Learning digital control systems with a low-cost educational platform

Proceedings of 2005 CACS Automatic Control ConferenceTainan, Taiwan, Nov 18-19, 2005Learning digital control systems with a low-cost educational platformChyi-Shyong Lee, Juing-Huei Su, Yu-Li Wang, Chia-Ruei Lee, and Jia-Shing FuLunghwa University of Science and Technology, Taiwan, cslee@mail.lhu.edu.twAbstractThe most critical needs for future engineeringgraduates are skills to integrate their knowledge tosolve complex engineering problems. Designs ofdigital control systems are such examples becausethey involve knowledge of mathematics for modeling,feedback controller design, and knowledge ofmicro-controllers for implementation of digital controlalgorithms. Therefore, this paper introduces alow-cost and integrated educational platform to helpstudents learn step by step to solve the designproblems of digital control systems. Two practicalproblems about the servo control of dc-motors andtemperature control of a water-tank are used to leadstudents to get familiar with the platform, and thetheory of system modeling, identification, stabilityanalysis, feedback controller design, and evenself-tuning adaptive controller design with recursiveleast square identification algorithms.Key Words: digital control systems, educationalplatform.1. IntroductionControl systems theory and design are oftenbased on abstract mathematical concepts and physics.They are used to help students get familiar with thedynamics of the system to be controlled, and then findways to design a successful feedback controller tomeet prescribed specifications. Moreover, thefeedback controller is often constructed nowadays viasoftware algorithms in micro-controllers and analoghardware circuits for input/output of signals. This isbecause of the convenience of updating the algorithmsin software forms and the fast performanceimprovements of micro-controllers. Designs ofdigital control systems therefore involve knowledge ofmathematics for modeling, feedback controller design,and knowledge of micro-controllers forimplementation of digital control algorithms. Inorder to make the education both conceptual andexperiential [1], fast development and educationaltools for constructing a digital control system tovalidate the theory in textbooks and to learn practicalissues in implementation are necessary for studentsand engineers to quickly grasp the working principlesof a successful digital control system.Although the Quanser Inc. (www.quanser.com)has recently developed an educational platform thatdemonstrate control fundamentals by using a widerange of control methods, the product usually costshigh and not affordable to students. Chen andNaughton [2] also proposed an undergraduatelaboratory platform for control system design,simulation, and implementation based on the popularMATLAB/SIMULINK environment. The platformpresents an excellent environment which allowsstudents to focus all their effort on learning the controlsystem theory when controlling real world systems.The only drawback of this platform is that studentscan not have a clear picture of how to construct thecontroller in a micro-controller and the correspondingprogramming and implementation issues. This isbecause the environment is built on top of thereal-time operating system, RTLinux, theMATLAB/SIMULINK software, and a DSP board tohandle all the necessary signal input and outputfunctions. Therefore, all the students have to do is tocode the corresponding control algorithms asMATLAB script languages (.m files) or SIMULINKmodels. The environment is easy to use for students,but difficult for teachers to maintain. Moreover, forthose schools which do not purchase theMATLAB/SIMULINK software, it is impossible forthem to adopt the approach as an educational tool. Inorder to remedy the above problems and to benefitthose undergraduate students who are in general notwealthy, this paper presents a low-cost and integratedplatform to meet the needs. It is cheap and simpleenough that every student can build his own platformduring the course. Two practical problems about theservo control of dc-motors and temperature control ofa water-tank are used to lead students step by step toget familiar with the digital feedback control theory,and the software and hardware developingenvironment of the platform through implementationof the corresponding control algorithms.2. System Overview2.1 Hardware moduleThe proposed educational platform whose blockdiagram is shown in figure 1 is a single boardcomputer and it costs less than 1500 NT dollars (see

Proceedings of 2005 CACS Automatic Control ConferenceTainan, Taiwan, Nov 18-19, 2005table 1 for cost analysis). It consists of anATmega128 RISC CPU, an RS232 port tocommunicate with a PC, an in system programming(ISP) port for downloading programs from a PC to the128K byte flash memory, 6 pulse width modulation(PWM) output channels to drive power switches, 8A/D ports for accessing physical signals, an encoderinput port with resolutions being increased 4 times viaa programmable logic device (PLD), and severaldigital I/O ports. The reasons to choose an 8-bitmicroprocessor whose price is comparable to a digitalsignal processor (TMS320C24x) are threefold: 1)internal flash ROM size (128Kbyte) is larger, and canbe easily accessed via the ISP port; 2) softwaredeveloping environment can be constructed withoutany additional cost, and 3) the undergraduate studentsare more familiar with 8-bit micro-controllers thandigital signal processors (TMS320C24x). Thedrawback for this choice is that the computationalspeed is slower for multiplication and division,although this does not create too much trouble in ourexperiments.To download programs into the microprocessorby using the ISP port of ATmega128, a simple andcheap hardware interface circuit connected to theprinter port of a PC is necessary(www.lancos.com/e2p/avrisp-stk200.gif). Thecorresponding software, PonyProg2000, which runs atthe PC side can also be freely downloaded from theweb page www.lancos.com/ppwin95.html. Theencoder input circuit which is capable of increasingthe resolution 4 times of the original signals comingfrom an encoder is shown in figure 2. The idea isfrom an application note [10] by Microchiptechnology, Inc., and the programming equations ofthe PLD are listed in the following table:Table 1: Programming equations of the PLD forresolution enhancementPLD programming equations;---------------------------------------MODULE ENCODEDECLARATIONSIA , IB ,CLK,Mode PIN 2,3,1,4;UP,DOWN,U_D,DIR PIN 16,17,15,14;S1 ,S3, S2, S4,X1 NODE;EQUATIONSS2 := S1;S4 := S3;S1 := IA;S3 := IB;UP =(!S1 & S2 & S3 & S4+S1 & S2 & S3 & !S4 & Mode+S1 & !S2 & !S3 & !S4 & Mode+!S1 & !S2 & !S3 & S4 & Mode );DOWN =(S1 & S2 & !S3 & S4 & Mode+!S1 & S2 & !S3 & !S4 & Mode+!S1 & !S2 & S3 & !S4+S1 & !S2 & S3 & S4 & Mode );U_D := UP + DOWN;X1:=DIR;DIR=(UP # X1) &!DOWN;ENDThe resolution enhancement circuit can not onlygenerate two separate 4 times resolution up and downcount signals, it can also give an up/down countingsignal and a direction signal to meet different needs.The entire hardware circuit is shown in figure 3.Sensor Circuits:Temperature orcurrent ...Download program via ISP 8 A/D portsPersonal computer:communication &controlFigure 1.Figure 2.RS2322.2 Software moduleMicro‐controller:AVR mega128downEncoder counter:PLD for resolutionenhancement (4x)up6 PWMchannelsPhysical variablesΦ 1Φ 2Driver Circuits:for Motor or RelayThe hardware configuration of theeducational platformThe encoder interface circuit that provides4 times resolutionThe programming language used in theeducational platform is C, because of its portabilityand easy readability when compared with theassembly language.Thanks to the GNU project (www.gnu.org), theGNU C compiler for ATmega128 can be freelydownloaded from the web site www.avrfreaks.net, tohelp us construct the programming environment at nocost. The communication program shown in figure 4is written by using visual basic and provides functionsof loading control parameters into the microprocessor,receiving data of controlled variables from themicroprocessor through the serial RS232 bus,graphical representation of data, and saving data asMATLAB m-file format. Sample software codes aregiven to students such that more sophisticated analysistools could be implemented on top of them.3. ExperimentsTwo basic control problems are devised to helpstudents turn digital control theories into workingalgorithms in the educational platform, such that all

Proceedings of 2005 CACS Automatic Control ConferenceTainan, Taiwan, Nov 18-19, 2005the theories, the practical implementation issues, andproblem solving skills can be more efficiently learnedduring the course. The first one is digital servocontrol of DC motors, and the second one is digitaltemperature control of a water tank. They are simplesingle input single output (SISO) systems, and yetprovide enough theoretical and practical issues forstudents to learn.AVR mega128LM18200 H-bridge motor driverwith current sensingDC motor[3]. The mathematical models are then transformedto zero-order-hold sampled-data models [4]. Oncethe students are familiar with the modeling process,the coefficients of the corresponding discrete-timemodel for a DC motor can then be obtained by usingthe least-square estimation method [4, p.511], and thecoefficients of the corresponding analog model forheat transfer of a water tank can be found by using theon-line method proposed in [5], or the offline methodsin [9].RS232 portISP portFigure 3.PWM, ADC, and I/O portsencoder signalresolution enhancementencoder signal inputThe photograph of the entire hardwarecircuitFigure 4. The operation window of thecommunication programIn these two experiments, the H-bridge driverfrom the National semiconductor Corporation(www.national.com/pf/LM/LMD18200.html) is usedas a DC motor driver, and a solid-state relay is used todrive the heater in the digital temperature control of awater tank. The entire setup of the target systems areshown in figure 5. Both experiments consist of threeparts to lead students step by step to learn thenecessary digital control theories and to implement thecorresponding software codes. They are: 1)modeling and identification of physical systems, 2)performance and stability requirements of feedbackcontrolled systems, and 3) design of PID controllerswith anti-windup function, and tuning of controlparameters.3.1 Modeling and identification of physical systemsModeling of DC motors and heat transfer of awater tank can be found in text book by Franklin et al.3.2 Stability and performance requirements forfeedback controlled systemsStability and performance analysis of a feedbackcontrolled system are very important skills forstudents to make sure they will not destroy thehardware circuits and implement a usable controlalgorithm. Closed-loop stability assured by applyingthe Routh’s and Jury’s stability criterion [3-4], theNyquist criterion, and Bode’s gain-phase relationshipare concepts that students should keep in mind duringthe course. Time-domain specifications forperformance requirements of a step response are alsointroduced such that students will try to fine tune thecontrol parameters to meet the requirements. It isbecause our objective is to lead students to solvepractical digital control problems by using theeducational platform in a semester that those moreadvanced stability theory and frequency-domainspecifications for performance requirements are notincluded in our course.Table 1. Cost analysis of the educational platformPrice,Components and subsystemsNTD$ATmega128_16MHz 300Resolution enhancement circuit for75encoder signalsRS232 communication circuit 30In system programming circuit 60PCB board 150LMD18200 H-bridge driver circuit fordc motors500Solid-state Relay (12A) and temperaturesensor circuits300Total 14153.3 Design of PID controllers with anti-windupfunction and tuning of control parametersWhen the model parameters are at hand, themethods in [6, 8] about PID controller design and itsdigital implementation [4, p.306] and implementationof anti-windup functions [7, 4 p. 310] are used astheoretical background for digital feedback controllerdesign. This is because PID controllers are mostoften used in industrial control. After discussions ofthese theories, an initial software example code of the

Proceedings of 2005 CACS Automatic Control ConferenceTainan, Taiwan, Nov 18-19, 2005digital feedback controller is given to students suchthat they can modify the controller parameters andeven the controller structure [6] to see if the responsescoincide with the theoretical predictions. If not,double check of the software codes and theories canmake them more familiar with problem-solvingtechniques. Experimental results which compare theperformances of the servo control of dc motors withand without the anti-windup function are shown infigure 5. The robustness of the digital temperaturecontroller is shown via experimental results in figure 6by changing the amount of water in the water tank.Figure 5. The experimental results of digital servocontrol of DC motors with and without anti-windupfunction4. ConclusionsA low cost educational platform is devised in thispaper. It can be constructed for servo control of dcmotors and temperature control of a water tank forless than USD$ 50. Two experiments are devised tohelp students become familiar with the necessarycontrol theories and the corresponding softwareimplementation for the servo control of a dc motorand temperature control of a water tank. This canhelp encourage students to make their owneducational platform and learn to solve by themselvesmore practical digital control problems. To make theeducational platform more versatile, the USB portshould be used to increase the communication speedbetween the educational platform and the personalcomputer. This may be done with the help of theUSB interface device [11]. Moreover, the digitalsignal controller (dsPIC) provided by the MicrochipTechnology Inc. is another affordable choice ofmicro-controller for its fast computational speed andversatility. It is also easy to setup the developmentenvironment for the digital signal controller (dsPIC)without too much money.Figure 6. Robustness analysis of the digital PIDtemperature controller with and without anti-windupfunctionSince tuning of PID controller parameters may betedious in practice, techniques in auto-tuning ofcontroller parameters [2, 4] are introduced to studentsafter they successfully apply theories to design PIDcontrollers in both the problems. Because of thecomputational complexity, the self-tuning adaptivefeedback controller for servo control of dc motors byusing recursive least square (RLS) estimation can onlybe demonstrated in our dSPACE real time controlenvironment if the order of the reference model isgreater than or equal to 2. The student can stillimplement a convergent RLS algorithm on theeducational platform if the sampling frequency is nottoo high and a reference model of order 1 is used.Figure 7 shows the experimental results of asuccessful self-tuning adaptive feedback controller,whose reference model is of order 1. On the otherhand, the algorithm described in [5] for on-lineidentification of system parameters and auto-tuning ofPID controller parameters can be successfullyimplemented in the educational platform, because thedynamics for heat transfer in the temperature controlof a water tank is slow.Figure 7. The experimental results of a successfulself-tuning adaptive feedback controller, whosereference model is of order 15. References[1] D. S. Bernstein, “Enhancing undergraduatecontrol education,” IEEE Control SystemsMagazine, pp. 40-43, October 1999.[2] Y.-C. Chen and J. M. Naughton, “Anundergraduate laboratory platform for controlsystem design, simulation, and implementation,”IEEE Control Systems Magazine, pp. 12-20,June 2000.[3] G. F. Franklin, J. D. Powell, and A.Mami-Naeini, Feedback control of Dynamicsystems, 4 th edition, , chapter 2, Prentice-Hall,Inc., 2002.

[4] K. J. Åström and B. Wittenmark,Computer-Controlled Systems: Theory andDesign, 3 rd edition, Prentice-Hall, Inc., 1997.[5] K. J. Åström and T. Hägglund, ”Automatictuning of simple regulators with specificationson phase and amplitude margins,” Automatica,Vol. 20, No. 5, pp. 645-651, 1984.[6] R. Kelly and J. Moreno, “Learning PIDstructures in an introductory course of automaticcontrol,” IEEE Transactions on Edcuation, Vol.44, No. 4, pp. 373-376, November 2001.[7] C. Bohn and D. P. Atherton, “An analysispackage comparing PID anti-windup strategies”IEEE Control Systems Magazine, pp. 34-40,April 1995.[8] E. Eitelberg, “A regulating and tracking PI(D)controller,” International Journal of Control,Vol. 45, No. 1, pp. 91-95, 1987.[9] J. C. Basilio and M. V. Moreira, “State-spaceparameter identification in a second controllaboratory,” IEEE Transactions on Edcuation,Vol. 47, No. 2, pp. 204-210, May 2004.[10] Microchip Technology, Inc., “Servo Control of aDC-Brush Motor,” application note AN532,1997.[11] Royal Philips Electronics, PDIUSBD12: USBinterface device with parallel bus,www.semiconductors.philips.com/pip/PDIUSBD12D.html.AcknowledgementsThe authors would like to thank National ScienceCouncil for its financial support under grantNSC-94-2613-E262-004.Proceedings of 2005 CACS Automatic Control ConferenceTainan, Taiwan, Nov 18-19, 2005