Learning digital control systems with a low-cost educational platform

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