IMPROVING SPEED PERFORMANCES OF INDUCTION MOTOR BY USING SYNERGETIC CONTROL THEORY *

Transcription

1 IJS, ansactions of Electical Engineeing, Vol. 39, No. E2, pp Pinted in he Islaic Republic of Ian, 25 Shiaz Univesity IMPROVING SPEED PERFORMANCES OF INDUCION MOOR BY USING SYNERGEIC CONROL HEORY A. YAHI AND L. BARAZANE 2, 2 Univesity of Science and echnology (USHB), Faculty of Electonic & Coputing, BP. 32, El-Alia, Bab-Ezzoua, 6, Algies, Algeia Eail: abdenou.yahi@gail.co Welding and ND Reseach Cente (CSC), BP. 64, Cheaga, Algies, Algeia Abstact he use of ico-contolles in actuatos povides extended flexibility fo on-line data acquisition and sophisticated contol ipleentation. Howeve, attepts to utilize the excellent featues of induction oto that is deeed by its stength, obustness, high toque, and elatively low cost in actuatos face a fundaental contol design challenge. he pupose of this pape is to intoduce the synegic contol theoy, and apply it to design a speed contolle fo an induction oto and optiize the paaetes of the contolle to ipove its esponses convegence with highe pefoances and iniu chatteing copaed to sliding ode contol. his pape pesents technological invaiant anifold based on vecto contol design with oto field oiented contol (RFOC) fo induction oto; the design uses Synegetic Contol theoy to ceate an analytical contol law which ensues asyptotic stability of the closed-loop opeation, eliinate the influences of both extenal distubances and paaetes vaiations. o validate this appoach, siulation study is caied out, and shows soe vey inteesting featues. Keywods Induction oto, field-oiented contol, synegetic contol theoy, electic taction, nonlinea contol. INRODUCION Motion contol deals with the design and ipleentation of contolles fo echanically oving objects. It plays an ipotant ole in oden industy such as ipoving achine accuacy and poductivity in the echanical anufactuing way. In the application of actuatos that use induction otos (IM) in electical taction, Electical vehicles (EV) contol systes is a poising appoach, because IM is a low cost, eliable, and obust oto [] that is widely used in electoechanical systes (EMS) with a wide ange of otation fequencies and angles. In addition, the use of ico-contolles in actuatos povides extended flexibility fo on-line data acquisition and sophisticated contol ipleentation. Howeve, attepts to utilize these excellent featues of IM in actuatos face a fundaental contol design challenge. One of the pobles is that IM itself is an electoechanical plant with sophisticated dynaics. he challenging popeties of the IM that coplicate the contol design ae high nonlineaity and a high ode of a dynaic odel descibing the behavio of IM in diffeent opeating odes. Anothe poble is that the load of the actuato is uncetain: exhibiting eithe a wide ange of vaiation, o nonlinea behavio, o both. Aong nueous contol stategies developed fo IM, howeve, those that teat IM as one contol channel syste ae the ost popula. Fo instance, the pinciple of constant V/Hz contol elates the aplitude of stato voltage to the fequency of feeding voltage [2]. In addition, these contol stategies ae Received by the editos Januay 6, 24; Accepted June 23, 25. Coesponding autho

2 84 A. Yahi and L. Baazane usually designed using siplified linea odels that ae unable to eflect the eal physics of the pocesses in adequate ways [3]. Moeove, contol design ethods eithe copensate o ignoe nonlineaity, ulti-connectivity, and soe of the available contol channels. Indeed, such ethods put significant liitations on achievable qualitative chaacteistics of IM such as the egion of stability, the ange of egulation, and the stiffness of the echanical chaacteistic. Coespondingly, all of the above entioned, liits the capabilities of IM in actuatos. In ode to fully utilize capabilities of IM in actuatos, a vecto contol should be designed that contols seveal inteelated coodinates such as fequency of otation, angula position, toque, agnetic flux, cuent, etc., and takes into account nonlineaity of the IM odel and the load [4, 2]. Synegetic contol theoy is a new diection in contol science that uses the natual nonlinea qualities of dynaic objects based on the pinciple of diect self-oganization. his pinciple clealy eveals the objectives of contol laws and deeply changes the ephasis of odeling by focusing attention on esult athe than pocess. Contol, as a easue of puposeful influence of a peson on a powe syste and as a eflection of his ais and equieents, should weave togethe all the aspects of the syste s functionality [5]. his pape pesents invaiant anifold based vecto contol design with oto field oiented contol (RFOC) fo induction oto. he design uses Synegetic Contol heoy to ceate an analytical contol law which ensues asyptotic stability of the closed-loop opeation, and suppesses the influence of the extenal distubance with optiization of the paaetes of the contolle to ipove the speed pefoance of the IM. a) Model of the induction oto 2. CONROL OF INDUCION MOOR Fo contol puposes the odel is often expessed in an abitay two axis otating efeence fae. his akes it easie fo the contol designe to fix the efeence fae to a paticula oto quantity and adjust the odel accodingly. he equations of the induction oto, in the synchonous efeence fae (d q), using oto fluxes as state vaiables ae given by [6] d v ds = L ds L s +R s ds L s s qs q d t v qs = L s d dt d dt d q d qs d t e d qs q ds 2 L +R s qs + L s s ds + ( d Li ds ) slq ( q Li qs ) sld d ( Ce C K f ) dt J 3 PL C ( i i 2 L L ; L L R s L d Fo a oto-flux oientation, the egulato iposes the oientation of the oto flux () with espect to the d-axis, giving = d and q =. Substituting these elations in (2), leads to the field-oiented odel of the oto which is given by the following equation syste IJS, ansactions of Electical Engineeing, Volue 39, Nube E2 Decebe 25 ()

3 Pak - Encod e Invete Hysteisis Ipoving speed pefoances of induction oto by 85 v ds = L s v qs = L s sl d ds d t d qs d t d L dt C i ds L i PL qs i e qs L +R s ds L s s qs +R s qs + L s s ds + L (2) he field-oiented contolle is based on the invesion of the above equation syste. he contol vaiables ( ids, iqs, vds, vqs ) ae geneated hee espectively by egulatos as it is shown in Fig.. he oto flux is estiated by eans of the stato cuent and speed easueents (indiect ethod) as follows [3]: di ds L v R ( ) I L I dt Ls 2 ds s ds s s qs diqs L 2 L vqs Rs ( ) Iqs Lss Iqs dt Ls he coesponding position is given by e = ( p sl ) dt (3) (4) ef e(t) ef PI Contolle qs PI Contolle ds e qs e ds d q abc I a I b I c Induction Moto Ɵs Estiation Of ɸ,Ɵs qs ds Fig.. Vecto contol schea of induction oto In ou case, hysteesis PWM contol will be adapted, so the Eq. (2) will be eplaced by I I ds d dd L L dt d ( Ce C K f ) dt J P Decebe 25 IJS, ansactions of Electical Engineeing, Volue 39, Nube E2 qs sl d L C PL I e d qs L (5)

4 86 A. Yahi and L. Baazane 3. SYNERGEIC CONROL Synegetic Contol heoy exploits the capability of open systes to self-oganize. he theoy invokes a holistic philosophy of contolled dynaic inteactions between enegy, atte, and infoation which is ipleented though a cobination of both positive and negative feedback [7]. he philosophy of synegetic contol is based on the pinciple of dynaic expansion and contaction of the state space of the contolled syste. he expansion of the state space eniches the syste dynaics by poviding additional infoation which is the key to ipoving the pefoance of the closed-loop syste. In contast to the expansion, the contaction of the state space that is pefoed by the contolle action eliinates the unwanted dynaics of the syste o educes excessive degees of feedo. At the contol design stage, these unwanted dynaics ae eoved by intoducing dynaic constaints that ae epesented as invaiant anifolds in the state space of the syste. In ode to apply the ideas of Synegetic in contol theoy, it is necessay to keep the conceptual coespondence to the ain qualities of self oganization: nonlineaity open systes coheence. Fo contol tasks the ost ipotant quality is that the syste ust be open [8]. In the initial stateent, the contol syste is descibed by the diffeential equations of the object x( t) F( x, u, q, M) It includes state coodinates x(t) and soe extenal foces consisting of sought contols u(t), setting actions q(t ) and possibly the distubing actions M(t ). In ode to ove fo the syste object - extenal foces to foing the self-oganization equations we ust exclude these foces in an appopiate way. o do that we should extend the initial equations of the syste object - extenal foces in such a way that excluded foces would becoe intenal fo the syste. heefoe, fo the new extended syste its equations can becoe the self oganization equations, i.e. as a esult of this extension, we can ove to self oganization of the syste [8]. In synegetic contol theoy the equieents put on dynaic and static qualities of the systes being synthesized ae epesented in the fo of a set of invaiants. Invaiants ente into the stuctue of invaiant anifolds foed in the phase space of the object accoding to the ethod of synegetic synthesis. hese anifolds seve as attactos of the closed-loop syste [9]. In the IM thee invaiants goups can be deteined: electoagnetic, enegetic and technological. echnological invaiant chaacteizes the desied static o dynaic state of the contolled vaiables like toque, angle and echanical speed. Enegetic invaiants ae coelated between object s coodinates chaacteizing ode of wok (inial enegy losses, inial enegy consuing) []. Fo the constancy o stabilization of the agnetic state of ou syste Electoagnetic invaiants can be used. he ain steps of the pocedue can be suaized as follows []. Suppose the syste to be contolled is descibed by a set of nonlinea diffeential equations of the fo (7) X f ( t, x, u) whee X is the state vecto, u is the contol input vecto and t is tie. Stat by defining a aco-vaiable as a function of the state vaiables ( x) he contol will foce the syste to opeate on the anifold Ψ=. he designe can select the chaacteistics of this aco-vaiable accoding to the contol specifications (e.g. liitation in the (6) (8) IJS, ansactions of Electical Engineeing, Volue 39, Nube E2 Decebe 25

5 Ipoving speed pefoances of induction oto by 87 contolle output, and so on). In the tivial case the aco vaiable can be a siple linea cobination of the state vaiables. he sae pocess can be epeated, defining as any aco-vaiables as contol channels. he desied dynaic evolution of the aco-vaiables is ( ) ; whee is a design paaete specifying the convegence speeds to the anifold specified by the aco vaiable. () he chain ule of diffeentiation gives d x dx () Cobining (7), (8) and (9), we obtain d f ( t, x, u ) dx Equation () is finally used to synthesize the contol law u. o suaize, each anifold intoduces a new constaint on the state space doain and educes the ode of the syste, woking in the diection of stability. he pocedue suaized hee can be easily ipleented as a copute poga fo autoatic synthesis of the contol law o can be pefoed by hand fo siple systes, such as the speed contol fo induction oto used fo this study. 4. APPLICAION OF SYNERGEIC SPEED CONROL FOR INDUCION MOOR o find the desied contol law, the fist step in the design of the synegistic contol is the choice of appopiate aco-vaiables; in geneal the aco-vaiable can be a function of the state vaiables. he objective is to obtain a contol law of a state function coodinate (Ω, Ф) which povides efeence values that ae equied fo the oto speed efeence Ω ef and a efeence flux Ф ef. heefoe a toque contol ust be satisfied. he above descibed ethod to solve the poble is used, i.e. to find a contol law u (Ω, Ф). he fist step is the selection of aco- vaiables. In geneal the aco-vaiable can be any function (non-linea functions including) of state vaiables. We have thee coponents ω, I ds and I qs, which allow us to ipose the following invaiants: technological (ω = Cst) and electoagnetic (Ф d =Cst, Ф q = ). -Expessions of law contols In the fist step, the synegetic contolle is applied only to the speed contol loop which pesents a technological invaiant (speed contol) in this pape. Fo agnetic stability contol of the syste, the electoagnetic invaiant can be added, so the synegetic contolle will be used in flux contol loop, this step is pespective fo futue wok. (9) () In ode to educe the static eo, an integal te of the eo on ω is added to Ψ k ( ) k ( ) dt ef 2 Ψ ust satisfy the following equation: With > ef (2) (3) Decebe 25 IJS, ansactions of Electical Engineeing, Volue 39, Nube E2

6 Encode Invete Hysteisis 88 A. Yahi and L. Baazane Equation (3) defines the evolution of the aco-vaiable ψ into the invaiant anifold (4). Unde contol (3), anifold (4) becoes an attacto in the state space of the closed-loop syste. As a esult, fo an adissible abitay initial location in the state space, the syste oves towads the anifold and then along the anifold to the equilibiu point. he stability of the syste's otion towads the anifold is deteined by using Lyapunov function. 2 (4) 2 V (5) V if Equation (6) shows that the stability of the otion towads the attacto is exponentially asyptotically stable, as long as the paaete is geate than zeo. he coefficient coesponds to the stability asyptotic conditions of Eq. (3). he deivation of Ψ gives (6) k ( ) k2 ef So k2( ef ) k Substituting the expession of Eq. (8) in the speed equation syste (5), we obtain (7) (8) PJ C k ( ) C K P e 2 ef f k (9) he ipleentation schea of this contol technique is given in Fig. 2. e f e(t ) e f Synegetic contolle q s PI Contolle d s e d e q Estiation Of ɸ,Ɵs d q ab c Ɵ s I a I b I c q d Pak - Inductio n Moto Fig. 2. Synegetic contol schea of induction oto 5. VALIDAION OF HE SYNERGEIC CONROLLER In ode to veify the pefoances of the synegetic contolle and its capability to suppess an extenal distubance, a siulation of the pocess dynaic is done by consideing the following two tests: he fist test concens a no-load stating of the oto with a efeence speed ef = ad/sec. hen a toque load ( L = N) is applied at t = sec, the esults ae shown in Fig. 3. IJS, ansactions of Electical Engineeing, Volue 39, Nube E2 Decebe 25

7 W(ad/s) - Ce (N.) Fd - Fq (web) W(ad/s) Ia(A) Speed Eo Ipoving speed pefoances of induction oto by 89 he second concens a no-load stating of the oto then a toque load ( L = N) is applied at t = sec with speed vaiation between (, 2, -5 ad/s).he esults ae shown in Fig ie (s) ie(s).5.5 Fq Fd 5 5 W Wef C ie (s) ie(s) Fig. 3. Dynaics siulation of synegetic contol a toque load of N 3 2 Syn ef Ce ie (s) Decebe 25 Fig. 4. Dynaics siulation of synegetic contol with speed vaiation between (, 2,-5 ad/s) he paaetes of the induction oto used ae given in Appendix. he esults shown in Figs. 3 and 4 show that the field oiented contol is established by setting the flux esponses q =, d =.8 wb, despite the load vaiations, and speed follows the efeence value with iniu ipacts induced by extenal distubance between (<t<2sec), which poves the obustness of this technique even with vaiation o change of the speed otation diection. Fo the two tests, it can be seen that the velocity is not influenced by the extenal distubance, neithe fo the constant efeence (ad/s) no fo speed efeence vaiation.(,2,-5 ad/s), it can be seen that the specified value of the oto flux linkage is achieved which confis that the technological IJS, ansactions of Electical Engineeing, Volue 39, Nube E2

8 Ce(N.) W(ad/s) W(ad/s) W(ad/s), Ce (N.) 9 A. Yahi and L. Baazane invaiant is eached. While the behavio of the stato cuent fo the two figues is the sae without exceeding the cuent liit of the oto (8A), the behavio of the cuent between t = 2 sec and t = 3 sec is due to the application of load toque which pesents a call of powe fo the oto, and at t=.5sec is due to the inceasing speed fo to 2 ad/s, so electoagnetic toque is ising, and at t=3sec a high vaiation is seen which is due to esistant toque to eet the speed set point and evese the otation sense fo 2 to -5ad/s. o opeate the oto above its noinal speed field weakening technique is used (Fig. 4), by educing the oto flux so the IM behavio is the sae as DC oto, the highe efficiency opeating ange of the dive can be extended beyond the noinal speed, this technique allows the oto speed to be quadupled unde cetain opeating conditions. o pefo this technique, an optiization of the contolle paaetes is done in the Figs. 5 and 6, whee a vaiation of the paaetes of contol setting is ade to view its ipact on the behavio of the oto contol. Stating fo Fig. 5, it is seen that inceasing in the paaete k ipoves the speed esponse of the syste and a high stating toque is seen which is intepeted by inceasing in the contol enegy, so the convegence ate will be highe. Howeve; a deceasing in this last iniizes the contol enegy so the speed esponse is salle. Othewise in Fig. 6 aise in the paaete ipoves the pusuit and theefoe iniizes the static and dynaic eo and ensues asyptotic stability of the closed-loop, but liitation (sat bloc) is needed to keep best contol of the syste. Decease in can aintain the sae esponse -see Iqsplot- without liitation (sat bloc) but in this case the choice of an optial value is equied. he convegence ate of the dynaical syste and hence the algoith is deteined by the value of the paaete, since can be any positive nube. he decease in can help to keep the tansition pocess unde contol. he pefoed siulation shows that the closed-loop syste is stable, obust against uncetain load distubances ie(s) ie(s)..5 Zoo Zoo ef ie(s) ie(s) Fig. 5. Dynaics siulation of synegetic contol with the vaiation ipact of paaete k IJS, ansactions of Electical Engineeing, Volue 39, Nube E2 Decebe 25

9 Iqs(A) Ce (N.) W (ad/s) W (ad/s) W (ad/s) Ipoving speed pefoances of induction oto by ie (s) 3 2 Ipact of inceasing. 5 wef Iqs without sat = Iqs with sat fo = Zoo Ipact ie of inceasing (s) Zoo Ipact of inceasing ie (s) Ipact of inceasing. 5 wef. 5 wef. 5 wef ie(s) ie (s) Fig. 6. Dynaics siulation of synegetic contol with the vaiation ipact of paaete 6. CONCLUSION In this pape we pesented a synegetic contol theoy design fo an induction oto which opeates unde a widely vaiable uncetain load and can be used in taction otion. he poposed synegetic appoach has evealed vey inteesting featues. In fact, the cobination of the nonlinea contol with the field oiented contol aintains an effective decoupling between speed and flux fo the whole ange of speed which allows high dynaic pefoances fo constant flux opeation to be obtained, siila to that of DC oto. Futhe, these high pefoances ae aintained above the noinal speed fo the constant powe opeation, which is not the case in the conventional field oiented contol. he addition of the synegetic contolle has ipoved the obustness towads odeling uncetainties and extenal distubances. he application of Synegetic Contol heoy exhibits contollable ate of convegence which can be ade faste o slowe than the ate of othe algoiths. APPENDIX: MACHINE PARAMEERS Squiel-cage induction oto of.5 Kw, 22 V, P= 2 poles, 42 t/in, 5 Hz. R s = 4.85 ; R = 3.85 ; L s =.274 H ; L =.274 H; L =.258 H ; J =.3 Kg. 2 ;K f =.4 Ns. ω ω ef C e P I d,i q V d,v q R s, R L s, L NOMENCLAURE the oto speed, in actual (echanical) adians pe second; W s : Supply fequency; efeence oto speed. electoagnetic toque; C : Load toque. nube of poles; J : Inetial constant. diect- and quadatue-axis coponents of the induction oto aatue cuent. diect- and quadatue-axis coponents of the induction oto voltage. stato and oto esistance. stato inductance. L : Mutual inductance. Decebe 25 IJS, ansactions of Electical Engineeing, Volue 39, Nube E2

10 92 A. Yahi and L. Baazane REFERENCES. Muenchhof, M., Beck, M. & Iseann, R. (29). Fault-toleant actuatos and dives-stuctues, fault detection pinciples and applications. Annual Reviews in Contol, Vol. 33, No. 2, pp Robyns, B., Labique, F. & Buyse, H. (995). Pefoance analysis of a siplified indiect field oiented contol algoith fo sall powe induction actuatos. Matheatics and Coputes in Siulation, Vol. 38, No Ioannides, M. G. Papazis, S. A. & Ioannidou, F. G. (23). Ipleentation of scala contol schee fo vaiable fequency induction oto actuato syste. Sensos and Actuatos A: Physical, Vol. 6, No Kondatiev, I., Dougal, R. & Veselov, G. (2). Synegetic contol fo aine actuatos. ONR gant N Kondatiev, I., Roge A. Dougal, R. (2). Application of the synegetic contol appoach in enegy systes fo hybid electic vehicles. Poceedings of IECEC', 36th Intesociety Enegy Convesion Engineeing Confeence, Savannah, Geogia. 6. Yahi, A. & baazane, L. (24). Application of fuzzy sliding appoach fo speed contol in field oiented pocess and to educe chatteing of an induction oto. Jounal of Electical Engineeing, Vol. 4, No.. 7. Kondatiev, I. (29). Synegetic contol: Convete based autonoous DC powe distibution systes. Labet Acadeic Publishing AG & Co. KG. 8. Kolesnikov, A. A. (29). Nonlinea syste s synthesis the cental poble of oden science and technology: synegetics conception. Pat II: Stategies of Synegetics contol. 2nd Chaotic Modeling and Siulation Intenational Confeence, Chania Cete Geece. 9. Kolesnikov, A. A. (22). Synegetic contol fo electoechanical systes. US office Naval Reseach unde Gant N Kondatiev, I., Dougal, R., Santi, E. & Veselov. G. (24). Synegetic contol fo DC-DC buck convetes with constant powe load. 3d Annual IEEE Powe Eleclonics Specialists Confeence Aachen, Geany.. Yahi, A., Baazane, L. & Khwaldeh, A. (2). Indiect field oiented contol (IFOC) by the application of the synegetic theoy applied to induction otos. Poceedings of the 9th Intenational Syposiu on Mechatonics and its Applications (ISMA3), Aan, Jodan. 2. Kianinezhad, R., Nahid-obaakeh, B., Betin, F. & Capolino, G. A. (29). Robust sensoless vecto contol of induction achines. Ianian Jounal of Science & echnology, ansaction B, Engineeing, Vol. 33, No. B2, pp Ben Azza, H., Jeli, M., Boussak, M. & Gossa, M. (2). Ipleentation of sensoless speed contol fo twophase induction oto dive using ISFOC stategy. Ianian Jounal of Science & echnology, ansaction B, Engineeing, Vol. 35, No, B2, pp IJS, ansactions of Electical Engineeing, Volue 39, Nube E2 Decebe 25