Fault Tolerant Control for Induction Motor Drive Using Descriptor Approach

Transcription

1 Faul olean Conol fo Inducon Moo Dve Ung Deco Aoach Habb Ben Zna, Moez Allouche, Manou Sou, Mohamed Chaabane and Lab Chf-Alou Laboaoy of Scence and echnque of Auomac (Lab-SA) Naonal School of Engnee of Sfax, una Laboaoy of Innovave echnology, Unvey of Pcade Jule vene, Cuffe Fance Abac: - h ae een an acve faul olean conol (FC) aegy fo nducon moo dve ha enue aecoy ackng and offe he effec of he eno faul dee he eence of load oque dubance. he ooed aoache ue a fuzzy deco obeve o emae mulaneouly he yem ae and he eno faul. he hycal model of nducon moo aoxmaed by he akag-sugeno (-S) fuzzy echnque n he ynchonou d-q fame oang wh feld-oened conol aegy. he efomance of he aecoy ackng ae analyzed ung he Lyaunov heoy and L omzaon. Fnally he effecvene of he ooed aegy ha been lluaed n mulaon eul. Key-Wod: - Inducon moo, Faul olean conol, aecoy ackng, akag-sugeno, LMI. Inoducon I well known ha faul nevable n nonlnea comlex yem. I can degade he conol efomance and n ome cae lead o he nably of he yem. o ovecome hee dawback, faul deecon and olaon (FDI) and faul olean conol (FC) ha been negaed n conol yem cheme. heefoe, eveal eeache have been develoed aound h ubec [,, 3, 4, 5, 6]. Faul-olean conol a conol ha oee he ably o accommodae yem falue auomacally, and o manan oveall yem ably and acceable efomance even n he fauly uaon. Geneally eakng, we fnd wo aoache fo he degn of faul olean conol: ave conol and acve conol. In he f aoach a o nfomaon abou he faul whch may affec he yem equed and condeed a unceany o dubance whch ae aken no accoun n he degn of he conol law [9]. In cona, he econd aoach ha he ably o comenae all oble faul on-lne. I ha he obly o change ucue accodng o he nfomaon ovded by he FDI block [,, 4]. Laely, akag-sugeno (-S) aoach ha been uccefully ued n nonlnea yem modelng and conol. I ha he ably o aoxmae exacly comlex yem. he dea o decomoe he model of he nonlnea yem no a ee of lnea model nvolvng nonlnea weghng funcon. he equvalen fuzzy model decbe he dynamc of behavo of he yem [3]. Recenly, he oblem of ackng conol fo -S and a fauly model ha been uded by few numbe of wok. Fo examle, n [] he auho decbe an acve faul olean ackng conol baed on he onlne emaon of acuao and eno faul. In [], a obu faul olean conol fo non lnea yem ubec o acuao faul degned. h FC aegy baed on he onlne emaon of he faul and allowng he yem ae o ack a deed efeence coeondng o faul fee uaon. In he la yea, nducon moo became vey fequen n ndual ocee. h due o he elably, obune and low co. Regeably, conol of nducon moo well known o be dffcul due o he fac ha he dynamc comlex and alway ubec o vaou faul, uch a ao ho ccu and oo falue ncludng boken ba o ng []. he oveall efomance of nducon moo dve wh a feedback ucue deend no only on he healh of he moo elf bu alo on he efomance of he dvng ccu and eno: he encode, volage eno and cuen eno. heefoe, FC oblem fo E-ISSN: Volume, 5

2 nducon moo ha eceved condeable aenon [3, 4, 5, 6, 7]. In h udy we exlo he efomance of he FC fo ae feedback ackng conol of nducon moo. he goal o guaanee he ably and he oeang n afe dee he eno faul. A fuzzy deco obeve degned o gve mulaneou emaon of yem ae and eno faul. h emaon wll be exloed n an obeve baed FC ackng conol o guaanee he conol efomance of he nducon moo wh eec o load oque dubance. h ae oganzed a follow: Secon noduce he hycal model of he nducon moo and an oen-loo conol aegy degned. A fuzzy obeve-baed faul olean ackng conol condeed n econ 3. Fnally, mulaon eul ovded o demonae he degn effecvene. Oen loo conol. Phycal model of nducon moo Unde he aumon of he lneay of he magnec ccu, he elecomagnec dynamc model of he nducon moo n he ynchonou d-q efeence fame can be decbed a x f ( x) g( x) u w () K K n K K n M f ( x) d d ( nm ) q M q ( n m ) d q nm f ( dq qd ) m JL J d q d m q d q m d q L g( x), L w ( ) C M u uq ud,,, LL L L M,, K R R L L J x() d q d q m m he oo eed, he eleccal eed of ao,, ae he oo fluxe,, d q ae he ao cuen, and u, u ae he ao volage. he load oque C condeed a an unknown dubance. he moo aamee ae momen of nea J, oo and ao eance R, R, oo and ao nducance L, L muual nducance M, fcon coeffcen f and numbe of ole a n.. Oen loo conol In h econ, he ucue of he oen loo conol aegy exloed. If we elace he ae vaable of he moo d q d q m d q d q by he efeence gnal d qc d c c mc n () we oban d K dc dc qc dc u dc L d K dc dc qc K n mc dc qc u qc L () M ( nwmc ) dc qc d M dc qc dc d nm f mc ( dcqc ) mc C JL J J he oen-loo efeence ao cuen he eleccal eed and he loo conol can be wen a follow: dc d dc dc M M (3) JL C f d qc mc mc nm dc J J M c nmc qc (4) dc d K udc L dc dc cqc dc (5) d uqc L qc qc cdc Knmc dc.3 akag Sugeno fuzzy model of nducon moo he nonlnea model of he nducon moo can be wen a x Ax Bu w (6) y Cx E-ISSN: Volume, 5

3 L B L, C K Kn m K Kn m M M A q dc M M q dc nm nm f q d JL JL J he fuzzy model can be conucng ung he wellknown eco nonlneay echnque. he yem (6) conued by he followng hee nonlneae: z d z q (7) z3 m he local weghng funcon ae defned by: z () z mn F () zmax zmn () z max z () F () zmax zmn hu we can anfom he non lnea em unde he followng hae: z F z max F z mn (9) Conequenly, he global fuzzy model of he nducon moo can be wen n he followng fom: x h( z)( Ax) Bu w () 3 ( z ( )) h ( z), ( ( )) ( ( )) z Fk zk k ( z ( )) h( z), h( z) () 3 Obeve baed faul olean conol 3. Refeence model A n [4], n ode o ecfy he deed aecoy, we conde he followng efeence model x A x () x () he d q d q m efeence ae of he cloed loo yem. Kn m K Kn m M M q A d M M q d nm nm f q d JL JL J K MK f ( K ), ( ), L m q dc M n and K, K ae degn ove conan noduced o move he dynamc of he nducon moo yem. () a bounded efeence nu gven a U () () B I w() n whch d dc ( K ) dc c qc Ud L MK LK dc U RL d qc ( K f ) qc c dc Uq L Kn mcdc Ung he ame echnque eened n.3, he efeence model can be wen n he followng fom x h ( z )( A x) (3) o aenuae he exenal dubance, we conde he H efomance elaed o he ackng eo x x a follow f E-ISSN: Volume, 5

4 f f x ( ) ( ) ( ) ( ) ( ) ( ) x Q x x (4) w w 3. Faul olean conol aegy he faul condeed n h wok eed eno faul. In ode o on u he ooed aoach addonal faul ae neced o he -S model () eeenng he nducon moo. he fauly yem can be wen n he followng ucue: x h( z)( Ax Bu w) (5) y Cx Df An augmened yem conng of he yem (5) and he eno faul can be wen n he followng fom ung deco aoach: Ex h ( z) A x Bu Hw Dx (7) y Cx Cx x x () x Df, x x (), I E n A B A, B, D I I I C C, C C I, H and he veco x () condeed a an auxlay ae of he augmened yem (7). he followng fuzzy obeve degned n ode o emae he yem ae and he eno faul: Ez h( z) Nz Bu () x ˆ z Ly n z () he auxlay ae veco and n x ˆ( ) he ae emaon veco. E, N, of he obeve. Le u defne he obeve eo a follow ( ) ( ) ˆ e x x e e (9) ( n )*( n ) ( n )* L ae he gan mace Fom (7) and (), we can oban E ELC x Exˆ h ( z) ( A NLC) x () Nxˆ ( D NL) x Hw f we chooe N A N LC E E ELC () D NL he dynamc eo can be wen n he followng fom Ee h( z) Ne Hw () In ode o guaanee he condon (), he obeve aamee EN, L ae choen a follow, A In N, L, E C I I RC R (3) * n whch R non ngula max. hen he dynamc eo can be wen a follow e h( z) Se Hw (4) S E Nand H E H. Suoe he followng fuzzy conolle emloyed o deal wh he above conol yem degn: u h ( ( )) ( ˆ z K x x ) (5) Fg.: Faul olean Conol Saegy he ackng eo can be wen a follow e x x (6) hen we oban: e h ( z) h ( z) ( A BK ) e B K e ( A A ) x w (7) Le u conuc and augmened yem conanng he ackng eo and he emaon eo: x h ( z) h ( z ) A x F () E-ISSN: Volume, 5

5 e A BK BK e e, A A e CA R C R I I A A w() F I, C x he H efomance (4) elaed o he ackng eo can be modfed a follow f e Qe f () (9) Q Q. heoem If hee ex a ymmec and ove defne max PP and a ecbed ove conan uch ha A P PA PF F P Q (3) hen he ackng conol efomance guaaneed. Poof. Le u conde he followng Lyaunov funcon: V( e, ) e Pe (3) o guaanee he H ackng efomance and he ably of he cloed loo yem, he followng ceon wll be hold: V( e, ) e Qe (3) hen we oban h ( z) h ( z ) e ( A P PA ) e e PF F Pe e Qe ( ) ( ) ( ) ( ) (33) Lemma : Fo any max X and Y wh aoae dmenon, he followng oey hold X Y Y X X X Y Y (34) Ung Lemma, we can oban e PF F Pe (35) e PF ( ) F Pe hen we oban he followng condon e A P PA PF ( ) F P Qe (36) Conequenly we oban he condon n heoem. Pocedue eoluon We choe P a follow P dag P P I (37) By ubung (37) no (3) we oban 3 3 (3) P ( A BK ) ( A BK ) P Q P ( A A )( A A ) I P PBK PP 3 PC P A A P P P 3 CA R C P C 33 R ( R ) CC Ung he Schu comlemen we can oban: D D D4 D D P (39) P D 34 D34 D34 D44 n whch D P ( A BK ) ( A BK ) P Q P ( A A )( A A ) I P D PBK PP 4 PC D D34 CA R C P C D44 R ( R ) CC he nequaly condon (39) conan he couled vaable of conolle gan and obeve gan. E-ISSN: Volume, 5

6 hee ae no effecve algohm fo olvng hem mulaneouly. Howeve, we can olve hem n wo-e. F, we can fnd P and K fom he block dagonal D and hen elace hee' mace n (39) o fnd he vaable P and R. In he f e afe conguence (39) wh dag Z I I I I and condeng he change of vaable Z P Y K Z, hen ung he Schu, comlemen D can be wen a: A Z ZA BY ( BY ) ( A A )( A A ) I Z he aamee P by olvng LMI (4). Z and K Z Q In he econd e by ubung P and we can ealy fnd P and R. he eno faul can be emaed by ( ) ( ) n ( ) (4) Y Z ae obaned K no (39) fˆ D D D I xˆ (4) 4 Smulaon eul In h econ numecal mulaon have been efomed o valdae he develoed conol cheme. he nducon moo chaacezed by he followng aamee: ABLE I Inducon moo aamee 3 f 3 Fg.. Roo eed Pole a numbe Sao eance Roo eance Sao nducance Roo nducance mh.47 mh Fg. 3. d-ax ao cuen Moo nea.93 K. g m Fcon coeffcen. N. m. ad A efeence oo eed of value 5d/ choen a low eed oeaon whch aed a =ec and end a =3ec. a, a hgh eed, he efeence oo eed fxed a d/ beween he nan 4ec and ec. A load oque of 5 N.m value aled a =.5ec. An exenal addve eno faul modeled a follow neced n eed eno: Fg. 4. q-ax ao cuen E-ISSN: Volume, 5

7 Fg. 5. d-ax oo flux Fg. 6. q-ax oo flux he mulaon eul lluaed n fg. -7 how he aecoe of nducon moo ae ogehe wh he efeence and he emaed ae. he mulaon eul n Fg. 7 clealy demonae ha he accuae emae of he eno faul gnal ae acheved va he deco obeve. In ummay, ha been hown ha he ooed cheme able o emae he eno faul, hough he deco echnque. I can alo comenae he unknown nu load oque dubance. I clea ha he ooed fuzzy F conolle foce he ae vaable o ack he efeence aecoy even n eence of eno faul and hen o acheve he decoulng conol chaacec. h confm ha he efomance of he FC aegy ae vey afacoy and allowng nomal funconng of he yem even n he occuence of faul. 4 Concluon In h wok, a fuzzy ackng conol ha been degned fo he feld oened nducon moo dve affeced by exenal dubance and eno faul. he -S fuzzy model ued o eeen he nducon moo n he ynchonou d-q fame oang. In ode o guaanee he ackng efomance, a fuzzy obeve ued o emae mulaneouly he yem ae and he eno faul. Fnally, Smulaon eul howed he effecvene of he ooed fuzzy conolle. Refeence: [] J. Lunze and J. Schode, Seno and acuao faul dagno of yem wh dcee nu and ouu. IEEE anacon Syem, vol. 34, no.,. 96-7, 4. [] D. Ichalal, B. Max, D. Maqun and J. Rago, New faul olean conol aegy fo nonlnea yem wh mulle model aoach. Confeence on Conol and Faul-olean Syem,. 66-6, Fance. [3] H. Noua, D. Saue, F. Hameln and D. hellol, Faul-olean Conol n dynamc yem: Alcaon o a wndng machne. IEEE conol yem Magazne, Vol., no., ,. Fg.7. Faul and emaed [4] J. J. Gele, Analycal Redundancy Mehod n Faul Deecon and Iolaon - A Suvey and Synhe. Poceedng of IFAC Safe oce Confeence, vol.,. 9-. Baden-Baden, Gemany, 99. [5] J. Chen, R. J. Paon and H. Zhang, Degn of unknown nu obeve and obu faul deecon E-ISSN: Volume, 5

8 flle. Inenaonal Jounal of Conol, vol. 63, no.,. 5-5, 996. [6] S. Sun, S. Wang and B. Wu, Degn of Luenbege obu faul deecon obeve. Jounal of Zheang Unvey, vol. 3, no. 6,. 7-7, 4. [7]. Bouaa, B. Max, D. Maqun and J. Rago, Faul olean ackng conol fo connuou akag-sugeno yem wh me vayng faul. 9h Medeanean Confeence on Conol and Auomaon,. 6-, Geece. [] A. Khedhe, K. Ben Ohman and M. Beneeb, Acve Faul olean Conol (FC) Degn fo akag-sugeno Fuzzy Syem wh Weghng Funcon Deendng on he FC. Inenaonal Jounal of Comue Scence Iue, Vol., no. 3, May. [9] M. Bouou, M. Chadl, M. Chaabane and A. Elhaa, Robu faul olean conol fo akag- Sugeno yem ung ngula aoach. Inenaonal Revew of Auomac Conol, vol. 3, n. 4, July. [] M. Sam and R. J. Paon, Acve Faul olena Conol fo Nonlnea Syem wh Smulaneou Acuao and Seno Faul. Inenaonal Jounal of Conol, Auomaon and Syem, vol., no. 6,. 49-6, 3. [] M. Chadl, S. Aouaouda, H. R. Kam and P. Sh, Robu faul olean ackng conolle degn fo a VOL acaf. Jounal of he Fankln Inue, ,. [] D. U. Camo-Delgado, D. R. Enoza-eo and E. Palaco, Faul olean conol n vaable eed dve: a uvey. IE Elecc Powe Alcaon, vol., no.,. -34,. [3] K. S. Leeand and J. S. Ryu, Acuao faul emaon wh dubance decoulng. IEEE Pece-Conol heoy Alcaon, vol. 47, no. 5,. 5-5,. [4] C. Bonveno, A. Ido, L. Macon and A. Paol, Imlc faul olean conol: Alcaon o nducon moo. Auomaca, vol. 4, no. 3, , 4. Inducon Moo Ung Sldng Mode Obeve. Inenaonal Wokho on vaable ucue yem, Mexco Cy Mexco,. 9-96,. [6] N. Deghal, M. Ghane, S. Dennoune and J. P. Pabo, Seno Faul olean Conol Fo Inducon Moo. Inenaonal Jounal of Conol, Auomaon and Syem, vol. no.3, , 3. [7] M. Oudgh, M. Chadl, and A. Elhaa, One- Se Pocedue fo Robu Ouu H Fuzzy Conol. Pocedng of he 5h Medeanean Confeence on Conol and Auomaon, Ahen- Geece, July -9, 7. [] B. abbache, N. Rzoug, M. Benbouzd and Abdelazz Khelou, A Conol Regonfuguaon Saegy fo Po-Seno FC n Inducon Moo- Baed EV. IEEE anacon on vehcula echnology, Vol. 6, No. 3, 3. [9] R. J. Vellee, J. V. Medanc, and W. R. Pekn, Degn of elable conol yem. IEEE anacon on Auomac Conol, vol. 37,. 9-34, Mach, 99. [] G. H. Yang, J. L. Wang and Y. C. Soh. Realable H conolle degn fo lnea yem. Auomaca, vol. 37, no. 5, ,. [] Z. Gao and P. J. Anakl, Sably of he eduo-nvee mehod fo econguable conol yem. In. J. Conol, vol. 53, , 99. [] J. Jang, Degn of econfguable conol yem ung egenucue agnmen. In. J. Conol, vol. 59, , 994. [3]. anaka and M. Sugeno, Fuzzy denfcaon of yem and alcaon o modellng and conol. IEEE anacon. Sy. Man. Cybe., vol. 5, no.,. 6-3, 95. [4] C. S. eng, B. S. Chen and H. J. Uang, Fuzzy ackng conol degn fo non lnea dynamc yem va S fuzzy model. IEEE an, fuzzy y, Vol. 9,. 3-39,. [5] N. Deghal, M. Ghane, S. Dennoune, J. P. Pabo and M. adne, Faul olean Conol Fo E-ISSN: Volume, 5