Journal of Cybernetics and Informatics. Slovak Society for Cybernetics and Informatics

Size: px

Start display at page:

Download "Journal of Cybernetics and Informatics. Slovak Society for Cybernetics and Informatics"

Teresa Heath
5 years ago
Views:

1 Journal of Cybernetics an Informatics publishe by Slovak Society for Cybernetics an Informatics Volume 13, 1 (home page) ISSN:

2 Journal of Cybernetics an Informatics 13 (1) PI CONTROLLER BASED ON GENETIC ALGORITHM FOR PMSM DRIVE SYSTEM Faeka Khater *, Ael Shaltout **, Essam Henawi *, an Mohame Abu El-sebah * * Electronics Research Institute, Dokki, Giza, Egypt. ** Cairo University, Giza, Egypt. Tel: Fax : khater@eri.sci.eg, aashaltout@yahoo.com, esam_henawi@hotmail.com, mohameibrahi3@hotmail.com Abstract This paper introuces a genetic-algorithm-base PI controller for position control of permanent magnet synchronous motor. The algorithm is propose for optimizing the PI controller gains in the position control. Different controllers' strategies are applie for the cascae-loop position controller, spee controller an current controllers. The controllers are compare together to select the best one. The objective target, which has been use for comparison, is the rise time, settling time, steay state error. In aition, the response of the evelope torque is investigate. Simulation results show that using genetic-algorithm-base PI controller gives the best performance. Keywor: PI controller, PMSM control, Genetic Algorithm 1 INTRODUCTION Permanent magnet synchronous motors (PMSM) have gaine an increasing popularity where they are wiely use in high performance rive applications such as servo systems, machine tool rives, computer peripherals, inustrial robotics, electric vehicles an other inustry applications [1-3]. This is because PMSMs have avantages as compare with inuction motors such as the absence of rotor copper losses which heats the rotor an ecreases the efficiency, high torque to inertia ratio, high efficiency an high power factor. These avantages make PMSMs competitive over inuction motors. Also PMSMs are preferre to c motors in applications that require variable spee rives because of the high torque-to-inertia ratio, an excellent power factor close to unity, high acceleration an high efficiency of PMSMs. PMSMs are use in many applications that require fast an accurate torque response in particular servo system with position control [4-6]. Position control system belongs to cascae control systems which require several control loops. In this paper, ifferent combinations of controllers are applie to the system using conventional PI controllers, fuzzy logic controller with conventional PI controller an PI controller optimize by Genetic algorithm. Simulation is carrie out to preict the performance of the rive system for all combinations. The objective target which has been use for comparison is the rise time, settling time, steay state error. In aition, the response of the evelope torque is investigate. It will be shown that applying genetic algorithm optimization to the PI controller in position control gives the best performance. This paper is organize as follows. Section 1 presents the introuction. In sections an 3, PMSM rive system escription an motor moel are given respectively. Fuzzy logic controller is reviewe in section 4. The propose technique using genetic algorithm is applie to optimize the PI controller parameters uring system operation using triangular istribution of controller parameters in sections 5 an 6. In section 7, simulation results will be shown. Section 8 gives conclusion.

3 F. Khater et al. / Journal of Cybernetics an Informatics 13 (1) 1-1 SYSTEM DESCRIPTION The block iagram of the PMSM rive system is shown in Fig. 1. The outer loop is the position controller. The intermeiate loop is the spee controller. The control action of this controller is the reference value of the q-axis current. The reference value of the -axis current is set to zero. The inner loops are the current controllers in which the control actions of these loops are the reference value of the q-axis voltage an the reference value of the -axis voltage. These reference values of the voltage vector (in the rotating reference frame) are transforme finally to stator three-phase reference frame. The main avantage of conventional PI controllers is that they are easy to implement. However, conventional PI controllers suffer from problems ue to changes in system ynamics or variation in operating points as a result of parameter variations. These problems may affect the system performance using controllers that have fixe parameters. To overcome such eficiency, more efficient controllers such as fuzzy logic controllers may be use or by on-line tuning of the parameters of the PI controller. Since the effects of the outer loop are ominant compare with the other loops, the inner loop (current controllers), are selecte to be conventional PI controller in all cases. The following combinations of controllers are to be consiere for investigation: Case 1: all the controllers are conventional PI controller Case : position controller is fuzzy logic controller an PI controller for spee an current controllers Case 3: position an spee controllers are fuzzy logic controllers an PI controller for current controllers Case 4: genetic algorithm-base PI controller (propose metho) for position controller an PI controller for spee an current controllers. For all controllers, the goal is keeping the absolute value of steay state error to be minimum. θ ref Position controller ω ref spee controller Iq Current controller Vq q-αβ transform inverter Loa M /t I = Current controller V abc-q transform ia ib θ 3 MOTOR MODEL Fig. 1 Block iagram of the PMSM rive system. The stator, q axes voltage equations of the PMSM in the synchronous rotating reference frame are given by:

4 F. Khater et al. / Journal of Cybernetics an Informatics 13 (1) V q = rsi q + Lq iq + Lωri + ωrλ m t (1) V = r s i + L i L q ω r i q t () For a uniform air gap motor (surface mounte PMSM), as in the case uner stuy, the -axis an q-axis inuctance L an L q are equal an can be enote as L s V q rsi q + Ls iq + Lsωri + ωrλ t V = (3) Where m = rsi + L s i L sω ri (4) q t V q an V are the q an axis voltages (v) i q an i are the q an axis currents (A) r s an L s are the resistance an inuctance per phase of stator wining respectively (Ω,H) λ is the flux linkage establishe by the permanent magnet as viewe from the stator m winings (wb) ω r is the rotor spee (ra/sec). Using the technique of fiel orientation control of the PMSM, the -axis current i is controlle to be zero to maximize the output torque [3, 7]. Thus, the motor torque expression can be given by the following equation: 3 P T e = * λmi (5) q The relation between the electromagnetic torque T e an the rotor spee ω r is expresse as the following: ω T + t r e = J + B m ω r T (6) L an Where: θ ω r r = (7) t J is the inertia of the rotor (kg.m ) B m T L θ r P is the amping coefficient (N.m.s/ra) is the loa torque (N.m) is the rotor spee (ra) is the number of poles 4 FUZZY LOGIC CONTROLLER The fuzzy logic is consiere as a mathematical theory combining multi-value logic, probability theory, an artificial intelligence to simulate the human approach when solving various problems by relating ifferent ata sets to make ecisions. It has been reporte that fuzzy controllers are more robust to parameter changes than conventional PI or PID controllers an have better noise rejection capabilities [8].

5 F. Khater et al. / Journal of Cybernetics an Informatics 13 (1) A stanar FLC is usually efine by a set of fuzzy parameters which specify any control action to be taken for a given process state. The FLC has two crisp inputs, error (e) an change of error (ce), an one crisp output, (out). FLC consists of three stages: fuzzification, rule base execution an efuzzification. In the first stage, the crisp variables (e), (ce) an (out) are converte into fuzzy variables E, CE an OUT. Each universe of iscourse is ivie into o number of fuzzy sets; seven fuzzy sets are use in this paper. Each fuzzy variable is a member of the subsets with a egree of membership ranging from (non-member) to 1 (full-member). In the rule base execution stage, the fuzzy variables E an CE are processe by an inference engine that executes a set of control rules containe in the rule bases. Different inference algorithms can be use to prouce the fuzzy set values for the output fuzzy variable OUT. The min-max inference algorithm is use in this investigation. In the last stage, efuzzification, the inference engine output variable is converte into a crisp value (out). Different efuzzification algorithms can be applie. The centroi efuzzification algorithm is use in this work. Due to its simplicity, the Mamani type fuzzy systems are use in the esign of FLC. 5 GENETIC ALGORITHM The Genetic algorithm is a metho for solving optimization problems that are base on natural selection (the process that rives biological evolution). The main avantages of the GA over other conventional optimization techniques are summarize as follows [9-13]: 1) GA technique uses a population of trials representing possible solutions of the problem, not a single point. As a result, the GA will be less susceptible to getting trappe on local minima. ) GAs use probabilistic rules to make ecisions when solving problems 3) GAs apply a performance inex assessment to guie the search in the problem space. A flow-chart of the GA algorithm optimization proceure is given in Fig.. Ranomly generate initial population Simulate system an compute the fitness of iniviuals Genetic rules: Reprouction Crossover Yes Is convergence criterion met? Maintain final parameters No Start new cycle En Fig. Flow-chart of the general GA

6 F. Khater et al. / Journal of Cybernetics an Informatics 13 (1) Iniviual solutions are initialize, then, the algorithm repeately moifies these solutions until a preefine convergence criterion is met. The convergence criterion of a genetic algorithm is a user-specifie conition. In general, the genetic algorithm uses three types of rules at each step to create the next generation from the current population; reprouction, crossover, an mutation. Details of these rules are liste in [1, 1]. The iniviuals are encoe in either binary or real numbers. Binary encoe numbers have many rawbacks. They take long time of calculation since they nee the real values to be converte to binary an at the en of each genetic algorithm cycle the binary numbers are converte back to real ones. In aition, ealing with binary numbers may affect the precision an conversion process. These problems affect the accuracy of the algorithm an as a result, real numbers are chosen in this work. 6 APPLICATION OF GENETIC ALGORITHM FOR TUNING PI CONTROLLER The escribe genetic algorithm that was applie successfully in [1] is use as a metho of tuning PI controller parameters of the position controller in this paper. The iniviuals are the parameter gains of the PI controller that are selecte in a certain interval. The gains are upate uring each generation achieving aaptive control which is the main ifference as compare to conventional controller that has constant gains. The population size, number of iniviuals is chosen as ten. Although bigger population size results in more accurate but this nee more time of calculations. Therefore, we see that population size of ten is a suitable choice in our stuy. Notice that ranom istribution of iniviuals is not suitable when applying them to the system because changing the controller parameters of the outer loop ranomly will result in ranom changes in the reference spee. As a result this paper proposes a triangular istribution of controller parameters to be applie to the system in successive short time intervals. The objective (fitness) function is selecte as the absolute of error an the target is to minimize this function. The operation of genetic algorithm base PI controller is explaine by the following steps: 1- Initialize a population of K p an K i having a size of '1'. i.e. K p (n) an K i (n) for n = 1 to n = 1. Define a perio of time equals 'ts', an objective function as absolute of error abs (error), an a constant R Є ],1[ - Set n = 1 an apply K p (n) an K i (n) to the system for a perio of 'ts' 3- At the en of 'ts' catch the value of error an hol it as abs (error). Then increment 'n' by one an apply K p (n) an K i (n) to the system for a perio of 'ts'. 4- Repeat step '3' until 'n' reaches Search for the minimum value of the objective function for n = 1 to n = 1 an catch the corresponing values of K p an K i. For example if the objective function is minimum when n = m then catch K p (m) an K i (m) an use them in the next generation. This is the reprouction stage. 6- Apply the crossover operation to the rest of K p (n) an K i (n). Again if the objective function is minimum when n = m, then apply the following formula [1, 1] to calculate the crossover iniviuals (new moifie K p (n) an K i (n) that will be use in the next generation for n = 1 to n = 1 an n m). K p (n) = R * K p (m) + (1-R) * K p (n) (8)

7 F. Khater et al. / Journal of Cybernetics an Informatics 13 (1) K i (n) = R * K i (m) + (1-R) * K i (n) (9) 7- Check meeting the conversion criterion then if it is not met repeat steps -6 otherwise stop genetic algorithm an maintain the final results of the fittest values of K p an K i an apply them continuously to the system. In the system uner stuy, the range of PI parameters is well known, therefore mutation rule may be eliminate. 7 SIMULATION RESULTS The combinations of controllers are applie to a loae PM rive system as a plant (given in section ). The reference position is a step function having a final value of 6 ra an the loa torque is 1 N.m. The motor parameters are given in the Appenix. The sampling time of the inner loop is set to µ sec, that of the intermeiate to 1 m sec, an of the outer loop to 5 m sec. Simulation has been carrie out using MATLAB Simulink. Case 1: Design of the conventional PI controllers is carrie out using Ziegler-Nichols metho [1, 14]. Figures 3-5 show the simulation results, notice that there is a torque ripple in T e, an the settling time is longer compare to the results of the later cases. The outer PI controller parameters have fixe values of 1 an.1 for K p an K i respectively. Case : FLC gives very goo performance compare with PI controllers but this controller suffers from the large calculations that have to be carrie out. Therefore, only the position controller is chosen as FLC an the spee an current controllers are selecte to be conventional PI controllers. Figures 6-8 show simulation results in this case. The steay state error of the output position, the percentage toque ripples an the settling time are reuce compare with case one. Case 3: Better performance is achieve as illustrate in Figures 9-11 but larger time of implementation of FLCs (both spee an position loops) slows on-line control. To overcome this problem, the fuzzy sets may be transforme to real values Є [-1,1] as shown in Table I. This transformation ecreases the calculation requirements but on the other han will increase rise an settling time. In case of using fixe values as in Table I, those values have to be on-line tune but will result in excessive execution time [15]. Case 4: The propose controller is simple to implement an gives goo performance at the same time. The propose controller is applie to the outer loop (position controller) since this controller has the ominant effects on the performance an the perios between successive samples is long enough for the optimization process to be carrie out. Transfer function of the controller is basically PI form with aaptive parameters through GA. Vector of initial population for K p an K i are given in Table II. Spee an current controllers are kept as conventional PI controller for the aim of simplicity. TABLE I. TRANSFORMATION FROM FUZZY SETS TO REAL VALUES NB NM NS ZE PS PM PB

8 F. Khater et al. / Journal of Cybernetics an Informatics 13 (1) TABLE II. INITIAL VALUES OF K P AND K I K p K i Figures 1-14 show simulation results in case 4. It is notice that applying genetic algorithm moifies the system behavior by reucing the rise time an settling time as compare to case 1 an very close to that of cases an 3 as shown in Fig. 15. The results show the superiority of the propose metho in the reuction of the algorithm an consequently the execution time. Steay state error is zero using the propose controller. Variations of proportional an integral gains are illustrate in Fig. 16 an Fig. 17 which result ue to triangular variations of the position controller gains to avoi any suen changes in the reference spee. The evelope torque has a percentage of torque ripples which can be minimize in a future stuy. Fig. 3 case 1: Rotor position an spee, t (sec) Fig. 4 case 1: Phase currents (A) t (sec) Fig. 5 case 1: Develope torque (N.m) t (sec).

9 F. Khater et al. / Journal of Cybernetics an Informatics 13 (1) Fig. 6 case : Rotor position an spee, t (sec) Fig. 7 case : Phase currents (A) t (sec) Fig. 8 case : Develope torque (N.m) t (sec). Fig. 9 case 3: Rotor position an spee, t (sec).

10 F. Khater et al. / Journal of Cybernetics an Informatics 13 (1) Fig. 1 case 3: Phase currents (A) t (sec) Fig. 11 case 3: Develope torque (N.m) t (sec). Fig. 1 case 4: Rotor position an spee, t (sec) Fig. 13 case 4: Phase currents (A) t (sec).

11 F. Khater et al. / Journal of Cybernetics an Informatics 13 (1) Figure 14 case 4: Develope torque (N.m) t (sec) ,3, Fig. 15 cases 1,, 3, an 4: Position θ (ra) t (sec) Fig. 16 Variation of proportional gain k p uring operation Fig. 17 Variation of integral gain k i uring operation.

12 F. Khater et al. / Journal of Cybernetics an Informatics 13 (1) CONCLUSIONS Combinations of controllers are applie to cascae control system to rive a permanent magnet synchronous motor in servo application. The controllers inclue conventional PI controller, fuzzy logic controller an PI controller with on-line tuning using genetic algorithm. Tuning of PI controller parameters base on genetic algorithm is propose an applie to the position controller of a PMSM. Triangular istribution of controller gains is introuce to avoi any suen changes in the reference spee which is the output of this controller. The controller is simple to implement compare with FLC. Simulation results show goo performance using the propose algorithm in rise time, settling time an steay state error. APPENDIX Motors parameters Power: 1.7 kw Frequency: 15 Hz Line Voltage: 38 V Line Current: 3.4 A No. of Poles: 6 Rate Spee: 3 rpm Stall Torque: 5.4 Nm Torque Constant: 1.6 N.m/A Rs: Ω /phase Ls: 7.75 mh/phase REFERENCES [1] Krause P. C. an Wasynczuk O.: Electromechanical motion evices, McGraw- Hill, [] Rahman A. an Zhou M. A: Analysis of brushless permanent magnet synchronous motors, IEEE Trans. In. Elect., vol. 43, no., April 1996, ] Khater F.M.H., Ahme F.I., an Abu-Elsebah M.I.: Design an implementation of avance PMSM rive system, in Proc. of Int. Symposium on Flexible Automation, Osaka, Japan, July 1-1, 6, [4] Lin F. J.: Real-Time IP position controller esign with torque feeforwar control for PM synchronous motor, IEEE Trans. In. Elect., vol. 44, no. 3, June 1997, [5] Su W. T. an Liaw C. M. : Aaptive positioning control for a LPMSM rive base on aapte inverse moel an robust isturbance observer, IEEE Trans. Power Elect., vol. 1, no., March 6, [6] Ogasawara S., an Akagi H.: Implementation an position control performance of a position-sensorless IPM motor rive system base on magnetic saliency, IEEE Trans. In. Appl., vol. 34, no. 4, July/August 1998, [7] Vas P.: Sensorless vector an -axis torque control, Oxfor University Press, May [8] Reznik L.: Fuzzy controllers, Biles Lt, [9] Genetic algorithm an -axis search toolbox user s guie, Copyright by the MathWorks, Inc, 4. [1] Man K. F., Tang K. S., an Kwong S.: Genetic algorithms: concepts an applications, IEEE Trans. In. Elect., vol. 43, no. 5, October 1996, [11] Kristinsson K., an Dumont G. A.: System ientification an control using genetic algorithms, IEEE Trans. Syst., Man, an Cybernetics., vol., no. 5, Septemper/October 199,

13 F. Khater et al. / Journal of Cybernetics an Informatics 13 (1) [1] Khater F., Shaltout A., an Henawi E.: Tuning of PI controller base on genetic algorithm, in Proc. Of the n International Conference on Avance Control Circuits & Systems (ACCS'8), Cairo, Egypt, March 3 April l, 8. [13] Silva W. G., Acarnley P. P., an Finch J. W.: Application of Genetic Algorithms to the Online Tuning of Electric Drive Spee Controllers", IEEE Trans. In. Elect., vol. 47, no. 1,Febr uary, [14] Jantzen J.: Tuning of fuzzy PID controller, Technical University of Denemark, Department of Automation, Tech. report no. 98-H 871, [15] Chan P. T., Ra A. B., an Tsang K. M.: Optimization of Fuse Fuzzy Systems via Genetic Algorithms, IEEE Trans. In. Elect., vol. 49, no. 3, June,

Interior Permanent Magnet Synchronous Motor (IPMSM) Adaptive Genetic Parameter Estimation

Interior Permanent Magnet Synchronous Motor (IPMSM) Aaptive Genetic Parameter Estimation Java Rezaie, Mehi Gholami, Reza Firouzi, Tohi Alizaeh, Karim Salashoor Abstract - Interior permanent magnet synchronous