SPEED CONTROL OF LINEAR INDUCTION MOTOR USING DTFC METHOD CONSIDERING END-EFFECT PHENOMENON

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1 Intenational Jounal on Technical Phyical Poble of Engineeing (IJTPE) Publihed by Intenational Oganization of IOTPE ISSN IJTPE Jounal Decebe 14 Iue 1 Volue 6 Nube 4 Page SPEED CONTRO OF INEAR INDUCTION MOTOR USING DTFC METHOD CONSIDERING END-EFFECT PHENOMENON H. Shadabi 1 A. Rahnaa Sadat 1 A. Pahaei M.B.B. Shaifian 1 1. Faculty of Electical Coute Engineeing, Univeity of Tabiz, Tabiz, Ian h.habai91@.tabizu.ac.i, a..adat@ieee.og, haifian@tabizu.ac.i. Deatent of Electical Electonic Engineeing, Faculty of Engineeing, Gazi Univeity, Ankaa, Tukey ali.ahaei@gazi.edu.t Abtact- In thi ae the eed contol ethod of IM, which lead to otial contol chaacteitic of oto uch a thut, flux cuent, i ooed. The efoance of the ooed DTFC ethod i analyzed with conideing end-effect. DTFC i one of the ioved contol ethod which eloy eveal PI contolle. Poe adjutent of coefficient of the PI contolle lay an iotant ole in the atifactoy efoance of contol yte that ae deteined uing MATAB otiization function. The obtained eult how that the DTFC ethod conideing end-effect ha led to a conideable eduction in the FORCER flux thut ile nea to.8%. The ot iotant featue of DTFC ethod i it efoance obutne againt the endeffect henoenon. Keywod: Diect Thut Contol, Indiect Vecto Contol, inea Induction Moto, End Effect. I. INTRODUCTION inea electic oto (EM) belong to the gou of ecial electical achine. Main alication of thee achine ae in high-eed gound tanotation, liding doo, flexible anufactuing yte, obotic yte, etc. [1]. In a linea induction oto (IM), the iay winding coeond to the tato winding of a otay induction Moto (RIM), while the econday coeond to the oto. Noally, the econday at of a IM i ade of aluinu teel late. A the iay ove, a new flux i continuouly develoed at the enty of the iay yoke, while exiting flux diaea at the exit ide. Sudden geneation diaeaance of the enetating field caue eddy cuent in the econday late. Thi eddy cuent affect the ai ga flux ofile in the longitudinal diection. The loe, a well a the fluxofile attenuation, becoe evee a the eed inceae. Such a henoena i called End Effect of IM []. So, the End Effect hould be conideed in both the odeling contolling of IM in ode to achieve eed o thut tacking. A cuent contol tye vecto contol i geneally ued a a contol ethod of IM [, 3]. The contol chee equie oto oition detecto, the otating coodinate tanfoation, the cuent contolle of which PI contol i geneal, which need the gain tuning. A a eult, the contolle configuation becoe colicated. In ecent yea, diect thut contol (DTC) i efeable to give a fat good dynaic thut eone in the all ediu owe ange alication. Thi contol ethod i diffeent in te of the oeation incile fo the field oiented contol (FOC) o the vecto contol technique. A the vecto contol i a ethod baed on ie cuent contol in the ynchonou efeence fae, DTC i a ethod baed on ie flux contol in the tationay efeence fae [4, 5]. DTC tuctue i vey ile in coaion with the conventional vecto contol i chaacteized by fat dynaic eone low thut ile. Diect thut contol doe not equie a oto oition detecto the cuent contolle in the otating coodinate yte. Thu, oition enole contol can be ealized eaily. DTCbaed dive do not equie the coodinate tanfoation between tationay fae ynchonou fae the invete i diectly contolled by the invete witching tate elected uing witching table. Thu, neithe cuent contolle no ule-width odulation (PWM) odulato i needed [6]. Howeve, the ain diadvantage of DTC i the need fo high aling ate vaiable witching fequency eulting fo hyteei baed contol loo. [7]. In addition, any tudie of DTC in linea induction oto dive ae efoed [1, 3]. inea oto have been exained with thee-hae oving agnetic field odel inufficiently-eeach at of the oble wee inteeted a diffeent odel in the liteatue ha been evaluated. Pola te-change on the oving aea wa odeled with vaiation of agnetic flux. The oto tato agnetic flux change wa deontated gahically envelo duing in diffeent tie calculated theoetically [8]. 75

2 Intenational Jounal on Technical Phyical Poble of Engineeing (IJTPE), I. 1, Vol. 6, No. 4, Dec. 14 Equivalent cicuit odeling of a linea induction oto i oe colicated than a otay induction oto becaue of the exitence of the End Effect. In a otay induction oto, an accuate equivalent cicuit odel i obtained due to it ole-by-ole yety. In the IM becaue of the exitence of the End Effect, electical condition vay at the enty exit oint, o the ole yety aguent i not aintained. Mot of the exiting odel of IM, which have been deived in ecent liteatue, cannot be diectly alied fo the vecto contol becaue of thei deendency on field theoy. Thu, an accuate equivalent cicuit odel of IM i eential fo vecto contol dive [1]. To eliinate diadvantage of conventional DTC uch a high ile of toque flux in low eed, the new contol ethod ha been ooed. In thi ethod the fequency of invete witching ha been inceaed. The ooed contol ethod, contol invete witche diectly by ean of edictive caability [11]. Thee ae eveal technique fo odeling of IM in otating efeence fae, which hel to iulate eciely [1]. The odel of IM with conideing end effect had been ooed in [13]. In thi ae, fit the dynaic odel of the linea induction oto with including End Effect i eeented. By uing diect thut contol, oition enole dive i available in linea eto that can be ued a a fail-afe function of the vecto contol when oition eno boke. Poe adjutent of coefficient of the PI contolle lay an iotant ole in the atifactoy efoance of contol yte. To adjut the coefficient of PI contolle FINDIMITS function COST function which ae two kind of otiization function of MATAB oftwae ae ued. In addition, the iulation eult at tating acceleating in both contol chee i dicued ha been hown by eloyed DTFC contol ethod. Contol chaacteitic have been ioved End Effect doe not have any influence on the contol of the thut the eed. II. DYNAMIC MODE OF INEAR INDUCTION MOTOR A atheatical odel of thee-hae, two-ole eanent-agnet ynchonou oto hould be develoed. Thee-hae, two-ole eanent-agnet ynchonou oto i illutated in Figue 1. DR Q v whee, R ae oto eitance inductance eectively, i the linea iay eed in /, D i the iay length in ete. It can be een in Equation () that the facto i inveely deendent on the velocity. I.e. fo a zeo velocity the End Effect can be v Q neglected ( Q, () f Q ). A the velocity inceae, the end-effect inceae thi caue a eduction of the agnetization cuent of IM. Thi effect ay be quantified by odifying the agnetization inductance a follow: 1 f Q (3) On the othe h, ohic loe occuing with the inceae of the eddy cuent induced at the enty exit end of the econday ut be taken into conideation when the equivalent cicuit i ceated. So, a eitance inet in eie with the inductance in the agnetization banch of the equivalent electical cicuit. Thi eitance eeent the ohic loe oduced by the eddy cuent it i decibed a the oduct of the econday eitance by the facto: R eddy R f( Q) R f Q (4) The equivalent cicuit of the IM i eeented a hown in Figue. Thi cicuit i on a e hae bai. At low eed, thee i no diffeence between the equivalent cicuit of IM RIM. Howeve, if the iay ove, the equivalent cicuit of RIM i not good fo IM becaue of the exitence of the end effect. In ode to develo the dynaic analyi odel-baed contol algoith of IM, the equivalent odel ut be exeed in d-q odel a hown in Figue 3 Figue 4 eectively. enty eddy cuent Seconday Piay Figue 1. End-effect concetion in IM exit eddy cuent A. Moto Modeling To obtain a uitable IM equivalent cicuit, we ut quantify the end effect duing enty exit fo the econday [14]. Figue 1 how the fluxe induced by oving at which called End Effect. Theefoe, the End Effect i odeled by f Q which i eeented by: Q 1 e f Q (1) Q whee, Q i a facto elated to not only the iay length but alo the achine velocity: V R l R f ( Q ) [1 f ( Q )] l Figue. Pe-hae IM equivalent cicuit R 76

3 Intenational Jounal on Technical Phyical Poble of Engineeing (IJTPE), I. 1, Vol. 6, No. 4, Dec. 14 Figue 3. The d-axi equivalent cicuit Figue 4. The q-axi equivalent cicuit Fo the d-q equivalent cicuit of IM, the iay econday voltage equation ae given a follow: V R i R f Q i i (5) d d d d d e q Vq Riq q ed (6) 1 1 V R i (7) d d d e q V R i (8) q q q e d i f Q i i (9) d l d d d i i i (1) q l q d d i f Q i i (11) d l q d d i i i (1) q l q d d whee R i the tato eitance, i d, i d i q, i q ae the tato oto cuent in d-q efeence fae eectively, l, l ae tato oto leakage fluxe,, q, q ae tato oto fluxe in d-q efeence fae eectively. The thut foce the otion equation ae exeed a Equation (13) (14), eectively: 3 Fe diq qid (13) d d V V dv Fe Bv F (14) dt whee, i the ole nube, i the ole itch, F i the load thut foce, i the vicou fiction coefficient of the IM, i the a of the IM. R R e q d ld d + - R f ( Q) [1 f ( Q)] III. PROPOSED DIRECT THRUST FORCE CONTRO FOR INEAR INDUCTION MOTOR Diect thut foce contol i hyteei contol of the foce flux thut, uing the flux linkage etiated by the co voltage the aatue cuent on the d-q coodinate. Outut tato voltage vecto i diectly elected accoding to vecto election table outut of the hyteei contolle. B - + R e d q l q q + - R f ( Q) [1 f ( Q)] - + R The diffeence between the efeence value the actual foce flux, which called the eo ignal, i inut of the hyteei contolle. To contol the thut flux, dual-b ingle- b hyteei contolle ae ued eectively. In thee contolle, the favoable bwidth of the foce flux eo ha been deteined, by conideing the thut flux eo ignal, co to inceae o deceae the foce flux i given baed on the witching table. At thi tage by knowing the cuent oition vecto of foce flux, deending on eithe inceae o deceae the aount of foce o flux, the otiu voltage vecto wee elected fo witching table (ooku-table) i ent to convete (Invete) to aly to the oto. So, thut foce flux linkage ae contolled diectly by electing an aoiate tato voltage vecto. Otiu witching equence in invete i exeed in Table 1. Figue 6 how a block diaga of DTFC. Flux linkage i etiated by the following equation: d vd Rid R f Q id dt (15) q vq Riq dt (16) d q (17) whee, d d-q coodinate, d-q coodinate, q v d i d ae the etiated flux linkage on the v q i q ae voltage co on the ae the etiated cuent on the d-q coodinate, i the tato flux linkage, i the tato eitance. The oition of ie flux i denoted by given by Equation (18): 1 q tan (18) d The thut value i etiated a follow: 3 Fe diq qid (19) Figue 7 how ile exeion odel of a theehae invete a oto. The elation between voltage vecto flux contol aea i deicted in Figue 8. PI T e e T e V DC Hytei contolle Hytei contolle Sa Sb Switching Table Sc Flux Thut etiato Figue 6. A block diaga of DTFC IM i abc,, R 77

4 Intenational Jounal on Technical Phyical Poble of Engineeing (IJTPE), I. 1, Vol. 6, No. 4, Dec. 14 with the oto flux ace vecto. If the d-axi iay cuent (flux cuent coonent) i ket contant, o the electoagnetic foce i diectly ootional to q-axi cuent. By uing vecto contol technique, the thut that i hown in Equation (13) can be calculated by the following equation: 3 Fe diq (3) Figue 7. Sile exeion diaga of a thee-hae invete - IM Figue 8. Relation between voltage vecto flux contol ection SW u SW v SW w Each witche, take eithe tate of 1 o. Thu, the nube of witching ode of thee-hae invete i eight. Fo exale, in ode to have, in outut witch tate of, take 1, eectively. A hown in Figue 6, hyteei coaato give the toque flux-linkage eo tate to vecto election table; then, aoiate tato voltage vecto i elected accoding to the voltage vecto election table hown in Table 1. u 1 SW u Table 1. Vecto election table SW v θ(1) θ() θ(3) θ(4) θ(5) θ(6) e F = e Φ = 1 e F = e F = e F = e Φ = e F = e F = SW w Accoding to above analyi, we obtain a flux contolle eed contolle fo Equation (1) to (8) a follow: * * 4 F f Q i q () * 3 1 f Q i d * * d d 1 1 T (1) Fo Equation (4) we can obtain the li fequency: 1 l i q T () d A entioned, the tato cuent of the linea induction achine ae eaated into flux- thutoducing coonent by utilizing tanfoation to the d-q coodinate yte, whoe diect axi (d) i aligned IV. OPTIMA CACUATION OF PI COEFFICIENT To iove the efoance of PI contolle, diffeent ethod uch a fuzzy logic technique genetic algoith ae ued. In thi ection, coefficient of the contolle ae deteined uing an otiization function. Advantage of thi ethod ae ilicity lack of need fo additional aaete. The fit te i to deteine the objective function. Regading the objective of thi tudy, the eduction of tato flux ile, toque ile the eed eo ate ae iotance. By contolling the toque ile, eed ile i alo ioved. Hence, the toque ile eed eo have been conideed in objective function. Since thee PI ae ued in contol yte the ain goal of thi tudy i PMSM eed contol the objective function exeed a follow: f k, k, j 1,,3 (4) I ef act j j k, k U (5) bj j I j bj b U b whee, ae ue lowe bound fo the coefficient in the defined ange. Two function of COST FINDIMITS ae ued a ain otiization function. A cheatic of the yte deteine the coefficient alongide the contol yte block diaga ae hown in Fig. 5. The axiu nube of iulation eeat, the ange of vaiable coefficient convegence inteval ae given a inut to the yte. FINDIMITS function alie defined bounday containt on the yte duing the coutation. Then, with an initial gue that accoding to bound of the ecified ange i defined, the yte tat calculation. Fo each iulation eeat, the oto eone i coaed with the efeence, oint- to -oint, the aveage eo i calculated fo the entie iulation eiod. If the eo i not within the inteval convegence, the iulation i eeated. A COST function efo convegent exaining. Thee two function with oga witten in a file, deteine the coefficient of contolle. K, K Deteination Cotol Syte i f K, K actual IM Figue 9. Otial PI Coefficient Deteination i 78

5 Intenational Jounal on Technical Phyical Poble of Engineeing (IJTPE), I. 1, Vol. 6, No. 4, Dec. 14 V. SIMUATION RESUTS In thi ection iulation eult to veify the caability feaibility of ooed contol ethod ae hown. The Main aid of thi ae i eed contol of IM. Fo thi uoe, the efeence value of IM eed i elected 8 / that i equal to 8.8 k/h. Thi eed value i highe than conventional ange fo linea oto otion. Figue 1 how the efeence actual eed of IM that i tacked by DTFC ethod eciouly. The ettling tie i equal to.65 ec that i good fo thi ange of eed. Achieving efeence value without any ocillation ile i evident. Fo ued IM accoding to aaete hown in Table,.5 wb i elected a the efeence value of oto flux that Figue 11 how the actual flux of oto. The IM can tack the efeence value at.1 ec that illutate fat ettling tie high dynaic eone. One of the ot iotant featue of DTFC i educing ile alitude. Figue 1 how the zooed view of flux. Maxiu ile alitude i le than. wb that i equal to le than.8% of alitude. With electing d-axi of d-q efeence fae in diection of flux oto, accoding to Figue 13, the flux alitude of oto in q-axi diection will be equal to zeo whole flux will be ceated in d-axi diection. The thee-hae fluxe how in Figue 14 that afte t.7 achieving efeence eed at ec, all aaete have contant value. The thut of oto to geneate deied eed i hown in Figue (15). The axiu alitude of thut i le than 1 N that illutate the caability of contolle to contol oughly high eed IM with low thut ile ocillation. In ode to ceate the flux thut of oto accoding to elated efeence, the cuent that oto conued though gid i hown in Figue 16. Figue 16(a) 16(b) how the cuent in d-q axi Figue 16(c) how thee-hae cuent eectively. A entioned ealie, the end-effect henoenon caue detuctive effect in the efoance of IM. By uing Equation (1) (), Figue 17 how the alitude of end-effect henoenon that i elevant to linea eed vaie with eed change. Afte achieving efeence eed alitude by oto, the change of f Q i contant. inea_eed (/) Figue 5. The linea eed of oto Refeence Actual Flux (wb) Flux_a (wb) Pi_d_foce (wb) Pi_q_foce (wb) Figue 11. The efeence flux alitude Figue 1. Zooed view of flux alitude x (a) (b) Figue 13. The efeence flux of FORCER (a) d-axi (b) q-axi (a) 79

6 Intenational Jounal on Technical Phyical Poble of Engineeing (IJTPE), I. 1, Vol. 6, No. 4, Dec. 14 Flux_b (wb) Flux_c (wb) Thut (N.) (b) (c) Figue 14. The thee hae of efeence flux (a) hae a (b) hae b (c) hae c - I_d_foce (A) I_q_foce (A) Figue 6. The thut of oto (a) -.5 (b) I_abc (A) f(q) (c) Figue 7. The cuent of FORCER (a) d-axi (b) q-axi (c) abc Figue 8. The f Q function Table. IM oto aaete R (Ω) 1.3 D ().38 R (Ω).66 Pole itch.66 (H).6 Nube of ole 4 (H).451 M (kg) 4.5 (H).376 Moto Width ().33 VI. CONCUSIONS In thi ae, eed contol of IM uing diect thut foce contol (DTFC) ethod baed on dynaic odel of IM with conideing end-effect henoenon i eented. In thi contol ethod, flux thut elation by conideing end-effect ae ewitten. Uing thee equation, thut foce flux value ae etiated fo uing in contolle. Becaue of the iotant ole of PI coefficient in it oeation, the coefficient ae deteined uing MAAB otiization function. The DTFC ethod ioved the ile of oto chaacteitic uch a flux thut which wee confied by iulation eult. Alo in the contol ethod DTFC, the end-effect han t any detuctive effect on eed contol, thut flux ditotion. REFERENCES [1] G. Mino Aguila, A.M. Doinguez, M.R. Alvaez, R. Cotez, G. Muoz, F. Gueeo, S. Maya, M. Rodiguez, F. Potillo, H. Azucena, A Diect Toque Contol fo a PMSM, Electonic, th Intenational Confeence on Counication Coute (CONIEECOMP),. 6-64, -4 Feb. 1. [] E.F. da Silva, C.C. Do Santo, J.W.. Ney, Field Oiented Contol of inea Induction Moto Taking Into Account End-Effect, 8th IEEE Intenational Wokho on Advanced Motion Contol 4 AMC 4, , 5-8 Mach 4. [3] J. Zhao, Y. Zhonging,. Jianqiang, T.Q. Zheng, Indiect Vecto Contol Schee fo inea Induction 8

7 Intenational Jounal on Technical Phyical Poble of Engineeing (IJTPE), I. 1, Vol. 6, No. 4, Dec. 14 Moto Uing Single Neuon PI Contolle with Without the End Effect, 7th Wold Conge on Intelligent Contol Autoation (WCICA 8), , 5-7 June 8. [4] A.Z. Bazghaleh, M. Naghahan, H. Mahoudianeh, M. Mehkatoddini, Effective Deign Paaete on the End Effect in Single-Sided inea Induction Moto, Method, Vol. 5,. 9, 1. [5] A. Meedov, T. Abbaov, M. Seke, Intantaneou Diect Contol of Both Magnetic Flux Outut Powe of Induction Moto Uing Fuzzy ogic Contolle, Intenational Jounal on Technical Phyical Poble of Engineeing (IJTPE), I. 11, Vol. 4, No.,. 76-8, June 1. [6] Y.S. ai J.H. Chen, A New Aoach to Diect Toque Contol of Induction Moto Dive fo Contant Invete Switching Fequency Toque Rile eduction, IEEE Tanaction on Enegy Conveion, Vol. 16,. -7, 1. [7] D. Caadei, F. Pofuo, G. Sea, A. Tani, FOC DTC: Two Viable Schee fo Induction Moto Toque Contol, IEEE Tanaction on Powe electonic, Vol. 17, ,. [8] A. Meedov, T. Abbaov, M. Seke, Soe Aect of the Magnetic Field Ditibution Poble of inea Induction Moto, Intenational Jounal on Technical Phyical Poble of Engineeing (IJTPE), Iue 19, Vol. 6, No., , June 14. [9] R.H. Manno, E.G. Diez, Diect Foce Contol fo a Thee-Phae Double-Sided inea Induction Machine with Tanvee Magnetic Flux, 8th Annual Confeence on IECON, Indutial Electonic Society, IEEE, Vol. 4, , 5-8 Nov.. [1] G.G. Kang, K. Na, Field-Oiented Contol Schee fo inea Induction Moto with the End Effect, IEE Poceeding Electic Powe Alication, Vol. 15, No. 6, , 4 Nov. 5. [11] J. Thoa, A. Hanon, Seed Tacking of a inea Induction Moto-Enueative Nonlinea Model Pedictive Contol, IEEE Tanaction on Contol Syte Technology, Vol. 1, No. 5, , Set. 13. [1] D. Hall, J. Kainki, M. Kefta, O. Chitianon, Tanient Electoechanical Modeling fo Shot Seconday inea Induction Machine, IEEE Tanaction on Enegy Conveion, Vol. 3, No. 3, , Set. 8. [13] C.I. Huang, H.K. Cheng, H.H. Chiang, K. Kuang Yang,. Tu Tian, Adative Fuzzy Sliding Mode Contol of inea Induction Moto with Unknown end Effect Conideation, Intenational Confeence on Advanced Mechatonic Syte (ICAMechS), , 18-1 Set. 1. [14] X. Wei, Z. Jian Guo, Zh. Yongchang,. Zixin,. Yaohua, W. Yi, G. Youguang,. Yongjian, Equivalent Cicuit fo Single-Sided inea Induction Moto, IEEE Tanaction on Induty Alication, Vol. 46, No. 6, , Nov.-Dec. 1. BIOGRAPHIES Haed Shadabi wa bon in Adebil, Ian. He eceived the B.Sc. degee in Powe Engineeing fo Univeity of Mohaghegh Adabili, Adebil, Ian in 1. He i cuently tudying the M.Sc. degee in Faculty of Electical Engineeing at Univeity of Tabiz, Tabiz, Ian. Hi cuent eeach inteet include electical dive of electical achine, electical hybid vehicle, owe electonic alication. Ain Rahnaa Sadat wa bon in Tabiz, Ian. He eceived the B.Sc. degee in Powe Engineeing with the fit ank hono in 11 the M.Sc. degee in Electical Machine Dive with the fit ank hono in 14 fo Univeity of Tabiz, Tabiz, Ian. Hi eeach inteet include electic dive, line oto, owe electonic alication electic hybid electic vehicle dive. Ali Pahaei wa bon in Tabiz, Ian. He eceived the B.Sc. degee in Electical Engineeing in 11 the M.Sc. degee in Electical Engineeing fo Gazi Univeity, Ankaa, Tukey, in 13. He i cuently Ph.D. tudent in Electical Engineeing in Gazi Univeity. Fo 1 he i woking a a Reeach Aitant in Gazi Univeity. Hi eeach inteet ae in the aea of enewable enegy ouce, enegy conveion yte, owe electonic electical achine. Mohaad Baghe Banna Shaifian wa bon in Tabiz, Ian in He tudied Electical Powe Engineeing at the Univeity of Tabiz, Tabiz, Ian. He eceived the B.Sc. M.Sc. degee in , eectively fo the Univeity of Tabiz. In 199, he joined the Electical Engineeing Deatent of the Univeity of Tabiz a a lectue. He eceived the Ph.D. degee in Electical Engineeing fo the ae Univeity in. In, he ejoined the Electical Powe Deatent of Faculty of Electical Coute Engineeing of the ae univeity a Aitant Pofeo. He i cuently a Pofeo of the entioned deatent. Hi eeach inteet ae in the aea of deign, odeling analyi of electical achine, tanfoe, electic dive, line electic oto, electic hybid electic vehicle dive. 81