Model Reference Adaptive Fuzzy Controller for Permanent Magnet Synchronous Motor

Transcription

1 Volume 50, Number 1, Moel Reference Aaptive Fuzzy Controller for Permanent Magnet Synchronous Motor A. MEROUFEL, M. MASSOUM an B. BELABBES Abstract: Conventional control epens on the mathematical moel of the plant being controlle. When this moel is uncertain, intelligent controllers promise better performance. This paper presents a theoretical stuy on moel reference aaptive fuzzy logic controller for vector controlle Permanent Magnet Synchronous Motor (PMSM) rive. In the propose system, Fuzzy Logic Control (FLC) is use to implement the irect current, the cascae spee, the quarate current an as well as the aaptation mechanism. The FLC requires expertise knowlege of the process operation for FLC parameter setting, an the controller can be only as goo as the expertise involve in the esign. To make the controller less epenent on the quality of the expert knowlege, the fuzzy spee controller is augmente by the moel following error riven fuzzy aaptive mechanism to compensate this eficiency an reuce the influence of parameter variations. The effectiveness an robustness of the propose scheme is emonstrate by some simulation results. Key wors: PMSM, Flux Oriente Control (FOC), FLC, an Moel Reference Aaptive Control (MRAC). 1. INTRODUCTION After the introuction of rare-earth magnetic materials, PMSM rapily gaine popularity in high performance, variable frequency rive applications. This popularity is justifie by several avantages over commonly use motors. The absence of the external rotor excitation eliminates losses on the rotor an makes PMSM highly efficient. In aition, the absence of the rotor wining reners slip rings on the rotor an brushes obsolete, an thus reuces the maintenance coasts. New magnetic materials are capable of creating high magnetic fiels which yiel high power ensity. This in turn implies rapi ynamic response ue to high torque to inertia ratio. In many applications, PMSM rives are preferre because the control system is usually less complex then that of fiel oriente inuction motor rives. In typical PMSM rives, classical PI controllers have been use, together with vector control metho, for spee control, but in inustrial applications, there are many uncertainties an the rive conitions are subject to change uring rive operation, so the performance quality of the pre-esign of the motor riving system iminishes. In orer to cope with this problem, many aaptive control techniques [1,2] have been propose. In most case, on line estimation of the system parameters is require resulting in complex controllers. Fuzzy control technique has been successfully applie to the control of motor rives in recent years [3,4]. It can be consiere as an alternative to conventional feeback approach in the control of complex nonlinear plants where mathematical moelling is inexact an uncertain. The avantage of FLC in compare to conventional systems resies in the fact that no mathematical moelling is require for the esign of the controller. The fuzzy controller uses a control rules set that is base essentially on the knowlege of the system behaviour an the experience of the control engineer. It has been pointe that fuzzy controllers, like 2009 Meiamira Science Publisher. All rights reserve.

2 26 ACTA ELECTROTEHNICA conventional PID controllers, cannot aapt themselves to changes in operation conitions such as varying mechanical parameters. To ensure optimum control performance over wie range of parameter variations an loa conitions some form of aaptation [5,6] is require. This paper presents a theoretical stuy on aaptive FLC for vector controlle PMSM rives using moel reference aaptive approach. This work is compose a review of PMSM FOC technique Then, FLC principle is presente an applie to rive PMSM fe by PWM voltage source inverter. The implementation of an aaptation mechanism using the reference moel approach an fuzzy reasoning is then consiere. The control performance of the fuzzy aaptive controller is evaluate by simulation uner Matlab/Simulink software for ifferent operating conitions. The results are compare with that provie by a non aaptive fuzzy controller. Implementation approaches of the propose aaptive FLC are iscusse an concluing putting into evience the interest an the impact of control metho which combines the avantages of fuzzy logic an aaptive control technique. 2. VECTOR CONTROL OF PMSM The voltage an flux equations for PMSM in the rotational -q reference frame can be expresse as: v = Ri s + φ ωrφq t vq = Ri s q + φ q +ωrφ (1) t φ = Li +φf φ q = Li q q The electromagnetic torque can be written as: 3 Te = p φfiq ( Lq L) i i 2 q (2) Where R s is the start resistance, stator inuctances in frame (,q), L, L are is the rotor spee, ( φ, φq) are stator flux, φ f rotor ω r q flux, ( ( i, i ) an ( v, v ) are respectively q q stator currents an stator voltages in the frame (,q) an T e is the electromagnetic torque. It is apparent that if we can control i to be zero then the torque is irectly proportional to i q. Hence, vector control is achieve by controlling i to be zero an i q to prouce the require torque. In orer to achieve a perfect control of each axis separately a ecoupling circuit is ae to the voltage equations (1) for eliminating the coupling terms. Then, the rive behaviour can be escribe by a simplifie moel expresse in the following equations v = Ri s + L i t (3a) vq = Ri s q + Lq iq t Te TL = J ω r + frωr t (3b) 3 Te = pφfiq = ktiq 2 Where J an f r are the rotor moment inertia an the friction coefficient, T L is the loa torque. Hence, the flux ( i ) an the torque ( Te ) are ecouple from each other an can be separately controlle as esire, we introuce a FLC in both inner an q current control loop an the outer spee loop PWM inverter Pulse With Moulation (PWM) technique is use to generate the require voltage or current to fee the motor or phase signals. This metho is increasingly use for AC rives with the conition that the harmonic current is small as large as possible. Generally, the PWM schemes generate the switching position patterns by comparing the three-phase sinusoial wave forms with a triangular carrier.

3 Volume 50, Number 1, va S1 V v = S (4) c b 2 3 v c S 3 Where v v v input voltages, V rectifie voltage a b c S ( i = 1, 2,3) i logic signals. V c e an e using the triangular or trapezoial membership functions shown in figure FLC DESIGN FOR PMSM The purpose of the work is to synthesize a controller without the exact knowlege of a moel, numerically simple an simulate on Matlab/Simulink allowing goo performance in terms of overshoot an fast accuracy uner the spee variations. The fuzzy logic toolbox base controller architecture is shown in figure1. Fig. 3. Membership functions an input output map. Each universe of iscourse is ivie into three fuzzy sets Negative (N), Zero (Z) an Positive (P). The fuzzy variable e an e prouce the fuzzification stage are then processe by an inference mechanism that executes a set of control rules containe in (3x3) table as shown in figure 4. e u N Z P N N N Z e Z N Z P P Z P P Fig. 4. Fuzzy control rules for u. The esign an synthesis of fuzzy controller will be presente using fuzzy logic toolbox with Matlab/Simulink. Four FLC blocks are use to control the spee, stator component currents ( i i q) an aaptation mechanism. These fuzzy controllers have the same structure with ientical inference mechanism an membership functions. The tuning of each FLC bloc is one separately. The FLC has three functional blocks as shown in figure 2 e t e Fig. 1. Fuzzy controller architecture. C 1j C 2j Fuzzification Inference mechanism Defuzzification Fig. 2. Internal FLC structure. u C 3j In the fuzzification stage, the input crisp variables are converte into fuzzy variables The number of rules is reuce in orer to optimise the inference mechanism execution output. The fuzzy rules are expresse uner the IF-THEN form. The crisp output of the FLC is obtaine by using Max-Min inference algorithm an the center of gravity efuzzification approach. In this paper, a trial an error approach is use to etermine an ajust these weighting factors C [( i = 1,2,3), ( j = sp, i, i, a _ mec)]. ij q 4. FUZZY MODEL REFERENCE ADAPTIVE CONTROLLER The esign of classical aaptive control systems is base on the mathematical moelling an the implementation of such systems is usually complex ue to the computationally intensive algorithms. However, in the fuzzy case, the aaptation is implemente using fuzzy reasoning which is simpler since it oes not nee complicate mathematical manipulation. The reference moel is use to specify the esire

4 28 ACTA ELECTROTEHNICA Fig. 5. Moel reference aaptive fuzzy controller for PMSM. performance that satisfies esign specifications. A fuzzy logic aaptation loop is ae in parallel to the fuzzy control feeback loop [7]. In the nominal case, the moel following is perfect an the fuzzy controller aaptation loop is ile. When significant parameter changes occur an or expert knowlege is not reliable an aaptation signal prouce by aaptation mechanism will be ae to the output signal of the irect fuzzy controller to preserve the esire moel following control performance [8]. Figure 5 Show a block iagram of the propose aaptive fuzzy controller for vector control PMSM. An ieal PMSM flux oriente control is chosen as reference moel. It is represente by a secon orer transfer function regaring to the state equation of the motor rive in the nominal conition. 5. SIMULATION RESULTS The control performance of the propose scheme in fig. 5 is evaluate by simulation using Matlab/Simulink software. The parameters of the PMSM are as follows: L = 1.4 mh L = 2.8 mh φ = 0.12 wb q f P 4 J = = kgm f = Nm / ra. s C =10 Nm R = 0.6 Ω I = 20 A e Fig.6 shows the spee FLC response uring the start up an abruptly step variation of loa at 0.1s et 0.2s for nominal inertia J an increase inertia 3*J. qn 1 It can be seen from the spee response that start up is faster with no overshoot an without state error. Similarly the isturbance rejection is quickly. The irect current is inepenent of the torque an is maintaine at zero after a short transient response. It can be note, when the moment of i nertia increases (3*J) the FLC response becomes slow an oscillatory with low amping. Fig.7 shows the same test with aaptive FLC uner increasing inertia (3*J). The spee Fig. 6. Step response of FLC uner loa an inertia variance. Fig. 7. Step response of aaptive FLC uner loa an inertia variation.

5 Volume 50, Number 1, aaptive FLC is much more robust with regar to the operating conitions as compare to spee FLC. Fig.7 shows the robustness of the spee response an the superiority of the aaptive FLC in the case of the external isturbances. The system output tracks very closely the reference moel even with inertia an loa variations. The obtaine results prove the effectiveness of the aaptive mechanism facing to inertia an loa variations. The efficiency of the aaptation scheme is evaluate by using specific profile as comman input. Fig. 8. Spee response FLC uner loa variation. In the changing operating conitions, the output response tracks the reference moel with slightly elay in increasing or ecreasing comman. Figures 9 an 10 show in spit of the isturbances, the system output tracks very closely the reference moel. The transient response of the aaptation is relatively short. Fig. 10. Spee response of aaptive FLC uner loa an inertia (3*J) variations. 6. CONCLUSION An aaptive fuzzy spee controller for fiel oriente PMSM fe by voltage source inverter has been propose in this paper. A comparison between aaptive FLC an FLC reveals the superiority of the first one. The aaptive FLC is less sensitive to the system parameter variations an this proves its robustness. The results obtaine show that the ecoupling is maintaine uner loa variations. The combination of FLC an aaptive FLC permits to ovoi the problem of flux orientation an the inexactitue of the representative system moel. This strategy of control gives a stable system with a satisfactory performance either with or without loa variation. The propose scheme is effective only uring transients since the parameters of the irect spee fuzzy controller are not upgrae by the aaptation mechanism. The simulation results have been confirme the efficiency of the propose aaptation scheme in maintaining goo performance uner external isturbances. REFERENCE Fig. 9. Spee response of aaptive FLC uner loa variations. 1. H. Zhang, Y. Li, Y. Zuo A DSP base fully igital PMSM servo rive using on line self tuning PI controller Proc. PIEMC 2000, vol.2, pp Ying Shich Kung, an Pin Ging Huang High performance position controller for PMSM rives base on TMS320F2812 DSP Proc. Of the 2004

6 30 ACTA ELECTROTEHNICA IEEE Int. Conf. on Control Applications. Tarpei, Taiwan, sept. 2-4, 2004, pp Y.F. Li an C.C. Lau Development of fuzzy algorithm for servo systems IEEE Contr. Syst. Mag. Vol.9, N o 3, pp.65-72, E.H. Mamani Application of fuzzy algorithms for control of simple ynamic plant Proc. IEE, Vol. 121, N o 12, pp , ec V.S.C. Raviraj an P.C. Sen Comparative stuy of PI, Sliing moe, an fuzzy logic controllers for power converters IEEE Trans. On In. Appl. Vol.33, N o 2, Marsh/April 1977, pp T.K. Yin Fyzzy moel reference aaptive control IEEE Trans. On Syst. Man. An Cybernetics, Vol.25, N o 12, Dec T.C. Minh an L.H. Hoang Moel reference aaptive fuzzy controller an fuzzy estimator for high performance inuction motor rives Proc. Of the annual Meeting of the IEEE, Inustry Applications Society California V.S. Kung an C. Liaw A fuzzy controller improving a linear moel following controller for motor rives IEEE Trans. On fuzzy. syst. Vol.2, N o 3, August A. MEROUFEL M. MASSOUM B. BELABBES Faculté es Sciences e L ingénieur Département Electrotechnique Laboratoire I.C.E.P.S Université Djilali Liabes BP 89, Sii Bel Abbes, Algérie Ameroufel@Univ-Sba.Dz