An educational tool for controlling of SRM - Wiley Online Library

An Educational Tool for Controlling of SRM TUNCAY YIGIT,1 CETIN ELMAS2 1

Faculty of Engineering and Architecture, Department of Computer Engineering, Suleyman Demirel University, Isparta, Turkey 2

Faculty of Technical Education, Department of Electrical Education, Gazi University, Ankara, Turkey

Received 13 February 2006; accepted 26 February 2007

ABSTRACT: This article introduces an educational tool for a switched reluctance motor (SRM) drive system. It is prepared for undergraduate and graduate level students. Classical PI and Genetic PI controllers are used in SRM drive system. The Genetic PI controller was applied to the speed loop, replacing the classical PI controller. The tool software was implemented using Cþþ Builder on a PC. It has flexible structure and graphical interface. The students can be easily establishing a thorough understanding of both classical PI and genetic PI controller for a SRM drive system. The education tool allowed the student to interact with the SRM drive system and it is using controllers. Then it is responses on a dynamic and instantaneous basis under different operating conditions. ß 2008 Wiley Periodicals, Inc. Comput Appl Eng Educ 16: 268279, 2008; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20148

Keywords: switched reluctance motor; genetic algorithm; educational tool; interactive learning environments

INTRODUCTION During the last years, computer-based educational tools have been increasingly used in educating students of traditionally hard engineering subjects such as, electrical, mechanical, and chemical. Teaching in practical subjects should be an appropriate combination of theory, exercises and laboratory experimentation. With regard to the exercises and laboratory experimentation, a number of software packages that provide suitable learning environments have appeared in this last decade [1,2].

Correspondence to T. Yigit ([email protected]). ß 2008 Wiley Periodicals Inc.

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The electrical machinery course curriculum is also being updated with the advance of technology. Switched reluctance motors (SRMs) and their control are being covered in revised course curricula, causing an increase in the quantity of the material to be taught. However, the increase in quantity does not increase the understanding of the course. The presence of PCs offers many possibilities to students, researches and lecturers at technical college, and even at home and also distance-learning at another university [35]. There are many studies in the literature related with the SRM drive systems. All of them have been achieved from the programming, either in C language or in simulation software package [6]. There are also several software packages in the areas of SRM drives. The simulation studies of the SRM have been

EDUCATIONAL TOOL FOR CONTROLLING OF SRM

achieved with several software packages such as Spice [7], MATLAB/Simulink [8]. Spice software package is not ‘‘elegant’’ because Spice is especially adapted to electronic circuit simulation. Well-known commercial software packages such as MATLABSimulink, developed by Mathworks, Inc. (Natick, MA). MATLAB/Simulink has a flexible modeling environment to electric machinery. However, it has limited capability and is not well suited to electrical machines. Although students may still use MATLAB/Simulink and Spice to create their own simulations in a sequence, the use of these programs might be time consuming for them. In this study, an educational tool for an SRM drive is presented for cost-effective education and training. It is prepared for undergraduate and graduate level students. In the educational tool, classical PI controller was used to control the speed of the SRM and later replaced by Genetic PI controller. The educational tool* has been developed at Gazi University by the authors and can be installed on a PC operating system in the Windows environment (Windows 2000, XP, 2003 or NT) and freeware. This tool may be used by instructors for curriculum development end teaching. The tool has flexible structure and graphical interface. Both of controllers and SRM parameters can be change easily under different load and speed. The tool does not require code for simulation. The students can be easily establishing a thorough understanding of both classical PI and genetic PI controller for a SRM drive system. Then it is responses on a dynamic and instantaneous basis under different operating conditions.

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the SRM has some limitations. It must always be electronically commutated and thus cannot run directly from a DC bus or an AC line. Its salient structure causes strong nonlinear magnetic characteristics, complicating its analysis and control. The SRM shows strong torque ripple and noisy effects [9]. In order to explain the control technique, the basic principle of the SRM drive is discussed first. The structure of the SRM used here is shown in Figure 1a. The motor is a four phase, 8/6 pole SRM. The motor is excited by a inverter, which is shown in Figure 1b.

THE CHARACTERISTICS OF SRM The SRM is a very simple machine that uses salient poles on both stator and rotor, which are constructed from a single stack of laminations. The windings on the stator are of simple form and no windings are required on the rotor. This very simple structure greatly reduces its cost. Motivated by this mechanical simplicity together with the recent advances in the power electronics components, much research has been developed in the last decade. The SRM, when compared with the AC and DC machines, shows two main advantages. It is very reliable machine since each phase is largely independent physically, magnetically and electrically from the other machine phases. It can achieve very high speed because of the lack of conductors or magnets on the rotor. However, *

The tool is available from the authors for no cost by sending an e-mail to [email protected].

Figure 1 SRM (a) structure, (b) inverter, (c) phase

currents, and (d) torque. [Color figure can be viewed in the online issue, which is available at www. interscience.wiley.com.]

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While the rotor rotates, the four-phase selfinductances of the motor are varied. The four-phase currents are energized according to the self-inductances or the rotor angle. Take the A-phase as an example. When the A-phase inductance increases, the A-phase current has to be energized. The A-phase current is regulated to track the A-phase current command. The A-phase voltage and the A-phase torque, can be individually expressed as va ¼ i a R þ

dla La dia ia dLa ¼ ia R þ þ oe dt dt dye 1 dLa Ta ¼ i2a Nr 2 dye

ð1Þ

ð2Þ

where va is the A-phase voltage, ia is the A-phase current, R is the stator resistance, la is the A-phase flux linkage, La is the A-phase self-inductance, d is the differential operator, t is the time, ye is the electrical rotor angle, oe is the electrical speed, Ta is the A-phase torque, and Nr is the rotor pole number. The A-phase torque (Ta) is proportional to A-phase current (ia). As a result, the torque does not depend on the polarity of the A -phase current. In addition, to obtain a positive torque, the A-phase current has to be energized while the self-inductance La is increasing. On the other hand, when the A-phase inductance reaches its maximum value, the A-phase current has to be blocked instantaneously to avoid producing negative torque. The B, C, and D phase currents are controlled in the same way. The four-phase stator currents, therefore, are sequentially switched according to the rotor position or the slope of the selfinductance of the SRM. The four-phase current commands are shown in Figure 1c. By consecutive energization of these successive phases, a smoothing torque, shown in Figure 1d, can be obtained. The total torque of the motor is expressed as 1 dLa Te ¼ Ta þ Tb þ Tc þ Td ¼ i2 Nr 2 dye

ð3Þ

or ¼

ð4Þ

ð5Þ

where or is the mechanical speed, J is the inertia, TL is the torque of the external load, and B is the viscous frictional coefficient.

PI AND GENETIC PI CONTROLLER DESIGN OF THE SRM PI Controller A closed-loop, PI speed controlled SRM drive is shown in Figure 2. The speed error is processed through a proportional plus integral (PI) controller and a limiter to yield the torque command, Te . From the torque command, the current command i is obtained using the torque constant, Kt. This torque constant is for the linearized inductance. A proportional-integral (PI) controller is designed here to compare with the Genetic PI controller. Today, most controllers are implemented by computer algorithms [10]. This implies that the controller inputs are measured at certain sampling rates. For examples, the linear part of a classical PI controller with amplitude of the current command can be represented by Z i ¼ Kp ðo oÞ þ Ki ðo oÞ dt ð6Þ where i is the amplitude of the current command, Kp is the proportional control gain and Ki is the integral control gain. The rotor position is sensed by the position sensor and the derivative of the rotor position information gives the motor speed (o). The motor speed is compared with the set reference speed (o ) and the speed error (oe) is processed in the PI speed controller. The speed error oe and change in speed error oce as input variables at kth sampling instant is given by

where Te is the total torque of the motor, Ta, Tb, Tc, Td are the separate torques produced by the A, B, C, D phases, and i is the stator current amplitude of each phase. The central idea of the SRM drive system is that the phase currents have to be commutated properly according to the self-inductance. As a result, the self-inductance is very important. The electromechanical equation of the SRM is d 1 1 1 2 dLa i Nr or ¼ ðTe TL Bor Þ ¼ TL Bor dt J J 2 dye

dy dt

oe ðkÞ ¼ o oðkÞ

ð7Þ

oce ðkÞ ¼ oe ðkÞ oe ðk 1Þ

ð8Þ

The block diagram of the classical PI speed controlled SRM.

Figure 2


The output of the PI speed controller is the torque signal Te which is fed to the reference current. The output variable of controller is change in the reference current Di (k). A computer implementation of a PI controller can be expressed as a difference equation i ðkÞ ¼ i ðk 1Þ þ Di ðkÞ i ðkÞ ¼ i ðk 1Þ þ Ki oe ðkÞ þ Kp oce ðkÞ

ð9Þ ð10Þ

The values of Kp and Ki depend on the parameters of the drive system. The complex control structure of the SRM drive does not necessarily lead optimum stable performance by conventional pole placement technique. Hence the controller gains are selected by comparing the effects of Kp and Ki on the speed response of the drive. In this application, feedback signals are the rotor position y and the phase currents ia, ib, ic, and, id and the rotor position signal is used to calculate the speed. The switching signal generator is used to control turn-on angle yon, turn-off angle yoff, and pulse width modulation duty cycle.

Genetic PI Controller Recent literature has also explored the potentials of the genetic algorithm (GA) for motor drive applications [1113]. As an intelligent control technology the GA can give robust adaptive response of a drive with non-linearity, parameter variation and load disturbance effect. The GA has found application in the area of the automatic tuning process for conventional and intelligent controllers. The conventional controller design (i.e., PI controller) is based on mathematical model of the plant, which may often be unknown, ill-defined, non-linear, complex and multivariable with parameter variation. Thus, the conventional PI controller is not an all-purpose solution for any motor drive applications. The GA is an optimization routine based on the principles of Darwinian Theory and natural genetics [14]. Since the inception of the GA concept by Holland in 1975 it has been useful in solving a wide variety of problem. In the use of the GA, there are two important aspects; *

*

chromosome coding; defining the evaluation criteria.

The GA performs a parallel search of a parameter space by using genetic operators to manipulate a set of encoded chromosome which represents system parameters. The operation of the GA changes slightly

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depending on the base of the numbers to apply the genetic operators (crossover, mutation, reproduction, elitism). The selection process evaluates each chromosome by some fitness mechanism and assigns it a fitness value. Crossover is the procedure where two ‘‘parent’’ chromosomes exchange genetic information (i.e., a section of the string of numbers) to form two chromosome offspring. Crossover can be considered a form of local search in the population space. Mutation is a form of global search where the genetic information of a chromosome is randomly altered. Elitism is used the most fit member of the population is moved without modification into the next generation. The fitness of each of the members of the population is calculated using a fitness function that characterizes how well each particular member solves the given problem. In the genetic PI controller tuning, each chromosome has a genes as a possible proportional and integral gain values. Let Ci denote the ith controller (a string of digits parameterize the controller structure) in the population of controllers. For the optimal settings of PI controller parameters, the following quadratic performance index J is considered: Ji ¼

n X

aj p2j

ð11Þ

j¼1

where pj is a parameter used to evaluate the ‘‘goodness’’ of Ci, n is the number of those parameters, and the aj are weight factor. For example, pj might represent the amount of error between the reference speed and actual speed. The index J is selected because it ensures small settling time, small steadystate error, and small overshoots. The tuning parameters are adjusted so as to minimize the index J is by Fi ¼

1 1 þ Ji

ð12Þ

where F is the fitness function. Traditionally GAs have been designed to operate over base-2 number system. Our genetic algorithm uses the base-10 number system. While base-2 systems can be advantageous because they consist of smaller ‘‘genetic building blocks,’’ they have the disadvantage of more complicated encoding/decoding procedures and longer strings. While both bases work well, we chose to use base-10 because of the ease in which controller parameters can be coded into a chromosome. The GA uses the principles of evolution and genetics to select and adapt the controller parameters (Kp and Ki ) rather than trial and error. The parameters

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Figure 3

The block diagram of the Genetic PI speed controlled SRM.

of the genetic PI controller are defined as members of the population. Each individual parameters of the genetic PI controller is defined by a seven digit numbers. The first three digits describe the proportional gain Kp and last four digits describe the integral gains Ki . The genetic PI controller for the SRM drives is shown in Figure 3. The steps for speed control are summarized as follows: 1. Sample the speed signal of the SRM. 2. Compute speed error oe and change in speed error oce between reference speed and actual speed. 3. Chose the number of digits to represent each controller parameter Kp and Ki Chose crossover probability (pc) and mutation probability (pm). Generate an initial population of Kp and Ki gains (we make a random selection). 4. Generate Di (k), for each population member Ci, i ¼ 1, 2, . . ., n using the PI control laws. 5. Assign fitness to each controller of the population Ci, i ¼ 1, 2, . . ., n using the following performance index: p1 ¼ oe ðkÞ oe ðk 1Þ ¼ oce ðkÞ

ð13Þ

p2 ¼ o ðkÞ oðkÞ ¼ oe ðkÞ

ð14Þ

1 1 ¼ 1 þ Ji 1 þ ða1 p21 þ a2 p22 Þ

ð15Þ

Fi ¼

The fitness function must capture such dynamical changes so that it can evolve a new set of controllers for the new conditions.

Figure 4

Flowchart of the genetic algorithm.


6. Produce the next generation using GA operators (selection, crossover, mutation and elitism) and go to step (4). 7. The maximally fit Ci becomes C and send the change of control action (Di (k)) to control the drive. Where i (k) is the inferred change of reference current by the controller at the kth sampling time and defined as i ðkÞ ¼ i ðk 1Þ þ DiðkÞ

ð16Þ

where i (k 1) is the previous reference current. The detailed flowchart of the GA optimization program implementation is shown in Figure 4. In this flowchart, the maximum number of generations is used to determine the best chromosome. The first population is generated under the following assumptions. There are two parameters to be optimized, which are coded into a set of seven digits according to the base-10. The initial population is composed of 20 chromosomes, which are randomly selected. The initial population is formed, the fitness of each chromosome is evaluated and selection mechanism. It is applied to the parent population in conjunction

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with the crossover and mutation operators in order to generate the child population. Moreover the crossover and mutation operations are performed at the end of the selection process aimed reorganized the chromosomes in a manner that the ones with high fitness are next to each other.

THE EDUCATIONAL TOOL The tool works in a Windows environment. The SRM drive system operation can be observed on a PC monitor and can be modified by choosing appropriate windows. A control window and another selected window can be seen simultaneously by pressing desired button on the top of the screen.

Main Window A view of the main program window is shown in Figure 5. The main window of the tool has divided into two sections, namely control window, which is on the left and menu window on the right. In the control window, operation of the entire system (i.e., the working of SRM, simulation time, reference and

Figure 5 The main window. [Color figure can be viewed in the online issue, which is available at www. interscience. wiley.com.]

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actual speed values and load value) can be observed. By using the buttons at the bottom, the user may control the working and simulation process. ‘‘Start’’ button is used to start simulation, ‘‘Stop’’ button is used to stop simulation, ‘‘Exit’’ button is used exit simulation and ‘‘Help’’ button is used to aid about the tool. The menu window has four sub-windows and the contents of the menu window changes according to the chosen window from the menu. When one of the windows is chosen, the chosen window replaces the previous menu window. These windows are shown in Figures 69. Although a student may start the tool directly by using default values of the program given for a specific SRM and classical PI and Genetic PI controller, to start a new simulation, parameters related to the motor, controllers, and simulation should be entered by the user. The user must select SRM and Controller setup. Once the simulation has

been started, the user may select any window to see how the system is working. SRM and Controller setup windows enable users to define motor and controller parameters. At the beginning of the simulation, SRM and Controller window is used to define parameters used in simulation.

SRM and Controller Setup Window In the SRM and controller setup window is shown in Figure 6. SRM mechanical and electrical parameters, selection of controller and reference signal are defined according to the simulation. For example, a motor can be simulated according to the chosen controller type, that is, proportional gain and integral gain values and their limits for Genetic PI controller. Moreover, a user may define mechanical parameters, then SRM rotor and stator pole arcs can be observed.

Figure 6 The SRM and controllers setup window. [Color figure can be viewed in the

online issue, which is available at www.interscience.wiley.com.]


275

Figure 7 Genetic algorithm setup window. [Color figure can be viewed in the online

issue, which is available at www.interscience.wiley.com.]

Genetic Algorithm Setup Window In the Genetic algorithm setup window (Fig. 7) shows, genetic algorithms parameters (i.e., the generation in the genetic cycle, crossover rate, mutation rate) are defined and choosing crossover type and elitism. In the each of the sampling time, which is running a genetic cycle, fitness value, chromosome structures and candidate controller values (Kp and Ki) can be observed. Moreover, during the simulation, space of Kp and Ki parameter graphics for individuals of the generation and best individual of the controller and fitness function of generation and according simulation time can be observed.

SRM Modeling and Energy Conversion Window In the SRM modeling and energy conversion window (Fig. 8) shows, choosing process which kind of modeling for the SRM and a table for the measured modeling of the SRM. Moreover, during the

simulation, in this window, change in the inductance and energy conversion graphics can be observed.

SRM Graphics Window SRM graphics window (Fig. 9) shows speed, current, voltage, and torque graphics of the SRM. In addition, right of the graphics, there is time scale for them. It is used to changeable axis of graphics. Moreover, on the graphics can be change with a mouse. Reference speed and actual speed of the motor are plotted in different colors in the graphics window. On the left of the graphics, ‘‘save’’ button is used to store the graphic the PC and ‘‘print’’ button is used to print the graphic the article.

THE EVALUATION OF THE EDUCATIONAL TOOL The SRM and their control are an integral part of an electrical machinery laboratory exercises in the

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Figure 8 SRM modeling and energy conversion window. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

revised course curricula of electrical engineering departments at universities and technical colleges. Traditional laboratory exercises require groups of students to carry out an electrical machine test in which they adjust motor speed and load, remote from the test-rig, and they record performance data. The facilities required to perform such a test include the motor itself, a dynamometer to control the load on the motor and suitable instrumentation for measuring the desired variables. The data would at least include voltage, current, speed, and torque. One problem that is encountered with such laboratory exercises is that individual student is unable to perform a test himself

because of limited time and resources. Generally, the laboratory assignments only require three to four students to make all of the required measurements and adjustments. For larger groups of students, some may feel left out of the experience. Furthermore, if the motor is tested under limited conditions, the motor performance over its working range is not adequately demonstrated. The first exposure of the tool to student usage was in a fourth year electrical engineering course of 25 students, in which one of the modules taught focused on SRM. One of the laboratory assignments was an actual SRM with classical PI and genetic PI


277

Figure 9 SRM graphics window. [Color figure can be viewed in the online issue, which is

available at www.interscience.wiley.com.] controller. Before studying with the tool, the students are required to attend four 2-h theoretical sessions. Two sessions were about the SRM’s construction, operation principle, modeling of the motor and the drivers. One session was about classical PI and genetic PI controller. At last session, 2-h lecture is spared for the description of the tool. After lectures on these controllers, the students performed a series of tests with the educational tool and presented the results in a report with 1 week deadline. The students were asked to obtain classical PI and genetic PI controller for the SRM drive system and reported the results. The educational tool was

made undertaken were similar to what was prescribed for the actual SRM test. Hence, it was intended that the tool assignment would provide reinforcement of what was expected for the actual test as well as give each student the opportunity to spend time with the tool and obtain a thorough understanding of the responses of the SRM under different speeds and loads. Then students were conducted to motor-control lab where the SRM is driven by bridge inverter which is controlled by the TMS320F240 DSP set to observe operation and control of the SRM. The tool is expected to achieve following educational goals. One who uses this tool should be able to:

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Table 1 Evaluation Sheets Questions How much prior knowledge of the SRM did you have before attending this lab session? How much prior knowledge of the SRM driver did you have before attending this lab session? How much prior knowledge of the Genetic Algorithm you have before attending this lab session? How much prior knowledge of the classical PI and genetic PI controller? Did you understand the classical PI and genetic PI controller before attending this lab session? Did you tool stimulate you to work with the lab session? How much experience did you have before attending this lab session? Did the experiments of the lab session with the tool fit previous knowledge? Is the tool easy to use and user friendly? How much do you feel you have benefited from the tool? How do you judge your own work with the tool at this time? Does this lab session with tool build on thing you have learned in theoretical session? *

*

*

*

*

*

understand basics of the SRM drive system given in lectures; relate system parameters to system response; do virtual experiments on a PC to be ready for real laboratory experiments; improve his/her knowledge on classical PI and genetic PI control; find an appropriate best controller parameters from search space for drive; save in time while developing his/her knowledge.

Afterward results obtained by the use of the tool and the results obtained without using the tool were compared. Student response to the use of the tool was obtained through evaluation sheets. The feedback from the introduction of the educational tool was very positive. The scores for the laboratory assignments were higher than previous years and the understanding of this material seemed to be more uniform across the class as a whole. The tool has been successfully used by many students. Student response to the use of the tool was obtained through evaluation sheets as shown in Table 1. Moreover, the lecturers also may develop new ideas and teaching methods by using the tool. With this philosophy, it is aimed that the tool is available for everyone who wants to use or try it so that students may use it in a laboratory or at home.

CONCLUSIONS In this article, an educational tool for SRM drive system is presented for cost-effective education and

Plenty/very well

Sufficient/well

Some

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0

1

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0

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5 24 18 16

20 1 7 6

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training. Classical PI and genetic PI controllers are used in SRM drive system. The tool helps students to improve their trough understanding on both controllers and SRM. It is intended as an aid to teaching and may be used by instructors for curriculum development. The tool can be installed on a PC operating in a Windows environment (Windows 2000, XP, 2003 or NT) and freeware. The tool has flexible structure and graphical interface and enables users to change controller and motor parameters easily under different operating conditions.

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[6] H. Zelaya De La Parra and C. Elmas, Computer analysis of drive systems for the switched reluctance motor, European Conference on Power Electronics and Applications, EPE’91, Frenze, Italy, (1991), pp 360365. [7] G. Franceschini, S. Pirani, M. Rinaldi, and C. Tasconi, Spice-assisted simulation of controlled electric drives: An application to switched reluctance drives, IEEE Trans Ind Appl 27 (1991), 11031110. [8] F. Soares and P. J. Costa Branco, Simulation of a 6/4 switched reluctance motor based on Matlab/Simulink environment, IEEE Trans Aerospace Electron Syst 37 (2001), 9891009. [9] R. Krishnan, Switched reluctance motor drives: modeling simulation, analysis, design, and applications. CRC Press, Boca Raton, FL, 2001. [10] B. Sing, V. K. Sharma, and S. S. Murthy, Comparative study of PID, sliding mode and fuzzy logic controllers for four quadrant operation of switched reluctance

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motor, Power Electron Drives Energy Syst Ind Growth 1 (1998), 99105. W. G. da Silva, P. P. Acarnley, and J. W. Finch, Application of genetic algorithms to the on-line tuning of electric drive speed controllers, IEEE Trans Ind Electron 47 (2000), 217219. C. Elmas and T. Yigit, ‘‘Genetic PI controller for a Switched reluctance motor drive’’, Procedding of the International XII. Turkish Symposium on Artificial Intelligence and Neural Networks- TAINN 2003, C¸anakkale, Turkiye, 2003, Vol. 4, pp 320323. F. Cupertino, E. Mininno, D. Naso, B. Turchiano, and L. Salvatore, On-line genetic design of anti-windup unstructured controllers for electric drives with variable load, IEEE Trans Evol Comput 4 (2004), 347364. D. E. Goldberg, Genetic algorithms in search, optimization and machine learning, Addison-Wesley, Reading, MA, 1989.

BIOGRAPHIES Tuncay Yigit received his BS degree from the Department of Electrical Education, Gazi University, in 1997 and MSc and PhD degrees from the Institute of Science and Technology, Gazi University, in 2000 and 2005, respectively. He is currently an assistant professor in the Department of Computer Engineering at Faculty of Engineering & Architecture, Suleyman Demirel University, Isparta, Turkey. His research interests include intelligent control, genetic algorithm, web-based distance learning, engineering technology education, and scheduling and timetabling problems.

Cetin Elmas received his BS degree in electrical and electronics education and the MSc degree in electrical education from Gazi University, Ankara, Turkey, in 1986 and 1989, respectively, and the PhD degree in electronic and electrical engineering from the University of Birmingham, Birmingham, United Kingdom, in 1993. From 1987 to 1989 he was a research assistant with Gazi University, Faculty of Technical Education. From 1994 to 1995 he was an assistant professor at Gazi University, and he was an associate professor from 1995 to 2001. He is currently a full professor and the head of the Department of Electrical Machinery. His research interests include power electronics, electrical machines and drives, intelligent control, digital signal processing, and engineering technology education.