 1
56. sistence of simulation and experimental results are achieved only if a proper identification procedures has been applied including both the static and dynamic characteristic curves of the process 6 1 DESIGN OF LINEAR CONTROLLER The tank system demo presented in this section deals with the control task reach and stabilize the levels in tanks at steady state point Ho by an adjustment of the pump operation The steady state points can be calculated using the formula from Section 4 The design of the continuous LQ controller is presented below For a very small value of the sampling time the response of the discrete system converges to the response of the corresponding continuous system It is just our case The linearised dynamical model of the triple tank system is described by the linear differential equations see Section 4 dh C Ah B di 5 6 1 where the matrices A and as follows um 0 0 awH A a 0 Ww pp w c b H H 2max H 2max 0 Ca Ca Ww kS Haa H PH w CH where is equilibrium state of the nonlinear tanks system and is the modified state vector deviation from the equilibrium state H 4 qois deviation of control relative to from A typical quadratic cost function has the form 1 W 6 2 0 where e Qis a nonnegative definite matrix 020 0 0 e Ris a posit
57. sults of the experiment are shown in Fig 3 19 Pump control m3 s x 10 T T 4 49 1 fe up p VAI _ Ba pap tlie a fla sie i ss Ib op HI E L 1a 1L 2al lL Jjb udbLb a H p 1 vc 9 dq Wc t ta 4 4 4l 4H 4F H 10 20 30 40 50 60 70 80 Time s Time s Fig 3 19 Results of the relay controller demo real time experiment The liquid in the upper tank starts from 0 0 m level and oscillates between 0 14 m and 0 15 m levels The DC pump control signal is the square wave in the range 0 1 Parameters characteristic curves and plots given in the manual and introduced into Simulink demo models are only examples Therefore it is recommended to identify the current system parameters before starting own experiments 4 MATHEMATICAL MODEL OF THE TANK SYSTEM Modern methods of design of advanced controllers usually require high quality models of the process The classical procedure of a model development consists of the following steps
58. the alert system is active Deactivate Activate The pushbutton deactivates the safety flags of all tanks for 15 seconds If the safety flags are inactive the pumps and the valves operate regardless the liquid levels The deactivation allows manual decreasing of the levels below the minimum safety levels When the deactivation is in progress the caption of the button changes from Deactivate to Activate The safety flags are activated back immediately after the Activate button is pressed 3 2 SIMULATION MODELS In this group some examples of simulation models are given These models can be used to familiarise the user with the tank system operation and give templates for developing and testing the user defined control algorithms Only one model is described below Other examples are given in Section 7 After clicking on the Open Loop button the model appears Fig 3 10 ix Fie Edit view Simulation Format Tools Help Dic ml m Normal gt Tank 3 Open Loop Control Level Tank3 Model Lavals T Zz Fig 3 10 The triple tanks system simulation model The mask of the Tank3 Model block is given in Fig 3 11 parameters of the tank system model significant for control are available in this window They correspond to the mathematical model of the tank system The description of the parameters is given in the Section 5 Notice that some parameters are fixed e g geometry of tanks
59. then Pump Control is Medium 26 f dHl is Minimum and 4 2 is Maximum and dH3 is Maximum then Pump Control is Medium 27 f dHl is Maximum and 4 2 is Minimum dH3 is Maximum then Pump Control is Medium Simulation Simulation of the fuzzy control is performed for the following parameters Desired levels and control values 0 096 m lt 0 166 m 0 0 172 m 40 34 33 4 m s The start point 1 0 lt gt 0 0 0 0 m Before running the simulation and experiment write in the MATLAB Command Window gt gt Tank3 Fis readfis Tank3_Fis The Tank3_Fis fis file so called FIS matrix is loaded to the MATLAB workspace and can be used by Fuzzy Logic Controller block The simulation model of the fuzzy controller is given in Fig 6 47 and Fig 6 48 Fuzzy Controller Control gt Saturation Level3 gt Tank3 Model Saturation1 H10 0 096 Fuzzy Logic Controller Saturation2 Saturation3 Je Fig 6 47 Real time fuzzy controller 0 3433e 4 Block Parameters Fuzzy Logic Controller FIS mask 5 Parameters FIS File or Structure Cancel Tank3 Fis Fig 6 48 Mask of the Fuzzy Logic Controller block The examples of simulation results are given in Fig 6 49 Fig 6 50 Fig 6 51 and Fig 6 52
60. to 1 and 0 6 respectively prepare data acquisition click the Tools External Mode Control Panel item after click the Signal Triggering button The window given in Fig 3 18 opens Select XT Tank set Source as the manual option mark Arm when connect to Target option and close the window To start experiment choose the Tools pull down menus in the Simulink model window The pop up menus provide a choice between predefined items Choose the RTW Build item A successful compilation and linking process is finished with the following message Successful completion of Real Time Workshop build procedure for model Tank3 Relay If any error occurs then the message corresponding to the error is displayed in the MATLAB command window Return to the model window and click the Simulation Connect to Target option Next click the Simulation Start real time code item Tank3_Relay External Signal amp Triggering Signal selection Block Path Select all off Trigger signal Go to block Trigger Source manual v Mode normal x Trigger sional Fort 1 Element any Pump Control Duration 12000 Delay 0 Arm when connect to target Hald off Revert Help Apply Close Fig 3 18 External Signal amp Triggering window Direction fi ing Level After while observe the plots in the scope and click Stop Simulation after some time The re
61. tor Each element of these vectors determines the parameters of the single PWM wave The values of the elements of this vector can vary from 0 to 255 if the 8 bit mode is used and Example See from 0 to 4095 if the 12 bit mode 15 selected The value 0 0 means the zero control and the maximum means the maximum control The values of the PWM property are equivalent to the internal RT DAC PCI board values The most convenient way to control the pump and the valves if use the Valves and the Pump properties set TankObj PWM 1024 10242048007 Pump Valve PWMPrescaler PWMMode 8 5 PWMPRESCALER Purpose Synopsis Description See Example Determine the frequency of the PWM waves Prescaler get TankObj PWMPrescaler set TankObj PWMPrescaler NewPrescaler The input frequency for the PWM channels is equal to 40MHz This frequency is divided by the counter called prescaler which creates the PWM base period The NewPrescaler variable is a 1x6 vector Each element of these vectors determines the parameters of the single PWM wave frequency The valid prescaler values are numbers from 0 to 65535 The frequency of PWM wave is calculated from formula fad eder 1055 for 8 bit mode Sait 2 n prescaler 1 4095 for 12 bit mode The recommended working conditions of the pump and the valves require that the PWM waves frequency is approximately equal to 300Hz In the 1
62. ve each other Fig 1 1 Some of the tanks have a constant cross section while others are spherical or prismatic so having variable cross section Liquid is pumped into the upper tank from the supply tank by the pump driven by a DC motor The liquid outflows the tanks only due to gravity The output orifices act as flow resistors but can also be controlled from the computer The levels in the tanks are measured with pressure transducers The frequency signals of the level sensors are connected to the digital inputs of the RT DAC PCI multipurpose I O board There are four control signals send out from the board to the multitank system three valve controls and one pump control signal The appropriate PWM control signals are transmitted from digital outputs of the I O board to the power interface and next to the valves and to the DC motor The speed of the pump motor is controlled by a sequence of PWM pulses configured and generated by the logic of XILINX chip of the RT DAC board The liquid levels in the tanks are the system states The general objective of the tank system control is to reach and stabilise a desired levels in the tanks by an adjustment of the pump operation and or valves settings For the real system the levels in the tanks as well as the flow rates of the pump are limited To use the multitank system the following software and hardware components are required Intel Pentium compatible PC with gt Windows XP W7 gt MA
63. versus frequency can be essential consider as linear Level 2 Gain Freq freq bias 5 1 The parameter of the sensor characteristic curve can be obtained by measuring the liquid level and the corresponding frequency output for at least two points and fitting the characteristic curve For instance the measured levels of liquid and corresponding output frequencies of three sensors Tank1 Tank 2 and Tank 3 are shown in Table 1 Fig 5 26 presents an example of approximation obtained by identification methods for sensor 1 data given in Table 1 Table 1 Level sensor 1 sensor 2 sensor 3 m freq1 Hz freq2 Hz freq3 Hz 0 05 2805 2795 2743 0 15 3507 3486 3419 0 25 4192 4177 4084 Sensor 1 characteristic 0 3 0 95 UB 0 15 Level m d eee eed MUR UM PPP PR mra 005 1 0 05 2400 2600 2800 3000 3200 3400 3600 3800 4000 4200 Sensor output Hz Fig 5 26 Pressure sensor characteristic Red points measurements solid line fitting line When Table 1 is transferred to MATLAB the command polyfit freq1 Level 1 for sensor 1 gives 4 0 00014418888640 b 0 35485335425418 in the linear fitting equation Level a Frequency b Comparison to equation 5 1 results Gain 1 0 0001441888864 and Bias 1 2461 03124248978 Similar procedure gives for sensor 2 and sensor 3 following values
64. void the liquid overflow only in the case when the manual valves are closed If they are not closed the overflow may occur This property returns five safety flags SafetyMax SafetyMin SafetyAlert 8 12 SAFETYMAX Purpose Return the maximum allowed liquid level Synopsis SLF get TankObj SafetyMax Description When the level in a safety active tank exceeds the maximum level the pump and the automatic valves are turned off The control is set by the I O board to zero regardless of the control value sent out from the MATLAB Simulink environment The system returns to the normal operating mode if all levels in safety active tanks go below the minimum level This property returns five maximum levels See SafetyFlag SafetyMin SafetyAlert 8 13 SAFETYMIN Purpose Return the minimum liquid level that deactivates the safety alert Synopsis SLF get TankObj SafetyMin Description When the safety alert flag is activated the system returns to the normal operating mode if all levels in safety active tanks fall under the minimum level This property returns five minimum levels See SafetyFlag SafetyMax SafetyAlert 8 14 SAFETYALERT Purpose Return the safety alert flag Synopsis SLF get TankObj SafetyAlert Description When the level in a safety active tank exceeds the maximum level the pump and the automatic valves are turned off Such conditions trigger the safety See alert flag as
65. well The control is set by the I O board to zero regardless of the control value sent out from the MATLAB Simulink environment The system returns to the normal operating mode the safety alert flag is inactive if all levels in safety active tanks go below the minimum level This property returns O value for inactive safety alert flag and 1 value otherwise SafetyFlag SafetyMin SafetyMax 8 15 THE TANK CLASS QUICK REFERENCE TABLE Duty cycle of the PWM channels Prescaler values of the PWM channels Frequency to level scaling coefficients Frequency bias levels SafetyFlag Safety function flags for the tanks SafetyMax Maximum safety function levels SafetyMin Minimum safety function levels SafetyAlert Safety alert flag Time Return time information 9 REFERENCES 1 Graebe S F Goodwin G C Control Design and Implementation in Continuous Steel Casting IEEE Control Systems August 1995 pp 64 71 2 Cheung Tak Fal Luyben W L Liquid Level Control in Single Tanks and Cascade of Tanks with Proportional Only and Proportional Integral Feedback Controllers Ind Eng Chem Fundamentals vol 18 No 1 1979 pp 15 21 3 Heckenthaler T Engell S Approximately Time Optimal Fuzzy Control of a Two Tank System IEEE Control Systems pp 24 30 1994 4 Galichet S Foulloy L Fuzzy Logic Control of a Floating Level in a Refinery Tank Proc Of 3 IEEE Int Conference on Fuzzy Systems Orlando June 1994 pp 1538 1542
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