NEURO-FUZZY COMPENSATION OF TORQUE RIPPLE IN A SWITCHED RELUCTANCE DRIVE

Transcription

1 NEURO-FUZZY COMPENSATION OF TORQUE RIPPLE IN A SWITCHED RELUCTANCE DRIVE L. O. P. Henrques, L. G. B. Rolm, W. I. Suemtsu,, P. J. Costa. Branco and J. A. Dente COPPE / PEE - UFRJ Ro de Janero - Brazl Fax: ()9- E-mal: porto@coe.ufrj.br EE/DEE - UFRJ Ro de Janero - Brazl Fax: ()-9 E- mal:{rolm, walter}@dee.ufrj.br Lab. de Mecatrónca-IST Lsbon - Portugal Fax: --77 E- mal: pbranco@alfa.st.utl.pt Abstract: Smple power electronc drve crcut and fault tolerance of converter are specfc advantages of SRM drves, but excessve torque rpple has lmted ts applcaton. Ths paper presents a novel method of controllng the motor currents to mnmze the torque rpple, usng a neuro-fuzzy compensator. In the proposed control concept, a compensatng sgnal s added to the output of a classcal PI controller, n a current-regulated speed control loop. The compensatng sgnal s learned pror to normal operaton, n a self-comssonng run, but the neurofuzzy methodology s also sutable for on-lne selflearnng mplementaton, for contnuous mprovement of the compensatng sgnal..- INTRODUCTION Many authors [-] have proposed the dynamc control of a SR drve usng fuzzy logc and neural networks. Ths type of control s today well establshed n the area of moton control and partcularly n drve systems. Artfcal ntellgencebased fuzzy, neural and fuzzy-neural controllers have a number of advantages over conventonal controllers [], and even helpng to ncorporate some "ntellgence" nto them [-7]. The most remarkable advantages for SR Drves are: no requrement of an accurate model; possblty of desgn based exclusvely on lngustc nformaton derved from experts or from the use of clusterng technques and capacty of ncorporaton of new data and nformaton as they become avalable by learnng mechansms. Fuzzy logc control of a SR drve has been mplemented wth success n [], and has shown to be effectve for the speed control n applcatons where some degree of torque rpple s tolerated, as s the case n many ndustral applcatons. Nevertheless, n servo control applcatons or when smooth control s requred at low speeds, the elmnaton of the torque rpple becomes the man ssue for an acceptable control strategy. In ths case, even usng a fuzzy PIlke control as the one descrbed n [] s not satsfactory, because the controller's output sgnal, whch s used as a reference sgnal for the current control n the power converter, gves rse to sustaned torque pulsatons n steady-state. Furthermore, ths torque rpple changes wth the speed of the SR motor and wth the load appled to t..- TORQUE PULSATION Wth a PI-lke control alone, t s not possble to obtan a rpple-free output speed at any speed range, because t would also requre a rpple-free output torque, for ths purpose. If t s supposed that the output speed s constant and equal to the reference speed n steady-state, then the PI controller's output sgnal (.e. the reference current) would be constant. However, a constant current reference would produce an oscllatng torque (Fg. ), renderng the rpple-free speed control unfeasble. The smulaton results shown n Fg. correspond to the current-regulated, full-load operaton of a 7W SR motor, at rated speed (rpm). Torque / Nm Fgure -Torque rpple produced by constant current reference sgnal (smulaton).

2 At hgh speeds, the torque pulsatons would occur at hgher frequences, thus causng less speed rpple, due to the natural flterng provded by the mechancal load nerta. Furthermore, SR drves are usually operated n sngle-pulse mode at hgh speeds, wthout current control. In ths case, the most effectve way of reducng vbratons caused by torque pulsaton s by way of turn-off angle control. At lower speeds, t s more convenent to compensate for the torque pulsatons through phase current waveshapng. In ths case, the current reference sgnal should vary as a functon of poston, speed and load torque, n er to produce the desred compensaton. In fact, the optmum compensatng sgnal s a hghly non-lnear functon of poston, speed and load. Several works [7-] have been publshed, whch use many dfferent strateges to produce a compensatng sgnal.. Some authors [,] use the nverse of the statc torque-current-poston relatonshp, whch are tabulated prevously and stored n memory. However, ths method s qute laborous and senstve to parameter varatons. In ths work, a novel compensaton method s proposed, whch s based upon a self-tunng neurofuzzy compensator. The proposed compensaton scheme s descrbed n the next secton..- PROPOSED METHOD Fgure presents a smplfed block dagram of the SR-drve speed control system, showng the proposed neuro-fuzzy compensatng scheme. The basc dea of the proposed method s llustrated n Fg.. The output sgnal produced by the compensator, I comp, s added to the PI controller's output sgnal, I ref, whch should be deally constant n steady-state but producng sgnfcant rpple, as shown n Fg. (a). The resultng sgnal after the addton s used as a compensated reference sgnal for the currentcontrolled SR drve converter, as shown n Fg. (b). The compensatng sgnal should then be adjusted n er to produce a rpple-free output torque. ω NEURO- FUZZY PI Controller I ref I comp Fgure - Dagram of proposed compensaton scheme. Converte SR Motor ω The compensatng sgnal s adjusted teratvely, through a neuro-fuzzy tranng algorthm, where the tranng error nformaton s derved from some nternal varable of the SR drve system. In the smulaton tests, the torque rpple tself has been used as the tranng error varable, but ths approach would not be very practcal for on-lne mplementaton n a real system, snce the dynamc torque s a varable whch s dffcult to measure. For contnuous on-lne tranng, other varables could be more approprate, such as acceleraton or speed rpple. However, the torque could stll be used drectly n an off-lne tranng system, e.g. for converter programmng on a test rg at the factory. Converter Motor (a) (b) Fgure - Basc dea of proposed compensaton method: (a) torque rpple produced by constant current reference; (b) rpple-free torque produced by compensated reference..- SIMULATION MODEL The neuro-fuzzy compensator s a Sugeno-type fuzzy logc system wth fve fxed trangular membershp functons for each nput. The rotor angular poston θ and the PI controller's output sgnal I ref, are used as nputs to the compensator representng a relaton as I comp = f ( θ, I ref ). The tranng procedure conssts on whose adjustng the rule consequents by a hybrd tranng algorthm, whch combnes back-propagaton and least-squares mnmzaton. At each tranng teraton, the dc component s removed from the compensatng sgnal, so that the rpple compensator does not try to change the mean value of the output torque. As a T Converter Motor T

3 result, when the control system operates n steadystate, after the tranng, the PI controller wll really produce a constant output sgnal, whle the neurofuzzy compensator wll produce a zero-mean-value compensatng current reference, the Icomp sgnal. Tranng data are obtaned from smulatons of steady-state operaton of the complete SR drve system. At each tranng teraton, the dc component s removed from the torque sgnal, so that just the rpple remans. Ths torque rpple data s then tabulated aganst the mean value of the PI output reference current, and aganst the rotor angular poston. Ths data set s then passed to the tranng algorthm, so that the torque rpple s nterpreted as error nformaton for each current-angle par. The output of the neuro-fuzzy compensator s then readjusted to reduce the error (whch s n fact the torque rpple), beng ths process repeated untl some mnmum torque rpple lmt s reached. The choce of stoppng crtera s very mportant for the stablty of the method, snce the converter may not be able to produce the requred compensated currents at any speed or load. In ths case, persstng on tranng may lead to output wndup at the compensator..- SIMULATION RESULTS For comparson purposes, the drve system has been smulated wthout compensaton, at full-load torque (approxmately Nm mean value), rpm. The rated speed s rpm. The output torque sgnal s plotted n Fg., and ts harmonc components are shown n Fg.. The torque sgnal shown n Fg. s produced by a constant current reference. As a result, the phase current pulses are flat-topped. As the motor has a / structure, the converter produces current pulses per rotor turn. So, the torque pulsatons occur at a frequency tmes hgher than the frequency of rotaton. For ths reason, the harmonc spectrum shown n Fg. exhbts non-zero components only for ers multple of. The magntudes of the harmoncs are expressed as percentage of the mean value. It should be notced that the frst non-zero harmonc (th) exhbts a qute hgh magntude (approxmately %). After one tranng teraton, the harmonc content of the output torque s already sgnfcantly lower, as shown n Fgures. and 7. The th harmonc has a relatve magntude of only % approxmately. In ths stuaton, the compensated current reference produces phase current pulses whch are no longer flat-topped, as wll be shown afterwards. Fgure Output torque for non-compensated (constant current reference) operaton at rpm. Fgure Harmonc content of non-compensated torque sgnal of Fg.. Fgure Compensated torque after frst teraton.

4 Fgures and 9 show the output torque waveform and ts harmonc content for a compensated current reference after tranng teratons. It can be seen that the total harmonc content s very low, and the th harmonc s lower than.% of the mean torque. Fgure 9 Harmonc content n torque sgnal of Fg.. Fgure 7 Harmonc content n torque sgnal of Fg.. / A Fgure Harmonc content n torque sgnal of Fg.. Fgure Compensated torque after teratons. After tranng teratons, the compensated current reference produces phase current pulses lke those shown n Fg.. As expected, the current values are hgher at the begnnng and at the end of the current pulse. Ths pulse shape s consstent wth the torque characterstcs of te SR motor, whch produces less torque at the begnnng of pole overlappng and just before the algned poston..- CONCLUSIONS The Neuro-fuzzy modelng and the learnng mechansm to rpple reducton n SR motor were nvestgated. The smulatons of the swtched reluctance drve show that s possble to ncorporate a compensatng sgnal n the current waveform to mnmze the torque rpple. Next steps are usng ths concept n an expermental drve and ncorporate another sgnal to be traned..- REFERENCES [] D.S.Reay, M.M.Moud, T.C.Green, B.W.Wllams; Swtched Reluctance Motor Control Va Fuzzy Adaptve Systems, IEEE Control Systems, June 99.

5 [] M.G.Rodrgues, W.I.Suemtsu, P.Branco, J.A.Dente, L.G.B.Rolm; Fuzzy Logc Control of a Swtched Reluctance Motor, IEEE Internatonal Symposum on Industral Electroncs, pp. 7-, Gumarães, Portugal, July 997. [] S. Bolognan, M. Zglotto; Fuzzy Logc Control of a Swtched Reluctance Motor Drve, IEEE Transactons on Industry Applcatons, pp. -, Vol., Number, September/October 99. [] Ç. Elmas, S.Sagroglu, I.Çolak, G.Bal; Modelng of a Nonlnear Swtched Reluctance Drve Based on Artfcal neural Networks, Power Electroncs and Varable Speed Drves Conference Proceedng, pp.7-, 99. [] A.F.Stronach, P.Vas; Desgn of Fuzzy-Neural Controllers for Varable-Speed Drves, ICEM9, Vol.III, pp.-7, 99. [] Kavanagh, R.C., Murphy, J.M.D. and Egan, M.; Torque Rpple Mnmzaton n Swtched Reluctance Drves usng Self-Learnng Technques, Proc. of IECON 9, pp. 9-9, Vol., Japan, 99. [7] Iqbal Husan, M. Ehsan; "Torque Rpple Mnmzaton n Swtched Reluctance Motor Drves by PWM Current Control", IEEE Transactons on Power Electroncs, Vol., Number, pp. -, January 99. [] H. C. Lovatt, J. M. Stephenson; "Computer-optmzed Current Waveforms for Swtched Reluctance Motor" IEE Proceedngs, Vol., Part B, Number, pp. -, March 99 [9] D. S. Shramm, B. W. Wllams, T.C. Green; "Optmum Commutaton-Current Profle on Torque Lnearzaton of Swtched Reluctance Motors" ICEM '9 Manchester Conference Proceedngs, pp. -, September 99 [] Ulrch Steert, H. Spath; "Torque Control of the Doubly-Salent Reluctance Motor" ETEP Vol., Number, July/August 99 [] Manfred Stert, Je Ge; "A Low Voltage Swtched Reluctance Motor wth Expermentally Optmzed Control" ICEM '9 Manchester Conference Proceedngs, pp. -, September 99 [] Rchard S. Wallace, Davd G. Taylor;" A Balanced Commutator for Swtched Reluctance Motors to Reduce Toque Rpple" ", IEEE Transactons on Power Electroncs, Vol. 7, Number, pp. 7-, October 99. [] Costa Branco, P.J.; Dente, J.A., "An Experment n Automatc Modellng an Electrcal Drve System Usng Fuzzy Logc," IEEE Transactons on System, Man, and Cybernetcs - Part C: Applcatons and Revews, Vol., No.., May. [] Costa Branco, P.J.; Dente, J.A., "The Applcaton of Fuzzy Logc n Automatc Modellng Electromechancal Systems". Fuzzy Sets and Systems, Vol. 9, No., pp. 7-9, 99. [] Costa Branco, P.J.; Dente, J.A., "Desgn of an Electro-Hydraulc System Usng Neuro-Fuzzy Technques", In Fuson of Neural Networks, Fuzzy Sets & Genetc Algorthms: Industral Applcatons, Chapter, Ed. L.C. Jan, CRC PRESS, 99. [] Costa Branco, P.J.; Dente, J.A., "Control of an Electro-Hydraulc System Usng Neuro-Fuzzy Modellng and Real-Tme Learnng Approaches". Invted paper n the Int. Journal of Knowledge-Based Intellgent Engneerng Systems, Vol., No., pp. 9-, October, EASA, Australa, 997. [7] Costa Branco, P.J. and Dente, J.A., Inverse-Model Compensaton Usng Fuzzy Modellng and Fuzzy Learnng Schemes. In Intellgent Engneerng Systems Through Artfcal Neural Networks, Smart Engneerng Systems: Neural Networks, Fuzzy Logc and Evolutonary Programmng, Eds. C.H. Dagl, M. Akay, C.L. Phlp Chen, B. Fernández, and J. Ghosh, Vol., pp. 7-, ASME Press, New York, U.S.A., 99.