DOUBLE STAR INDUCTION MOTOR DIRECT TORQUE CONTROL WITH FUZZY SLIDING MODE SPEED CONTROLLER

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1 Rev. Roum. Sci. Techn. Élecroechn. e Énerg. Vol.,, pp. 3 3, Bucares, 7 DOUBLE STAR INDUCTION MOTOR DIRECT TORQUE CONTROL WITH FUZZY SLIDING MODE SPEED CONTROLLER ABDELKADER MEROUFEL, SARRA MASSOUM, ABDERRAHIM BENTAALLAH 3, PATRICE WIRA 4, FATIMA ZOHRA BELAIMECHE, AHMED MASSOUM Key words: Double sar inducion moor (DSIM), Direc orque conrol (DTC), Sliding mode conrol (SMC), Fuzzy logic conroller (FLC), Fuzzy sliding mode conroller (FSMC), Flux and orque esimaors. In his paper, we presen a speed fuzzy sliding mode conrol for a direc orque conrolled double sar inducion moor (DSIM). Direc orque conrol (DTC) uses only a couple of hyseresis comparaors o perform boh orque and flux dynamic conrol. The proposed conrol scheme uilizes a fuzzy sliding mode conroller (FSMC) for he speed conrol. The FSMC is formed wih he robusness of sliding mode conrol (SMC) and he smoohness of fuzzy logic (FL). Few fuzzy rules are used for his sraegy conrol. The sliding mode conrol is used o achieve robus performance agains parameer variaions and exernal disurbances. The problem wih his convenional conroller is ha i has large chaering on he orque and he drive is very noisy. In order o reduce chaering, he sign funcion is subsiued wih a fuzzy conrol law which draws he sysem sae variables ino prespecified bounds of sliding mode surface. The compuer simulaions are conduced o demonsrae he saisfacory racking performance and robusness of he conrol wih reduced chaering problem.. INTRODUCTION During he las years, he modeling and conrol of double sar inducion moor (DSIM) has been he subjec of invesigaions [, ]. The vecor conrol of inducion moor drive has made i possible o be used in applicaions requiring fas orque conrol such as racion. In a perfec field oriened conrol, he decoupling characerisics of he flux and orque are affeced highly by he parameer variaion in he machine. One possible alernaive o he vecor conrol is he use of direc orque conrol (DTC) sraegies wih several advanages based on possible conrol direcly he saor flux linkage and he orque by selecing appropriae swiching volage vecors of he inverer. The DTC echnique possesses advanages such as less parameer dependency, fas orque response and simple conrol scheme [3]. The speed classical conroller used in DTC- DSIM presens sensiiviy in performance o he parameer variaions and inadequae rejecion of inernal disurbances and load changes. One way o improve sliding mode conroller performance is o combine i wih fuzzy logic o form a fuzzy sliding mode conroller (FSMC). In his paper, he fuzzy sliding mode conroller is designed for he speed regulaion of a DTC-DSIM. To evaluae he usefulness of he proposed mehod, we compare i o oher conroller.. DSIM MATHEMATIC MODEL The sudy presened in his paper is based on he following assumpions: The air gap is uniform and he windings are sinusoidally disribued around he air gap. The magneic sauraion and core losses are negleced. The DSIM has wo ses of hree-phase windings spaially shifed by 3 elecrical degrees wih isolaed neural poins. Volages equaions: dds = Vds ds d ls dqs = Vqs qs d l s dds = V ds ds d ls d qs = Vqs qs d ls d R dr r = Vdr dr d lr dqr Rr = Vqr qr d lr Mechanical equaion: dω = Ce Cr K f Ω d lm Te = p dr Iqs + Iqs lm + lr dm + ωsqs qm + ωsds dm + ωsqs. () qm + ωsds dm + ωsqr qm + ωsdr [ ( ) ( I + I )] qr ds ds. () The flux equaions are given by he following expressions: = ll +, = ll + qs= ll s qs+qm, qs = ll s qs + dr = ll r dr +dm, qr = ll r qr +qm ds s ds dm ds s ds dm ( ) = l I + I + I = l I + I + I dm m ds ds dr ( qs qs ) qm m qr qm ( ) ( ) s ds ds qs qs, (3), (4) = () The erms used in he previous expressions are he following: V ds, V qs, V ds, V qs, respecively saor vol-, ICEPS, UDL Sidi Bel Abbes, ameroufel@yahoo.fr ICEPS, UDL Sidi Bel Abbes, lalem_sarra@yahoo.fr 3 ICEPS, UDL Sidi Bel Abbes, ba_asmo@yahoo.fr 4 MIPS, IUT Mulhouse, parice.wira@uha.fr

2 3 Abdelkader Meroufel el al. ages in d axis and q axis of and ; I ds, I qs, I ds, I qs respecively saor currens in d axis and q axis of and ; I dr, I qr roor currens in d axis and q axis; ds, qs, ds, qs respecively saor fluxes in d axis and q axis of and ; ω r, ω s roor speed and naural frequency; p pole number of he roor; C e elecromagneic orque; C r load orque; ineria sysem; K fricion coefficien. f 3. VOLTAGE SOURCE INVERTER MODELING PWM is used in power elecronics o digialize he power so ha a sequence of volage pulses can be generaed by he on and off for he power converer. Then, he PWMvolage source inverer (VSI) is expressed by he imposed sequencings a semiconducors which realize modulaion of volages applied o saor windings. Volages a load neural poin, for one SVI, can be given by he following expression [3]: Va Vd Vb = Vc S S. () S3 4. DIRECT TORQUE CONTROL STRATEGY Basically, DTC schemes require he esimaion of he saor flux and orque. The saor flux evaluaion can be carried ou by differen echniques depending on wheher he roor angular speed or (posiion) is measured or no. The saor flux can be evaluaed by inegraing from he saor volage equaion: s() = ( Vs Is)d. (7) This mehod is very simple requiring he knowledge of he saor resisance only. The effec of an error in is usually quie negligible a high exciaion frequency bu becomes more serious as he frequency approaches zero [4]. Fig. Block diagram of simulaed swiching able direc orque conrol (ST-DTC) wih speed FSMC. The basic idea of he DTC concep, whose block diagram represenaion of he DSIM-DTC wih a speed conrol loop is shown in Fig., is o choose he bes vecor of he volage, which makes he flux roae and produce he desired orque. During his roaion, he ampliude of he flux ress in a predefined band. Basically, he saus of he errors of saor flux magniude s and elecromechanical orque C e are deeced and digialized by simple wo- and hree-level hyseresis comparaors. An opimum swiching able is hen used o deermine he saus of hree swiches S a, Sb, Sc and he corresponding volage space vecor V i, (i =,,,,7) depending on he saor flux region θ s. The saor flux posiion θ s is deermined by dividing he d-q plane ino six o regions. Simple hree sign deecors are used o deermine he secor where he saor flux exiss. In order o exploi he operaion possible sequences of he inverer on wo levels, he classical selecion able of he DTC is summarized in able. I shows he commuaion sraegy suggesed by Takahashi [], o conrol he saor flux and he elecromagneic orque of he machine. The following able shows he differen choices of he volage vecor o be applied according o he resuls given o he oupu of boh flux and orque comparaors. Table Selecion of volage vecors in he basic ST-DTC s C e z z z 3 z 4 z z d c = V 3 V 4 V V V V d = d c = V V 7 V V 7 V V 7 d c = V V V V V 3 V 4 d c = V V 3 V 4 V V V d = d c = V 7 V V 7 V V 7 V d c = V V V V 3 V 4 V Selecion of volage vecors in he basic ST-DTC. FUZZY SLIDING CONTROL FSMC is a presen employed as an alernaive o develop conroller for sysems ha canno be precisely modelled and whose parameers vary [, 7]. The basic principle of he sliding mode conrol consiss in moving he sae rajecory of he sysem oward a surface S(X) = and mainaining i around his surface wih he swiching logic funcion U n. The basic sliding mode conrol law is expressed as: Uc = Ueq + Un. (8) This expression uses wo erms, U eq and U n : U eq is deermined wih a model ha represens he plan as accuraely as possible. I is used when he sysem sae is in he sliding mode and U n a sign funcion. To design a sliding mode speed conroller for he double sar inducion moor DTC drive, consider he mechanical equaion: p K f r + ωr + Cr = Ce p ω, (9) where ω r is he roor speed in elecrical rad/s, rearranging o ge: p K f p r = Ce ωr Cr ω. ()

3 3 Direc orque conrol wih fuzzy sliding mode speed conroller 33 Considering Δa and Δb as bounded uncerainies inroduced by sysem parameers and K f, () can be rewrien as [7]: ( a + Δa) ωr + ( b + Δb) Ce + ccr ω r =, () K f p p where a =, b =, c =. Defining he sae variable of he speed error as: e * () ω ( ) ω ( ) = r r, () combining () wih () and aking he derivaive of () yields { } () = ae() + b C d() e e +, (3) where d() is he lumped uncerainy defined as: Δa Δb c d () = ωr () + Ce + Cr (4) b b b a * Ce () = Ce () + ω. () b Defining a swiching surface s() from he nominal values of sysem parameers a and b [7]: s s () = e() ( a + bk)( e τ)τ d () = e() ( a + bk)( e τ)τ d, (). (7) Such ha he error dynamics a he sliding surface s() = s ( ) = will be forced o exponenially decay o zero, hen he error dynamics can be described by: e = a + bk e, (8) () ( )() where k is a linear negaive feedback gain. A speed conrol law can be defined as: C e () βsign( s() ) = ke, (9) where β is known as hiing conrol gain used o make he sliding mode condiion possible and he sign funcion can be defined as [7]: if s > sign ( s) = if s =. () if s < The final elecromagneic orque command C e of he oupu of he sliding mode speed conroller can be obained by direcly subsiuing () ino (9). Basically, he conrol * law for C is divided ino wo pars: equivalen conrol Ueq e which defines he conrol acion when he sysem is on he sliding mode and swiching par Us which ensures he exisence condiion of he sliding mode. If he fricion B is negleced expressions for U eq and U s can be wrien as: Ueq = ke U s = βsign ( ) ( s() ). () To guaranee he exisence of he swiching surface consider a Lyapunov funcion []: V () = s (). () Based on Lyapunov heory, if he funcion V () is negaive definie, his will ensure ha he sysem rajecory will be driven and araced oward he sliding surface s() and once reached, i will remain sliding on i unil he origin is reached asympoically [7]. Taking he derivaive of () and subsiuing from he derivaive of (3): ( ) = s( ) s ( ) = s( ) { e ( ) + ( a + bk) e( ) } V. (3) Subsiue (3) ino (3): { } ( ) s( ) = s( ) bc () + bd() bke() s e. (4) Using (9) gives: ( ) s( ) = s( ) { sign( s( ) ) d( ) } s. () To ensure ha () will be always negaive definie, he value of he hiing conrol gain β should be designed as he upper bound of he lumped uncerainies d(), i.e. β d. () However, i is difficul pracically o esimae he bound of uncerainies in (9). Therefore he hiing conrol gain β has o be chosen large enough o overcome he effec of any exernal disurbance. Therefore he speed conrol law defined in (3) will guaranee he exisence of he swiching surface s() in () and when he error funcion e() reaches he sliding surface, he sysem dynamics will be governed by () which is always sable. Moreover, he conrol sysem will be insensiive o he uncerainies Δa, Δb and he load disurbance C r. The use of he sign funcion in he sliding mode conrol (3) will cause high frequency chaering due o he disconinuous conrol acion which represens a severe problem when he sysem sae is close o he sliding surface. To overscome his problem an approach which combines FL wih SM is used [8]. The conrol sysem is based on fuzzy logic. This ype of conrol, approaching he human reasoning ha makes use of he olerance, uncerainy, imprecision, and fuzziness in he decision-making process, manages o offer a very saisfacory performance, wihou he need of a deailed mahemaical model of he sysem, jus by incorporaing he expers' knowledge ino fuzzy rules. This sysem has hree main pars. Fuzzificaion defined as he mapping from a real valued poin o fuzzy se. Inference mechanism used o combine he fuzzy IF- THEN in he fuzzy rule base, and o conver inpu informaion ino oupu membership funcions. Defuzzificaion used for convering he conclusions of he inference mechanism ino he acual inpu for he plan. Cener of graviy defuzzificaion mehod is used for he FSMC, he sauraion funcion is replaced by a fuzzy inference sysem in order o avoid he chaering phenomenon [8]. The FSMC is a single inpu single oupu fuzzy logic conroller. I is consruced from he following forma IF.THEN rules or equivalenly. The max-min composiion is chosen as he inference mehod. The crisp oupu is obained by he cener of he area defuzzifier. ()

4 34 Abdelkader Meroufel el al. 4. SIMULATION RESULTS AND DISCUSSIONS The proposed scheme has been implemened wih Malab/Simulink in order o evaluae is performances. The DSIM used for he simulaions has he following parameers: P = 4. kw, Un = / 38 V, f = Hz, In =. A, = = 3.7 Ω, Rr =. Ω, Ls = Ls =. H, Lr =, H, Lm =, 37 H, =. kg.m, K =. Nms/rad, p =. Torque (Nm) Saor flux (Wb) s f Ce Ce- ref Saor flux Saor-ref Saor curren s (A) Fig. Sysem responses for classical DTC. Figure shows classical DTC where he references are he orque reverse from 4 Nm o 4 Nm and he flux. Wb. I is clear ha he sysem follows hese references. From his analysis, he orque and flux presen a high dynamic performances and good precision in seady sae. I can be observed ha he orque and flux are decoupled. The orque and he flux ripples are due o he hyseresis-band comparaor. Noe ha he dynamics of orque is faser compared wih oher mehods of conrol (FOC). In Fig. 3, he moor sars under no load. The saring elecromagneic orque is 4 Nm, which drops o zero when speed is reached. A = s, a 4 Nm load is applied. The disurbance is no rejeced under he classic DTC. Roor speed (rad/sec) Elecromagneic orque (Nm) saor flux s(wb)... 3 Fig. 3 Torque, speed and saor flux responses under classical DTC. roor speed (rad/s) elecromagneic orque (Nm) roor speed reference speed -4 3 saor curren (A) Fig. 4 Torque, speed and saor flux responses under classical DTC. Figure shows clearly ha he saor flux is no disruped by he applicaion of such load. From he sysem responses given in Fig. 4 for SMC, he mechanical speed racks he reference speed wihou overshoo, wih zero seady sae error and wih an insananeously perurbaion rejec. The resuls show ha high precision racking can be achieved using he speed SMC in spie of large parameer variaions. The chaering effec can be observed when using SMC. Figure shows he FSMC responses. We remark he same performances as SMC. The orque ransien is improved and he orque ripple is gradually reduced. moor speed (rad/s) elecromageic orque (Nm) roor speed reference speed 3 saor curren (A).. 3 Fig. FSMC responses Robusness ess. In order o es he robusness of he proposed conrol, we have sudied ineria and saor resisance variaions. Ineria variaion. Figure shows he speed response obained wih uncerainy in he moor ineria.

5 Direc orque conrol wih fuzzy sliding mode speed conroller 3 R o roor or speed (rad/sec) (rad/s ) 3 3 * 3 * Elecromagneic (Nm) Elecrom orque (N m ) Sa or flux(w b) Fig. Speed responses o ineria variaion. The FSMC scheme shows ha he seady sae error wih % uncerainy is insensiive o moor ineria. While, he ime response is doubled. Saor resisance variaion. The sensiiviy of saor resisance is invesigaed because is variaion grealy affecs he performance of he DTC drive. Figure 7 shows he response of he proposed scheme in where he differen responses are insensiive o saor resisance variaion. Roor roor speed (rad/sec) (rad/s) 3 3 reference Reference speed speed (rad/s) Moor speed moor speed (rad/s) 3 Elecromagneic orque (Nm) (Nm) S aor flux(w b) Fig. 7 Speed responses o saor resisance variaion. Chaering phenomenon. The influence of chaering is invesigaed hrough a flucuaions comparison under firsly SMC and FSMC and secondly classic DTC and FSMC. T orque orque oscilla oscillaions ions (Nm) (N m ) elecromageic orque (Nm) SMC SMC T orque orque oscilla oscillaions ions (Nm) ( N m ).. 9. Fig. 8a Zoom of orque. DTC classique elecromagneic orque (Nm) 9 FSMC FSMC Speed FSMC Fig. 8b Zoom of saor flux and elecromagneic orque. In Fig. 8a, low orque ripple is observed wih FSMC. The proposed conrol produces beer resuls in ripple reducion hen he convenional conrol. 7. CONCLUSION The proposed conroller presens high robusness in he presence of inernal and exernal perurbaions. The direc orque conrol (DTC) allows direc and independen elecromagneic orque and flux conrol, selecing an opimal swiching vecor, making possible fas orque response, low inverer swiching frequency and low harmonic losses. However, wo major problems associaed wih DTC drive: elecromagneic orque ripple and variable swiching frequency. The chaering effecs are reduced, and he orque flucuaions are decreased. FSMC proves robusness agains saor resisance variaion and insensiiviy o load orque disurbance as well as faser dynamics wih zero seady sae error a all dynamic operaing condiions. When using he FSMC he bes racking resuls are obained. This regulaion presens a simple robus conrol algorihm ha has he advanage o be easily implemened in a calculaor. The simulaion resuls show ha our mehod has achieved very robus and saisfacory performance. Received on November, REFERENCES. Y. Zhao, T.A. Lipo, Space vecor PMW conrol of dual hreephase inducion machine using vecor space decomposiion, IEEE Transacions on Indusry Applicaions, 3, pp. 9 (99).. L. Zong, M.F. Rahman, W.Y. Hu, K.W. Lim, Analysis of direc orque conrol in permanen magne synchronous moor drives, IEEE Transacions Power Elecronics,, pp. 8 3 (997). 3. R. Zaimeddine, E.M. Berkouk, A Novel DTC scheme for a hree-level volage source inverer wih GTO hyrisors, SPEEDAM 4, Symposium on power elecronics, elecrical drives, auomaion & Moion, Algeria, une h 8 h, Z.A. Alnasir, A.H. Almarhoon, Design of Direc Torque Conroller of Inducion Moor (DTC), Inernaional ournal of Engineering and Technology (IET), 4, pp. 4 7 ().. I. Takahashi, T. Noguchi, A new quick-response and high efficiency conrol sraegy of an inducion machine, IEEE Trans. Indusry Appl.,, pp (98).. A. Meroufel, A. Massoum, P. Wira, A Fuzzy Sliding Mode Conroller for a Vecor Conrolled Inducion Moor, IEEE Symposium on Indusrial Elecronics, U.K, une 3 uly, M. Dhirajkumar, S.P. Gargi, S. Salunkhe, Sliding Mode Speed Conroller for Vecor Conrolled Inducion Moor, Inernaional Research ournal of Engineering and Technology (IRET),, pp. (). 8. G.C Hwang, S.C. Lin, Sabiliy approach o fuzzy conrol designs for nonlinear sysems, Fuzzy ses and sysems, 48, pp (99). 9. S.M. Gadoue, D. Giaouris,.W. Finch, Geneic Algorihm Opimized PI and Fuzzy Sliding Mode Speed Conrol for DTC Drives, Proceedings of he World Congress on Engineering, London, U.K, uly 4, 7.