Intenational Jounal of Intumentation and Contol ytem (IJIC) Vol., No., Octobe HIGH PERFORMANCE CONTROLLER FOR PEED AND POITION INDUCTION MOTOR DRIVE UING NEW REACHING LAW alah Eddine Rezgui, Hocine Benalla Contantine Electotechnic Laboatoy, Enginee cience Faculty of Mentoui Contantine Univeity, ALGERIA _alaheddine@yahoo.f benalladz@yahoo.f ABTRACT Thi pape peent new appoach in obut indiect oto field oiented (IRFOC) induction moto (IM) contol. The intoduction of new exponential eaching law (ERL) baed liding mode contol (MC) impove ignificantly the pefomance compaed to the conventional MC which ae well known uceptible to the annoying chatteing phenomenon, o, the elimination of the chatteing i achieved while implicity and high pefomance peed and poition tacking ae maintained. imulation eult ae given to dicu the pefomance of the popoed contol method. KEYWORD Field Oiented Contol; Induction Moto; liding Mode Contol; Exponential Reaching Law, Poition and peed Tacking.. INTRODUCTION The field-oiented contol technique ha been widely ued when high-pefomance otay machine dive i equied, epecially the indiect field oiented contol (IFOC) which i one of the mot effective vecto contol of IM due to the implicity of deigning and implementation []. Advent of high witching fequency PWM invete ha made it poible to apply ophiticated contol tategie to AC moto dive. The pace vecto modulation (VM) technique ha become one of the mot impotant PWM method. It appea to be the bet altenative fo a thee phae witching powe convete becaue it povide an optimization of convete opeation; educing the commutation of the powe emiconducto, doe not geneate ubhamonic component, with capacity about 9.6% of DC link exploitation, and it become the bet technique to educe the ipple in the toque ignal []. Howeve the claical popotional-integal and deivative (PID) contolle' which ae the main contol tool being ued in AC machine dive, have majo dawback that ae the enitivity to the ytem-paamete vaiation and bad ejection of extenal ditubance. To umount thee dawback and impove the induction moto contol technique, a et of pape ae peented in the liteatue, we cite a non exhautive example; the fuzzy and neuo-fuzzy contol [3,4], the DOI :.5/ijic..3 3
Intenational Jounal of Intumentation and Contol ytem (IJIC) Vol., No., Octobe neual netwok contol [5], the liding mode contol [6], and the neuo-fuzzy-liding mode contol [7]. All of afoementioned technique peent a good pefomance, but in tem of fat epone and obutne againt uncetaintie including; paametic vaiation, extenal ditubance ejection, and unmodelled dynamic, the liding mode contolle i computationally imple compaed to adaptive contolle with paamete etimation and have the advantage and bet high eult that lead to the impovement of IM contol [8]. The MC wa fitly invetigated fo electic moto by Utkin [9], it deign method i geneally baed on two tep, fit, the election of an appopiate liding uface, and econd, the ynthei of a contol law uch that a eaching condition i atified which make the elected uface attactive, then, that evolve two mode; eaching mode and liding mode. Nevethele, befoe attaining the liding uface (i.e. eaching mode), the ytem cannot dominate the vaiation in paamete and extenal ditubance, thu making weak obutne of the ytem []. It i a well known opinion that the majo dawback of liding mode contol i the chatteing phenomenon. The chatteing conit of the ocillation of the contol ignal, tied to the dicontinuou natue of the contol law, at a fequency and amplitude which cannot be toleated in ome pactical application, epecially mechanical and electo-mechanical one, alo thi hamful phenomenon, i caued by unmodeled dynamic o dicete time implementation []. A lage numbe of wok deal to educe the chatteing have been developed, fit of them conit of a oft continuou appoximation of the dicontinuou law, when bounday laye of definite width on both ide of liding plane i intoduced [], Thi method can give a chatteing eduction ytem but a finite teady tate eo mut exit, othe wok intoduce new witching uface; a nonlinea and time-vaying paabolic liding uface to impove the dicontinuou contol law pat of a claical liding mode contolle [3], alo in [4], the popoed modification conit in modifying the liding uface uing fuzzy ule. Thee tuctue make the implementation of contolle moe complex and affect ytem convegence to the uface. The appoach, called highe ode MC, ha been popoed in ode to educe the chatteing phenomenon. Intead of influencing the fit liding vaiable time deivative, the ignum function act on it highe ode time deivative, then the chatteing poblem i avoided by emoving dicontinuity fom contol input. The pape popoed econd, and high ode contolle epectively in [5,6] but, in pite of chatteing attenuation, uch method ae ovely complex and difficult to implement in pactice. Beide of thee wok, in lat decade a new concept called Reaching Law Method (RLC) had been intoduced in liding mode contol [7]. In thi method the eo dynamic i pecified in the eaching mode, with electing appopiately paamete both the dynamic quality of the MC ytem can be contolled and the chatteing i emoved. Many eeache pay attention to thi appoach. In [8] autho ha applied contant plu popotional ate RLC ued in [7] fo Pemanent Magnet ynchonou Moto PMM dive ytem. The eult howed that, the popoed method gave fat peed epone time, with good ejection of ditubance, but the obutne of the ytem againt paametic uncetaintie wa not conideed. In [9] autho popoe an impovement of powe ate RLC of the aticle [7], accoding the ditance between the initial tate and the liding uface, the ytem tate can each the witching uface fat when fa away fom it, and the peed low down when the tate ente into cetain cope. The popoed method give the ytem moe apidne and the dynamic ytem without high fequency chatteing ha been achieved. The main aim of thi tudy i to invetigate the RLC method in vecto-contolled IM fo peed and poition contol ytem baed on new exponential eaching law (ERL) that atify the 3
Intenational Jounal of Intumentation and Contol ytem (IJIC) Vol., No., Octobe condition of tability accoding to Lyapunov theoem. Thi method wa applied uccefully fo obot am in []. Thi pape i oganized a follow; the dynamic model of induction moto and deciption of field-oiented contol ae given in ection, Detail of liding-mode contolle deign i given in ection 4, In ection 5, we have focued inteet on the theoetical of the popoed method. Thi wok will be completed by a imulation in ection 6, and finally, ome concluding emak ae given in ection 7.. FIELD ORIENTED CONTROL OF IM. Dynamic Model of Induction Moto The dynamic model of thee-phae, Y-connected induction moto can be expeed in the d-q ynchonouly otating fame a []: did R = ( R + ) id + ωi dt σ L L di R = ω id ( R + ) i dt σ L L dψ d R R = id ψd + ωlψ q dt L L dψ q R R = i ωlψ d ψq dt L L R + ( ) ψd + ( ) ωψq + v σ L L σ L L σ L R ( ) ωψd + ( ) ψq + v σ L L σ L L σ L d () whee i d, i, ψ d, ψ d, and v d, v a ae epectively the d-axi and q-axi tato cuent, oto flux linkage, and tato voltage, R and R ae the tato and oto eitance, L and L ae the tato and oto inductance, L m i the mutual inductance between the tato and the oto winding, σ = ( / L L ) i the total leakage facto, ω i the ynchonouly otating angula peed, ω i the electical angula peed of the oto, and ω l = ω ω i the lip fequency. Moeove, the electomagnetic toque T e can be expeed in tem of tato cuent and oto flux linkage a: T e 3 L m = p ( ψ d i ψ q id ) () L whee p i pole pai numbe. The motional equation of IM i decibed a: dω J = Te TL fv Ω (3) dt Whee J i the moment of inetia, T L i the load toque, f v i the vicou fiction coefficient, and Ω = ω / p i the mechanical oto peed.. Deciption of Indiect Field-Oiented Contol The pinciple of indiect field-oiented contol ytem of an induction moto i that the d-q coodinate' efeence fame i locked to the oto flux vecto, thi eult in a decoupling of the vaiable o that flux and toque can be epaately contolled by tato diect-axi cuent i d, and quadatue-axi cuent i, epectively, like in the epaately excited dc machine. To pefom the 33
Intenational Jounal of Intumentation and Contol ytem (IJIC) Vol., No., Octobe alignment on a efeence fame evolving with the oto flux equie infomation on the modulu and poition of the oto flux. When the efeence fame d-q i aligned with the oto flux a in Figue, we have: ψ ψ d q = ψ = (4) q i d i i d ψ = ψ d Figue. Field oientation in d-q efeence fame Whee ψ, i, ae the flux and cuent vecto. Then the ytem () i ewitten a: did R = ( R + ) id + ωi dt σ L L di R = ω id ( R + ) i dt σ L L dψ d R R = id ψ d dt L L L i m ω l = T ψ d R + ( ) ψ d + v σ L L σ L ( ) ω ψ d + v σ L L σ L d (5) Whee T =L /R i the oto time contant. The electomagnetic toque and the ynchonou angula peed can be expeed then a: T = K i (6) e t Whee : 3 Kt = p L ψ d L m = pω (7) ω + T i ψ The poition i detemined then a follow: d 34
Intenational Jounal of Intumentation and Contol ytem (IJIC) Vol., No., Octobe θ = ω dt (8). 3. LIDING MODE CONTROLLER The tanient dynamic epone of the ytem i dependent on the election of the liding uface. fou liding uface ae defined, Ω fo peed contolle, θ fo poition contolle, d and q fo diect and quadatic cuent contolle epectively. Fit, let deign the new exponential eaching law. 3.. Deign of the Exponential Reaching Law (ERL) ince the conventional MC may not handle intenal and extenal uncetaintie duing the eaching mode, the intoduction of exponential appoach in IRFOC method guaantee liding behavio thoughout entie epone. In the RLC appoach, a diffeence equation that pecifie the dynamic of the witching function i fit choen: = k ign () The tem k foce the tate to tee towad the choen uface apidly when i lage in a finite time given by: = () k t It i obviou that, inceaing k lead to a hote time of eaching mode. Howeve, one mut take into conideation when detemining the coefficient k, becaue lage value induce high fequency ocillation. Accoding to [], an exponential tem of eaching law i popoed which can adapt to the vaiation of the witching function. Thi i given by: k = ign ( ), N( ) k > () (9) Whee: α P N( ) = δ + ( δ ) e () and: < δ < p >, p N (3) α > Fom () it can be een that, fo lage value of, N() tend δ and then k/n() convege to k/δ which i geate than k. Othewie, if deceae, N() appoache one, and convege to k. Thi mean that, in the fit cae, the convegence towad the liding uface will be fate, and in econd cae, k/n() deceae gadually, which limit the chatteing. Fom thi analyi, one can ee that, the popoed ERL appoach i adaptive to the vaiation of the witching uface. 35
Intenational Jounal of Intumentation and Contol ytem (IJIC) Vol., No., Octobe Moeove, in popoed ERL appoach, the time to each the liding uface i hote than conventional MC given in (), indeed, let define the eaching time, integating () between zeo and yield: t = δ + ( δ) ign( ) e k P α d (4) Fo and, (3) can be ewitten a: P α t = + e δ ( δ) d k (5) ubtacting (3) fom (3) yield: P ( δ = t t ) α [ e ] k d (6) Knowing that ( e P α ),, thent t. Thi demontation how that, eaching peed in the popoed ERL i inceaed fo the ame gain k, in othe hand, fo the ame eaching time the popoed appoach educe chatteing (becaue k i malle). Thu, the contol law in Equation (9) may be enitive to uncetaintie and ditubance acting on the ytem duing the eaching phae. Theefoe, it may be adjuted to impove the ytem pefomance. Fo moe detail on how to chooe the ERL paamete ee []. 3.. Deign of peed Contolle We chooe integal liding uface []: Ω ( t) e( t) k = Ω Whee k Ω i a negative contant. t ( a) e( τ ) d ( τ ) (7) Conideing the mechanical equation we have: Ω + a Ω + f = b (8) i Whee: f T L K t a = v, f =, b &, J J = and ( ) i the deivative. J Now, we conide the peviou mechanical equation with uncetaintie a follow: 36
Intenational Jounal of Intumentation and Contol ytem (IJIC) Vol., No., Octobe Ω = a + a) ω ( f + f ) + ( b + b) (9) ( i Whee the tem a, f, b ae the uncetaintie of the tem a, f and b epectively. The eo of peed tacking i defined a: e Ω ( t ) Ω ( t) Ω ( t) = () Whee Ω (t ), i the efeence oto peed. The time deivative of () give: e Ω( t) = Ω( t) Ω ( t) = a e( t) + u( t) + d( t) () Whee: u( t) = b i a Ω ( t) f( t) Ω ( t) () d( t) a Ω( t) f + b i ( t) = (3) The command u(t) i defined by: u( t) = k e ( t) β ign ( ( t)) (4) Ω Ω Whee β i the witching gain, it mut be choen o that β d ( t ) Ω t, o the peed tacking eo e Ω (t) tend to zeo a the time tend to infinity. ubtituting (4) in () give the toque cuent efeence: i = [ kω eω β ign( Ω) + aω + Ω + f ] (5) b 3.3. Deign of Cuent Contolle Pecie and fat cuent contol i eential to achieve high tatic and dynamic pefomance fo the IRFOC of induction moto. If the tato cuent ae not adjuted peciely and with fat dynamic to the command value, co coupling will appea between the moto toque and oto flux. Thu, the pefomance of the IRFOC degade. The cuent contolle deign ue two liding uface fo d-axi and q-axi tato cuent epectively defined a: d = i * i (6) d d q = i * i (7) 37
Intenational Jounal of Intumentation and Contol ytem (IJIC) Vol., No., Octobe whee i d, i ae the command value of tato cuent component. The contolle ha to maintain the ytem on the liding mode alway, that i d = q =. Fo thi, the diect method of Lyapunov i ued in tability analyi. Conideing the Lyapunov function candidate: It time deivative i: = > V (8) = V (9) Fom Lyapunov theoem we know that if V i negative definite, the ytem tajectoy will be diven and attacted towad the liding uface and emain liding on it until the oigin i eached aymptotically. * The contol input v v ae elected a follow: *, d v = v + v * d * deq v = v + v eq dn n (3) (3) I noted that, v, v ae the equivalent contol, it can be etimated fom the model paamete deq eq and meaued tate, a follow: v deq = σ L R L * m m * ( id ω i) + R + i d ψ d L L L R (3) v deq = σ L R L * m m * ( i+ ω id) + R + i PΩψd L L L (33) v dn and v n ae the dicontinuou contol law which foce the ytem to move on the liding uface. v = k ign ) (34) dn id ( d v = k ign ) (35) n iq ( q Whee K id, K iq, ae a poitive contant, epeenting the maximum contolle output equied to ovecome paamete uncetaintie and ditubance [9]. And ign i the ignum function. 38
Intenational Jounal of Intumentation and Contol ytem (IJIC) Vol., No., Octobe If we chooe the ign function a uually, thee will be lage chatte in the output. Thi poblem can be emedied by uing a continuou function in the liding uface neighbouhood, a uually doing in the vaiable tuctue contol, that i: if ε at ( ) = ε (36) ign( ) if > ε Whee the contant facto ε define the thickne of the bounday laye and at i the atuation function. 3.4. Poition Contol of IM The poition eo i defined a follow: = (37) when the liding uface i given by: = + (38) The motional equation (8) can be ewitten: Then: = + (39) = + + + (4) Fo =, we dive the equivalent contol a: = [ + + + ] (4) The dicontinue contol i: = (4) Whee k θ i a poitive gain. The ign function i eplaced by at a in (36). 4. IMULATION REULT In ode to veify the pefomance of the popoed ERL method the block diagam of the IM dive hown in Figue, wa imulated in Matlab/imulink. Accoding to [], the induction moto ued i a thee phae, Y connected, fou pole, 3 kw, 45 pm/, /38V, 6.9A, 5Hz. Electical and mechanical paamete ae, R =.84Ω, R =.84Ω, L =L =.7 H, L m =.6 H, J =.54 kg.m, Coφ =.89. The oto flux i et at it ated value i.e..99wb, and the electomagnetic toque cuent command (i * ) i limited at 7 A, to avoid atuation and oveload tanient, and the VI fequency at 5 khz. 39
Intenational Jounal of Intumentation and Contol ytem (IJIC) Vol., No., Octobe 4.. peed Pefomance Analyi Figue. Global cheme of IM contol The value of the MC and ERL paamete ae in the following; k Ω = -5, β=5, k id =3, k iq =5. = = =., =3, =3, =3, = = =. The tet i deigned fo peed egulation with multiple tep command, tating without load and with ditubance application (T L = Nm) at t=.65. 5 actual and command oto peed actual efeence peed [pm/mn] 5-5 - -5..4.6.8..4.6.8 Time () peed eo 5 peed [pm/mn] -5 - -5 - -5-3..4.6.8..4.6.8 Time [] 4
Intenational Jounal of Intumentation and Contol ytem (IJIC) Vol., No., Octobe 3 Electomagnetic and Load Toque Te [Nm] - - Te TL -3..4.6.8..4.6.8 Time []. oto flux component.8 flux [Wb].6.4. -...4.6.8..4.6.8 Time [] Figue 3. Field oientation in d-q efeence fame On the eult hown in Figue 3 one can ee a high pefomance peed epone obtained depite the ditubance, and the electomagnetic toque ie to it efeence intantly afte the tanient. Fom the oto flux wavefom, it i obviou that the ideal IRFOC i achieved in all woking condition. 4.. Poition Pefomance Analyi The poition tacking contol i teted with ectangula wavefom efeence limited at θ * = ± 4, tating at t=.5 with no-load and when the ditubance i applied at t=.6. And the MC paamete ae; k θ =, λ=3.85, k id =5, k iq =5. The ERL paamete ae the ame a peviou. 4
Intenational Jounal of Intumentation and Contol ytem (IJIC) Vol., No., Octobe actual and efeence oto poition oto poition [deg] - - actual efeence.5.5.5 3 3.5 4 4.5 Time [] oto peed peed [pm/mn] 5-5 -.5.5.5 3 3.5 4 4.5 Time [] 3 Electomagnetic and Load Toque Te [Nm] - - Te TL -3.5.5.5 3 3.5 4 4.5 Time [] oto flux component..8 flux [Wb].6.4. -..5.5.5 3 3.5 4 4.5 Time [] Figue 4. Field oientation in d-q efeence fame 4
Intenational Jounal of Intumentation and Contol ytem (IJIC) Vol., No., Octobe The eult depicted on Figue 4, how a vey high pefomance tacking contol without ovehoot o teady-tate eo even afte applying of the load toque on the moto haft. We can alo ee the oto flux component which fully maintained the pinciple of the IRFOC. 4.3. Paamete Uncetaintie Tet The obutne of the method i now conideed when a tep vaiation about 7% of nominal oto eitance value i intoduced at t=.7, and fo diffeent value on moment of inetia. The Figue 5 and Figue 6, how that the behavio of the contolle i inenitive to thee paamete uncetaintie fo both peed and poition contol. 5 Roto eitence vaiation tet actual efeence peed [pm/mn] 5-5 - -5..4.6.8..4.6.8 Time [] peed [pm/mn] 5 5-5 oto peed fo diffeent value of J J=Jn J=.5Jn J=.5Jn efeence - -5..4.6.8..4.6.8 Time [] Figue 5. peed tacking obutne tet 43
Intenational Jounal of Intumentation and Contol ytem (IJIC) Vol., No., Octobe Roto eitance vaiation tet oto poition [deg] - - actual efeence..4.6.8..4.6.8 Time [] oto poition fo diffeent value of J oto poition [deg] - - J=Jn J=.5Jn J=.5Jn poition ef..4.6.8..4.6.8 Time [] 5. CONCLUION Figue 6. Poition obutne tet In thi tudy, a new appoach of obut IM contol wa given to impove the dicontinuou contol law pat of a claical liding mode contolle. The eult have hown that the popoed method impove the ytem tanient epone and leen the effect of ditubance a it deceae the eaching time. The ditinctive featue of the cheme compaed to conventional MC, i it obutne and high tacking pefomance to diffeent command value and paamete mimatch fo both poition and peed contol without chatteing uffeing. The imulation eult confim the effectivene of the popoed ERL contol appoach. REFERENCE [l] B. K. Boe, Moden Powe electonic and AC dive, The Univeity of Tenneee, Knoxville, UA, Pentice Hall,. [] H. van de Boeck, H.C. kudelny, G.V. tanke, Analyi and Realization of a Pule Width Modulation Baed on Voltage pace Vecto, IEEE Tan, Ind. App. vol 4, pp 4-5, Jan/Feb 987. [3] Fnaiech, M.A., Betin, F., Capolino, G.-A., Fnaiech, F., Fuzzy Logic and liding-mode Contol Applied to ix-phae Induction Machine With Open Phae, IEEE Tanaction On Indutial Electonic, Vol. 57, No., januay. 44
Intenational Jounal of Intumentation and Contol ytem (IJIC) Vol., No., Octobe [4] Uddin, M.N.; Hao Wen, Development of a elf-tuned Neuo-Fuzzy Contolle fo Induction Moto Dive, IEEE Tan. On Induty Application, Vol. 43, No. 4, pp. 8-6, July-Aug. 7. [5] Chih-Min Lin, Chun-Fei Hu, Neual-netwok-baed adaptive contol fo induction evomoto dive ytem, IEEE Tan. On Indutial Electonic, Vol. 49, No., pp. 5-3, Feb.3. [6] K. Jamoui, M. Ouali, H. Chaadi, A liding Mode peed Contol of an Induction Moto, Am. J. Applied. ci. 4(): pp 987-994, cience Publication 7. [7] Vadim I. Utkin, Adaptive liding-mode Neuo-Fuzzy Contol of the Two-Ma Induction Moto Dive Without Mechanical eno, IEEE Tan. Ind. Electon. Vol. 57, No., pp. 553 564, Feb.. [8] Aif abanovic, Vaiable tuctue ytem With liding Mode in Motion Contol A uvey, IEEE Tan. Ind. Inf. vol 7, No. pp. 3, May. [9] Vadim I. Utkin, liding mode contol deign pinciple and application to electic dive, IEEE Tan. Ind. Electon. vol 4, pp. 3 36, 993. [] Zhimei Chen, Wenjun Meng, Jinggang, He Wang, Fuzzy Reaching Law liding Mode Contol of Robot Manipulato, IEEE Pacific-Aia Wokhop on Computational Intelligence and Indutial Application, pp. 393-397, 8. [] Hoon Lee, Vadim I. Utkin, Chatteing uppeion method in liding mode contol ytem, Annual Review in Contol 3, pp. 79-88, Elevie Ltd. 7. [] J. C. Hung, Chatteing Handling fo Vaiable tuctue Contol ytem, Poceeding of the IECON, Intenational Conf. on vol. 3, pp. 968-97, Nov 993. [3] L. K. Wong, F. H. F. Leung, P. K.. Tam, A chatteing elimination algoithm fo liding mode contol of uncetain non-linea ytem, Mechatonic 8, pp. 765-775, Elevie Ltd. 998. [4] E. Igleia, Y. Gacía, M. anjuan, O. Camacho, C. mith, Fuzzy uface-baed liding mode contol, IA Tanaction, Volume 46, Iue, pp. 73-83, Feb. 7. [5] Damiano, A., Gatto, G.L., Maongiu, I., Piano, A., econd-ode liding-mode Contol of DC Dive, IEEE Tan. Ind. Electon. Vol. 5, No., pp. 364 373, 4. [6] Taoe, D., Pletan, F., Glumineau, A., de Leon, J., enole Induction Moto: High-Ode liding-mode Contolle and Adaptive Inteconnected Obeve, IEEE Tan. On Ind. Electon. Vol. 55, No., pp. 388-387, Nov. 8. [7] Weibing Gao; Hung, J.C., Vaiable tuctue Contol of Nonlinea ytem: A New Appoach, IEEE Tan. On Ind. Electon. Vol. 4, No., pp. 45-55, Feb. 993. [8] Ying Liu, Bo Zhou, Haibo Wang, ichen Fang. A New liding Mode Contol fo Pemanent Magnet ynchonou Moto Dive ytem Baed on Reaching Law Contol, 4th IEEE Conf. Indutial Electon. And Appl., pp. 46 5, ICIEA 9. [9] hibin u, Heng Wang, Hua Zhang, Yanyang Liang, Wei Xiong, Reducing Chatteing Uing Adaptive Exponential Reaching Law, ixth Intenational Confeence on Natual Computation (ICNC), Vol.6, pp. 33-36,. [] Fallaha, C.J., aad, M., Kanaan, H.Y., Al-Haddad, K., liding-mode Robot Contol With Exponential Reaching Law, IEEE Tan. On Ind. Electon. Vol. 58, No., pp. 6-6, Feb.. [] Baambone O., Gaido A.J., Maeda F.J. A Robut Field Moto with Flux Oiented Contol of Induction Obeve and peed Adaptation, Emeging Technologie and Factoy Automation, IEEE Confeence, vol.. pp.45 5, eptembe. 3. [] Maek Jaińki, Diect Powe and Toque Contol of AC/DC/AC Convete-Fed Induction Moto Dive, Ph.D. Thei (Faculty of Electical Engineeing) Waaw, Poland, 5. 45
Intenational Jounal of Intumentation and Contol ytem (IJIC) Vol., No., Octobe Autho alah Eddine Rezgui wa bon in Contantine, Algeia in 97. He eceived the B.T., L.T., and magiteial degee in electic machine dive, fom the Mentoui Contantine Univeity in 9. Now he i PhD tudent and eeache' membe in Contantine Electotechnic Laboatoy, Hi eeach inteet include moden theoy application contol, electic machine dive, and powe electonic. Hocine Benalla wa bon in Contantine, Algeia in 957. He eceived the B.., M.., and Doctoate Enginee degee in powe electonic, fom the National Polytechnic Intitute of Touloue, Fance, epectively in 98, 984. In 995, he eceived the Ph.D. degee in Electical Engineeing fom Univeity of Juieu-Pai VI, Fance. ince 996, he i with the depatment of Electotechnic, at Contantine Univeity Algeia, a a Pofeo. Hi cuent eeach field include Active Powe Filte, PWM Invete, Electic Machine, and AC Dive. 46