FUZZY-SIDING MODE CONTROER FOR INEAR INDUCTION MOTOR CONTRO ABDEKRIM BOUCHETA, ISMAI KHAI BOUSSERHANE,, ABDEDJEBAR HAZZAB, BENYOUNES MAZARI, MOHAMMED KARIM FEAH 3 Key wod: inea induction moto (IM), Vecto contol, Sliding mode and fuzzy-liding mode integal contol. In thi pape, the poition contol of linea induction moto uing fuzzy liding mode integal contolle deign i popoed. Fit, the indiect field oiented contol IM i deived. Then, a deigned liding mode integal contol (SMIC) ytem with an integal-opeation witching uface i invetigated, in which a imple adaptive algoithm i utilized fo genealized oft-witching paamete. Finally, a fuzzy liding mode contolle i deived to compenate the uncetaintie which occu in the contol, in which the fuzzy logic ytem i ued to dynamically contol paamete etting of the SMIC contol law. The effectivene of the popoed contol cheme i veified by numeical imulation. The numeical validation eult of the popoed cheme have peented good pefomance compaed to the conventional liding mode contolle.. INTRODUCTION Nowaday, IM ae now widely ued, in many indutial application including tanpotation, conveyo ytem, actuato, mateial handling, pumping of liquid metal, and liding doo cloe, etc. with atifactoy pefomance [, ]. The mot obviou advantage of linea moto i that it ha no gea and equie no mechanical otay-to-linea convete. The linea electic moto can be claified into the following: D.C. moto, induction moto, ynchonou moto and tepping moto, etc. Among thee, the IM ha many advantage uch a hightating thut foce, alleviation of gea between moto and the motion device, eduction of mechanical loe and the ize of motion device, high-peed opeation, ilence, and o on [, ]. The diving pinciple of the IM ae imila to the taditional otay induction moto (RIM), but it contol chaacteitic ae moe Univeity Cente of Becha B.P 47 Becha 8 Algeia, boucheta_ak@yahoo.f, bou_ima@yahoo.f. aboatoie de développement de Entaînement Electique (DEE), Univeity of Science and Technology of Oan, Algeia. 3 Univeity of Djilalil iabe, Sidi Belabba, Algeia. Rev. Roum. Sci. Techn. Électotechn. et Éneg., 54, 4, p. 45 44, Bucaet, 9
46 Abdelkim Boucheta et al. complicated than the RIM, and the moto paamete ae time vaying due to the change of opeating condition, uch a peed of move, tempeatue, and configuation of ail. Sliding mode contol theoy, due to it ode eduction, ditubance ejection, tong obutne and imple implementation by mean of powe convete, i one of the popective contol methodologie fo electical machine [3 8]. The featue of liding mode contol (SMC) ytem i that the contolle i witched between tow ditinct contol tuctue. In geneal, the deign of vaiable tuctue contolle geneally conit of two tep, which ae hitting and liding phae [6 8]. Fit, the ytem i diected towad a witching uface by a feedback contol law, the liding mode occu. When the ytem tate ente the liding mode, the dynamic of the ytem ae detemined by the choice of liding uface. The mentioned ituation ae independent of paametic uncetaintie and load ditubance. Hence, SMC ha been employed to the poition and peed contol of AC machine. But becaue of the non-continuou witch featue of SMC, the chatteing can occu in the contol ytem [3, 6 8]. In ode to educe o ovecome the ytem chatteing, eeache have popoed the fuzzy contol deign method baed on the liding-mode contol cheme [5, 9 ]. Recently, fuzzy liding-mode contolle have been eeached and applied to diffeent ytem; howeve, thee ae not many application to an induction moto. in et al. [5] utilized an adaptive FSMC ytem fo a PM ynchonou moto dive, but thee till exited chatteing contol effot. On the othe hand, intoducing SMC into fuzzy neual netwok i one anothe eeach field. Wong et al. [] combined a fuzzy contolle with SMC and tate feedback contol o popotional-integal contol to emedy the chatteing phenomena and to achieve zeo teady-tate eo. In thi pape, a fuzzy liding mode contolle which combine the meit of the liding mode contol and the fuzzy infeence mechanim i popoed. In thi cheme, a fuzzy liding mode contolle i invetigated, in which the fuzzy logic ytem i ued to dynamically contol paamete etting of the claical SMC. The eminde of thi pape i oganized a follow. Section II eview the pinciple of the indiect field-oiented contol (FOC) of linea induction moto. Section III how the development of liding mode contolle deign fo IM contol. The popoed fuzzy liding mode contol cheme i peented in Section 4. Section 5 give ome imulation eult. Finally, ome concluion ae dawn in Section 6.. INDIRECT FIED-ORIENTED CONTRO OF THE IM The dynamic model of the IM i modified fom taditional model of a theephae Y-connected induction moto and can be expeed in the d-q ynchonouly otating fame a [,, 4]:
3 Fuzzy-liding mode contolle fo linea induction moto contol 47 di d π π ; d σ φ φ m m R P m = R R i σ d ve iq d q v v () d t h h d q d t π π φ φ m P = σ m m R ve id R R i q d v q vq σ h h i () d φ d d t m R = i d R φ d π v h e π P v h φ q ; ; (3) d φ q d t m R = i q π v h e π P v h φ d R ( ), F = K φ i φ i = M v& D v F (5) e f d q q d φ q ; (4) whee R i the winding eitance pe phae, R i the econday eitance pe phae efeed pimay, m i the magnetizing inductance pe phae, i the econday inductance pe phae, i the pimay inductance pe phae, v i the move linea velocity, h i the pole pitch, P i the numbe of pole pai, φ d and φ q ae d-axi and q-axi econday flux, epectively, i d and i q ae d-axi and q-axi pimay cuent, epectively, v d and v q ae d-axi and q-axi pimay voltage, epectively, τ = R i the econday time-contant, σ = ( m ( )) i the leakage coefficient, K f = 3Pπ m ( h ) i the foce contant, F e i the electomagnetic foce, F i the extenal foce ditubance, M i total ma of the moving element and D i the vicou fiction and ion-lo coefficient. The main objective of the vecto contol of linea induction moto i, a in DC machine, to independently contol the electomagnetic foce and the flux; thi i done by uing a d-q otating efeence fame ynchonouly with the oto flux pace vecto [, 4, 5]. In ideally field-oiented contol, the econday flux linkage axi i foced to align with the d-axi, and it follow that [, 3, 5]: d φq φq (6) dt φd φ contant. (7) By ue of the indiect field-oiented contol technique and with the fact that the electical time contant i much malle than the mechanical time contant, the
48 Abdelkim Boucheta et al. 4 electomagnetic foce hown in (5) can be eaonably epeented by the following equation: F e = K i ; (8) f q K f 3 π m = P id. (9) h Moeove, uing (4) the feedfowad lip velocity ignal can be etimated uing φd and i q a follow: v l * h i m q =. () π τ φ d 3. SIDING MODE INTEGRA CONTRO OF IM A Sliding Mode Contolle i a Vaiable Stuctue Contolle (VSC). Baically, a VSC include eveal diffeent continuou function that map the plant tate to a contol uface, and the witching among the function i detemined by the plant tate and i epeented by a witching function [3, 5 8]. VSS contol i developed that all tajectoie in the tate pace ae diected towad ome witching uface, i.e. epeatedly coe and immediately ecoe the uface. The popoed liding-mode poition contolle i hown in Fig.. The tate vaiable ae defined a follow: x * = d d ; () x& = d & = v = x. () Then, the linea induction moto can be epeented in the following tatepace fom: x& = x & x D M x K f i q F M The tajectoy, which the SMIC foce the ytem to lide along [, 3], i a taight line decibed in (4). (3) S = c x x&. (4)
5 Fuzzy-liding mode contolle fo linea induction moto contol 49 The dynamic decibed in (4) i a fit-ode epone with a defined peed epone time contant. Vaiou contol law can be ued to foce the ytem epone. In cae of the above ytem, the dicontinuou contol ignal ha the fom u fo S >, u = u fo S <. (5) i: Fo the linea induction moto contol ytem, the equivalent contol ignal i eq = ( c a ) x f ( x) β, (6) K f D F whee: a =, β =, f ( x) =. M M M We ued the ame liding-mode peed contolle, a in [], which i a vaiation of that peented in [3] that i a poition contolle ( ) iq =ϕ x ϕ x k gn S, (7) whee ϕ and ϕ ae nonlinea function defined in thi fom α if S x > if, α if S x& > ϕ = β S x < ϕ = β S x& < if, (8) whee α, β, α, β and k ae contant. Uing a ign function often caue chatteing in pactice. One olution i to intoduce a bounday laye aound the witching uface [5, 7, 8]: whee: i i = i i (9) *, q eq = k at ( ) ξ, () whee the contant facto ξ define the thickne of the bounday laye and at () i the atuation function.
4 Abdelkim Boucheta et al. 6 α * x d - C k at ( ξ ) - x β α τ F F - e M D v d β Fig. Block diagam of the conventional liding mode integal contolle of IM. 4. FUZZY-SIDING MODE INTEGRA CONTROER FOR IM CONTRO The diadvantage of liding mode contolle i that the dicontinuou contol ignal poduce chatteing dynamic; chatte i aggavated by mall time delay in the ytem. In ode to eliminate the chatteing phenomenon, diffeent cheme have been popoed in the liteatue [5, 9 ]. In thi ection, a fuzzy-liding mode contolle i developed, in which a fuzzy infeence mechanim i ued to geneate the equivalent contol law paamete in (6). The popoed fuzzy-liding mode integal contolle cheme fo IM poition contol i hown in Fig. 4. The fuzzy logic contolle eplace the inequalitie given in (8) which detemine the paamete of the equivalent contol action. In the popoed fuzzy-smc cheme, the liding uface S, the vaiable x and it time deivative x& fom the input pace of the fuzzy implication of the majo witching ule. Becaue the data manipulated in the fuzzy infeence mechanim i baed on fuzzy et theoy, the aociated fuzzy et involved in the fuzzy contol ule ae BN, MN, ZE, MP, BP, N and P. The membehip function of the vaiable x, x& and S, coeponding to the fuzzy et, BN, MN, ZE, MP and BP, ae the ame a hown in Fig.. The two membehip function of ϕ and ϕ, coeponding to the fuzzy et, N and P, ae hown in Fig. 3. In thi wok, tiangula Membehip function ae choen fo BN, MN, ZE, MP, BP, and ingleton membehip function fo N and P fuzzy et. With fuzzy implication, ϕ and ϕ ae witched paamete and hence the fuzzy infeence mechanim can eplace the oft-witching law geneated by the if tatement in the claical SMC. The fuzzy oft-witching wok in uch way that when S and x ae in the poitive ide, ϕ ha a poitive value (bold-gay ub-table), when S and x ae in the negative ide, ϕ i adjuted to the negative value (nomal-white ub-table). Fo the contant ϕ, the ame logic i ued to
7 Fuzzy-liding mode contolle fo linea induction moto contol 4 geneate it paamete uing S and x& a input of the econd fuzzy logic contolle. The eulting fuzzy infeence ule fo the tow output vaiable ( ϕ and ϕ ) ae hown on Table and Table : S x Table Fuzzy ule of ϕ BN MN ZE MP BP BN P P N N N MN P P N N N ZE N N P P P MP N N P P P BP N N P P P S x& Table Fuzzy ule of ϕ NB MN ZE MP BP BN P P N N N MN P P N N N ZE N N P P P MP N N P P P BP N N P P P Fig. Membehip function of the uface S, x and x&.
4 Abdelkim Boucheta et al. 8 N µ P N µ P -,, ϕ -,3,3 ϕ Fig. 3 Output membehip function of the FSMC: ϕ and ϕ. * x d - C k at ( ξ ) - x τ F F - e M D v d Fig. 4 Block diagam of the Fuzzy-liding mode contolle of IM. 5. SIMUATION RESUTS We demontate the effectivene of the popoed contol cheme fo poition contol of the linea induction moto. Fit, we peent the imulated eult of the fuzzy-liding mode integal contol ytem fo peiodic inuoidal and tiangula input. The paamete ued in imulation ae choen a: φ =.978 Wb, R =. 34 Ω, R =. 95 Ω, =.77 H, =.77 H, =.4 H, M = 5.47 kg, D =.36 Nm d, P =, α =. 3, α =. 3, k = 5. 5, β =., β =. and ξ =. 5. The imulated eult of the fuzzy-liding mode integal contol ytem fo peiodic tep, inuoidal and tiangula input with load foce ditubance (contant load foce) ae hown in Fig. 5 and 6. Fom imulated eult, the tacking epone of the popoed contolle ae inenitive to load foce application. A compaion between the popoed contolle (fuzzy-integal liding mode contolle) and the liding mode with integal action i hown in Fig. 7 fo tep and tiangula efeence ignal (eo poition). In Fig. 7, it can be obeved that the poition epone of the fuzzy liding mode with integal action contolle peent bette tacking chaacteitic and i moe obut than the conventional contolle.
9 Fuzzy-liding mode contolle fo linea induction moto contol 43.5 -.5 Time [] 4 [ec] 6 8 5 5 4 Time [ec] [] 6 8 Fig. 5 Fuzzy-liding integal contol fo IM poition contol with contant load foce vaiation..5 -.5 4 6 8 Time [ec] [] 5 4 6 Time [ec] [] 8 Fig. 6 Fuzzy-liding integal contol fo IM poition contol with inuoidal load foce vaiation. x -4 4 Sliding Mode Contol Fuzzy Sliding Mode Contol 4 x -3 Sliding Mode Contol Fuzzy liding mode contol - 5 5. 5. 5.3 Time [ec] [] - 4 6 8 Time [ec] [] Fig. 7 Simulated eult of the compaion between the liding mode contol and fuzzy-liding contol with integal action fo IM eo tacking (quae and tiangula).
44 Abdelkim Boucheta et al. 6. CONCUSIONS Thi pape ha demontated the application of a hybid contol ytem to the peiodic motion contol of a IM. Fit, a liding mode integal contolle fo IM contol wa deigned. Moeove, a imple fuzzy infeence mechanim wa intoduced to contuct a obut contol law baed on the conventional liding mode integal contolle fo IM poition tacking. The contol dynamic of the popoed hieachical tuctue ha been invetigated by numeical imulation. Simulation eult have hown that the popoed fuzzy-liding mode integal contolle ha peented atifactoy pefomance (no ovehoot, minimal ie time, bet ditubance ejection) fo time-vaying extenal foce ditubance. Finally, the popoed contolle povide dive obutne impovement. Received on 4 Febuay, 8 REFERENCES. Po-Kai Huang, Recuent fuzzy neual netwok contolled linea induction moto dive baed on genetic algoithm, Mate Thei, Chung Yuan Chitian Univeity,.. F. -J. in, C. -C ee, Adaptive backtepping contol fo linea induction moto dive to tack peiodic efeence, IEE Poc. Elect. Powe Appl., 47, 6 (). 3. M. Zhiwen, T. Zheng, F. in, X. You, A New Sliding-Mode Cuent Contolle fo Field Oiented Contolled Induction Moto Dive, IEEE Int. Conf. IAS, pp. 34 346, 5. 4. A. Hazzab, I. K. Bouehane, P. Sicad, M. Rahli, M. Kamli, B. Mazai, Adaptive Fuzzy Integal- Backtepping Contolle fo inea Induction Moto Poition Contol, Poceeding of IECON 6, Pai, pp. 46 4. 5. F.-J. in, S.. Chen, Adaptive fuzzy liding-mode contol fo PM ynchonou evo moto dive, IEE Poc. Conf. Theoy Appl., 998, pp. 63 7. 6. J.-J. Slotine, Applied nonlinea contol, Pintice Hall, 996. 7. V. I. Utkin, Sliding Mode Contol Deign Pinciple and Application to Electic Dive, IEEE Tan. Ind. Elect., 4, (993). 8. R.-J. Wai, Adaptive Sliding-Mode Contol fo Induction Sevomoto Dive, IEE Poc. Elec. Powe Appl., 47, pp. 553 56 (). 9. C. -M. in, C. -F. Hu, Adaptive Fuzzy Sliding-Mode Contol fo Induction Sevomoto Sytem, IEEE Tanaction on Enegy Conveion, 9,, pp. 36 368, 4... K. Wong, F. H. F. eung, P. K. S. Tam, A fuzzy liding contolle fo nonlinea ytem, IEEE Tan. on Ind. Appl.,, pp. 3 37.. R.-J. Wai, C.-M. in, C.-F. Hu, Adaptive Fuzzy Sliding-Mode Contol fo Electical Sevo Dive, Fuzzy Set and Sytem, 43, pp. 95 3 (4).. I. Senol, M. Demita, S. Rutemov, B. Gumu, Poition Contol of Induction Moto: a New- Bounded Fuzzy Sliding Mode Contolle, Int. Jou. fo Computation Mathematic in Electical and Electonic Engineeing (COMPE), 4,, pp. 45 57 (5). 3. E. Y. Y. Ho, P. C. Sen, Contol dynamic of peed dive ytem uing liding-mode contolle with integal compenation, IEEE Tan. Ind. Appl., 7, 5 (99).