Department of Electrical Engineering, University of Tiaret, Tiaret BP 078, Tiaret, Algeria

Transcription

1 Jounal of Netwok an Innovatve Computng ISSN 6-74 Volume (4) pp MIR abs A New Appoach Fuzzy-MRAS Spee Sensoless Slng moe Contol fo Inteo Pemanent-Magnet Machne Dve Khalfallah Tah M Hame Doum Chekh Belfeal Tayeb Allaou Abel Ghan Assaou an Aballah Mlou Depatment of Electcal Engneeng Unvesty of Taet Taet BP 78 4 Taet Algea tah.commane@gmal.com Depatment of Electcal Engneeng Unvesty of Becha Becha BP 47 8 Becha Algea oumcanaa@gmal.com Depatment of Electcal Engneeng Unvesty of Saa Saa BP 8 Saïa Algea amlouz@yahoo.f Abstact: Ths pape pesents a spee sensoless slng moe contol stategy of nteo pemanent magnet synchonous moto (IPMSM). The estmaton of the oto poston an spee s acheve by usng a moel efeence aaptve system (MRAS) to allevate the nee of physcal sensos. Slng moe contol s able to ncease the pefomance of the Fuzzy MRAS obseve n tems of spee eveson an loa ejecton. Smulaton esults wth IPMSM shows that the esgne sensoless slng moe contol base Fuzzy MRAS obseve éalses a goo ynamc behavou of the moto wth a ap settlng tme no oveshoot an has bette pefomance than sensoless vecto contol PI MRAS obseve. Keywos: Sensoless contol Fuzzy MRAS nteo pemanent magnet synchonous moto (IPMSM) slng-moe contol vecto contol I. Intoucton Pemanent Magnet Synchonous Motos (PMSM) ae wely use n nustal ves ue to the hgh powe ensty hgh toue-to- neta ato small toue pple an pecse contol at low spee ange possblty to toue contol at zeo spee hgh effcency an small sze []. To explot pesente avantages a slng moe contol shoul be use. The man avantage of the slng moe technue s that the contolle system pesents obustness to paametes vaatons an ejecton to extenal stubances. The slng moe contol of a pemanent magnet synchonous moto s usually mplemente though measung the spee an poston []. In oe to obtan pecse sgnals of the oto poston an spee many etecton evces wee evelope n ecent yeas such as Hall Effect senso photoelectc encoe an esolve etc []. Due to mechancal senso ncease the system cost an the elablty of the system has many lmtatons such as tempeatue humty an vbaton non-spee senso becomes hot n ecent yeas [4]. Seveal appoaches to ths poblem ae epote n the lteatue. In ths pape a novel nonlnea aaptaton scheme base on fuzzy logc s popose to mpove the spee estmaton pefomance. The popose spee contolle s evaluate by smulaton usng MATAB/SIMUINK une ffeent opeaton pont. II. Mathematc Moel of IPMSM et we evelop the state space moel of the IPMSM n a synchonous efeence fame. Fg. shows a geneal pupose of thee-phase nvete fe IPMSM ve. Fgue. Voltage souce nvete fe IPMSM ve A smplfe schematc thee phase IPMSM ve fe by voltage souce nvete (VSI) contolle by SVPWM Dynamc Publshes Inc. USA

2 A New Appoach Fuzzy-MRAS Spee Sensoless Slng moe Contol fo Inteo Pemanent-Magnet Machne Dve 59 technue. The powe ccut of a thee-phase VSI s shown n Fg. whee v a v b an v c to the sta-connecte IPMSM wnngs an ae the output voltages apple V DC s the DC voltage nput nvete [6]. The - moel n the otatng efeence fame s use to analyze the IPMSM an the popose metho of spee an poston estmaton. The stato voltage an flux euatons of the IPMSM n the otatng - efeence fame ae gven by: v Rs t v Rs t () () ange on tmes s calculate as follows Ts 6 Vs _ ef sn T.. V sn DC Vs _ ef sn T.. T V sn DC s 6 (6) (5) whee v espectvely v ae the stato voltages an cuents R s s the stato esstance ae the - axs stato nuctances espectvely an ae the - axs stato magnetc flux espectvely s the electcal oto spee s the oto flux as P.. The electo-mechancal toue s T P () e s the mechancal oto spee The mechancal euaton of the PMSM ve s escbe as: J PT et t P Whee J an ae the neta an the fcton coeffcent of the oto spee an poston. The pmay methos the moto espectvely T e an T (4) ae the electomagnetc toue an the loa toue espectvely P s the pole pas [7]. III. SVPWM Base Thee Phase Invete The pncple of SVM s base on the fact that thee ae only eght possble swtchng combnatons fo a thee phase nvete to calculate nvete tanssto on tmes. The tanston fom one swtchng state to the next nvolves only two swtches n the same nvete leg when one beng swtche ON the othe beng swtche OFF n oe to mnmze the evce swtchng loss [8]. Sx non-zeo vectos ( V ) calle the V to 6 actve vectos shape the axs of hexagonal an the angle between any ajacent two non-zeo vectos s 6 [9].The tps of these vectos fom a egula hexagon. Two of these states ( V anv 7 ) coespon to a shot ccut on the output calle the zeo vectos whle the othe sx s consee to fom statonay vectos n the complex plane [] as shown n Fg.. The efeence voltage s geneate by two ajacent non-zeo vectos an two zeo vectos. In lnea opeaton Fgue. Space vecto hexagon IV. Dect Fel Oente Contol Smlaly to the IM n the IPMSM a ecouple contol of the toue an flux magntues can be acheve emulatng a DC moto by means of the FOC stategy []. Ths s one usng the - tansfomaton that sepaates the components an of the stato cuent esponsble fo flux an toue poucton espectvely. Due to the pesence of the constant flux of the pemanent magnet thee s no nee to geneate flux by means of the cuent an ths cuent can be kept to a zeo value s whch n tuns eceases the stato cuent an nceases the effcency of the ve. The contol scheme of the FOC stategy s shown n Fg.. Fgue. IPMSM Vecto Contol Algothm Ovevew The contol system s ve nto thee ffeent loops: the loop whch contols the flux; an the loops whch contol the spee an toue. The loop pefoms the contol of s wth a cuent PI egulato. The efeence value fo ths loop

3 6 K. Tah et. al can be set to. The loops ae connecte n cascae. The nne loop contols the toue by means of contollng wth a cuent PI egulato. The fact that the toue can be contolle by means of s s comes fom the followng smplfcaton of () val fo Suface Mounte (SM) IPMSM: The efeence fo ths nne loop s gven by the spee PI egulato of the oute loop. Fom the voltage euatons of the IPMSM moel () t can be seen that an axs ae not completely nepenent an thee ae couplng tems whch epen on the cuent fom the othe axs. To acheve completely nepenent egulaton t s necessay to cancel the effect of these couplng tems at the output of the cuent PI egulato (see Fg. ). The use of ecouplng acheves the lneazaton of the contol system as well as hghe ynamcs. V. Slng Moe Contol A. Desgn of Slng Moe Contolle The slng moe contol can be justfe an esgne usng the noton of lyapunov stablty. Whateve the applcaton the esgn of slng moe contol can summaze n steps []: ) The choce of the numbe of the slng sufaces: Geneally the numbe of the slng sufaces s eual to the menson of the nput contol vecto. ) The choce of the slng suface euaton fom: It must satsfy the convegence of the contol an the stablty of the system. Ths goal can be eache f the contol vaable u c pemts to satsfy the yapunov functon: ss (7) Base on ths conton Slotne [] popose a geneal fom of slng suface: s x x x t x n (8) ef ) The contol law esgn: The contol vaable s ecompose n two pats: u eu u c an eu u n u u (9) : n The ynamc whle n slng moe can be wtten as s ( x) () By solvng ths euaton ( s ) the euvalent contol ueu can be obtane. The u n component satsfes s. s an s gven by: () u n k. sgn( x)) Whee k s the contol gan. The contolle escbe by the euaton () pesents hgh obustness nsenstve to paamete fluctuatons an stubances [] but t wll have hgh-feuency swtchng (chatteng phenomena) nea the slng suface ue to sgn functon nvolve. These astc changes of nput can be avoe by ntoucng a bounay laye wth wth ε []. Thus eplacng sgn ( x)) by n () we have u c Whee u k. sat( x)) () eu / x) sgn( ) sat ( ) B. Spee contol f f The spee eo s efne by [4]: e (4) ef () n the poston contol manfol euaton can be Fo obtane fom euaton (8) as follow: ) (5) ef The evatve of ths suface s gven by the expesson: T s ( ) c ef ( c c) J (6) Dung the slng moe an n pemanent egme we have ) s ( ) (7) The cuent contol eu n (8) The contol voltage ef ef n s efne by: s efne by: T c ef k sgn( )) j c c C. Dect cuent contolle The ect cuent eo s efne by: e () ef Fo obtane fom euaton (8) as follow: ) () (9) n the ect cuent contol manfol euaton can be ef Substtutng the expesson of gven by euaton () an () n euaton () we obtan: s ( ) ef a a v () t Dung the slng moe an n pemanent egme we have ) s ( ) v () The contol voltage v s efne by: v ef ef n ef a a k sgn( )) t (4) D. Quaatue cuent contol The uaatue cuent eo s efne by: e( ) (5) ef Fo n the uaatue cuent contol manfol euaton can be obtane fom euaton (8) as follow: ) (6) ef

4 A New Appoach Fuzzy-MRAS Spee Sensoless Slng moe Contol fo Inteo Pemanent-Magnet Machne Dve Substtutng the expesson of n euaton (5) we obtan: s t ( ) ef b b b gven by euaton () an () (7) Dung the slng moe an n pemanent egme we have ) s ( ) v (8) The contol voltage v ef Wth: t Rs a b P ef f a b P v ef n b B c J s efne by: b Rs b c b v ksgn( )) (9) P P( ) J The sutable choce of the paametes k c k P J an f k []: Ensues the apty of the eachng moe. Imposes the ynamc of the convegence an slng moe. Allow to the ve to wok wth maxmum enegy ung tansent state. VI. Fuzzy ogc MRAS Spee Obseve As the oto spee s nclue n cuent euatons we can choose the cuent moel of the IPMSM as the ajustable moel an the moto tself as the efeence moel. These two moels both have the output an Accong to the ffeence between the outputs of the two moels though a cetan aaptve mechansm we can get the estmate value of the oto spee. Then the poston can be obtane by ntegatng the spee [5]. The euaton () can be wtten as below fom: t t R s R s v v () The - axs cuents ae the state vaables of the cuent moel of the IPMSM whch s escbe by (). Rewte () nto matx fom as below R v Rs s () t Rs v Fo the convenence of stablty analyss the spee has been confne to the system matx Rs A Rs To be smplfe efne: x x x u u u v Rs v () () (4) 6 Then the efeence moel can be ewtten as: x Ax u (5) t The aaptaton mechansm uses the oto spee as coectve nfomaton to obtan the ajustable paamete cuent eo between two moels n oe to ve the cuent eo to zeo when we can take the estmaton value as a coect spee. The pocess of spee estmaton can be escbe as follows: t xˆ xˆ Wheeˆ Rs ˆ ˆ Rs xˆ xˆ uˆ uˆ (6) s to be estmate (6) can be smplfe as below: xˆ Ax ˆ ˆ uˆ (7) t The eo of the state vaables s e x xˆ (8) Accong to euaton (5) an (6) estmaton euaton can be wtten as: e Ae Iw t (9) v De Whee w ( Aˆ A) xˆ choose D I the v Ie e Accong to Popov Supe Stablty Theoem f the followng contons ae met [6]: () H( s) D( si A) s a stctly postve matx t T () t ) v wt t whee ( lm e( t) a lmte postve numbe the n othe wos t the moel efeence aaptve system s asymptotcally stable. Fnally the eo between the two moels s: e x xˆ ˆ ) (4) ( xx Replacng x wth : s

5 6 K. Tah et. al ˆ ˆ e ( ˆ ) (4) The oto poston can be obtane by ntegatng the estmate spee: ˆ t ˆ (4) The eo between two moels s the nput of a fuzzy logc contolle whose output s the estmate oto spee; ths estmate spee s use to ajust the aaptve moel [6]. Fuzzy contol poves a fomal methoology fo epesentng manpulatng an mplementng a human s heustc knowlege about how to contol a system an fo constuctng nonlnea contolles va the use of heustc nfomaton. Ths kn of fuzzy contolle s also known as PI fuzzy contolle. The plant contol u s nfee fom the two state vaables eo (E) an change n eo e. The aeuate choce of Gεe an Gεce Gεu pemts to aapt the estmaton. Fuzzy contol uses a set of ules to epesent how to contol the plant. Table I shows one of possble contol ule base. The ows epesent the ate of the eo change DE an the Columns epesent the eo E. Each pa (E DE) etemnes the output level NB to PB coesponng to U. Hee NB s negatve bg NM s negatve meum ZR s zeo PM s postve meum an PB s postve bg ae labels of fuzzy set san the coesponng membeshp functons ae epcte n Fg. 5 6 an 7 espectvely. The contnuty of nput membeshp functons easonng metho an efuzzfcaton metho fo the contnuty of the mappng U (E DE) s necessay. In ths pape the Tangula membeshp functon the max-mn easonng metho an the cente of gavty efuzzfcaton metho ae use as those methos ae most feuently use n many lteatues []. Fgue 5. Membeshp Functons fo Input E Fgue 6. Membeshp Functons fo Input DE Fgue 7. Membeshp Functons fo Output DU Fgue 4. Fuzzy logc contolle fo aaptaton mechansm DU E n Table. Rule base fo fuzzy contolle. DE n NB NM ZR PM PB NB NB NB NM NM ZR NM NB NM NM ZR PM ZR NM NM ZR PM PM PM NM ZR PM PM PB PB ZR PM PM PB PB Fgue 8. Contol suface of fuzzy contolle The oveall MRAS spee obseve wth F spee estmaton mechansm (MRAS-F) s shown n Fg. 9. The nputs of the spee an poston estmaton block ae the voltages an cuents of the eal moto an the outputs ae the estmate spee an poston. Fgue 9. Contol block scheme of MRAS

6 A New Appoach Fuzzy-MRAS Spee Sensoless Slng moe Contol fo Inteo Pemanent-Magnet Machne Dve 6 VII. Smulaton Results Dscusson An Compason In oe to vefy the popose contol stateges as scusse above gtal smulaton stues wee mae the system escbe n Fg.. Fgue. Block agam SSMC of IPMSM base MRAS The spee an cuents loops of the ve wee also esgne an smulate espectvely wth slng moe contol. The paametes of IPMSM use n the smulaton ae lste n Table II. The smulaton s ealze usng the SIMUINK softwae n MATAB envonment. Fg. shows the settlng pefomance of the contolle an ts stubance ejecton capablty. Intally the machne s state up wth a loa of 8.5 N.m. At. s a N.m loa s apple ung a peo of. s. The tansent spee the spee eo the cuent an the toue esponses also have a goo ynamc pefomance when the loa toues change. Especally the spee of the moto an estmate spee uckly appoach to the efeence spee n case of two suenly oa vaaton. The spee eo s always kept at zeo ung the steay state. The ecouplng of toue-flux s mantane n pemanent moe. Fgue. Contolles oa Dstubance Rejecton Pefomance Fg. show the spee tackng pefomance of the contol popose une no loa. The efeence spee change fom pm to -pm at t=.sec. We emak that the estmate spee was n acco wth the eal spee an spee efeence thus the sensoless slng moe contol usng Fuzzy MRAS was foun to pefom well n hgh spee egons nclung a fowa evese otaton. The Fg. shows the pefomance of MRAS technue n low spee. The fuzzy logc contolle poves hgh contol n ths egon. Fgue. Contolles Spee Tackng Pefomance n hgh spee Fgue. Contolles Spee Tackng Pefomance n low spee In oe to test the obustness of the use metho we have stue the effect of the paametes uncetantes on the pefomances of the spee contol. Thee cases ae consee: The moment of nete (+5%) at.sec. The stato esstances (+5%) at.sec. Fg.4 shows the eacton of the popose contol metho to moment of neta vaaton.

7 64 K. Tah et. al Fg.5 shows the eacton of the popose contol metho to stato esstance vaaton. Fo the obustness of contol an ncease of the moment of neta J oesn t have any effects on the pefomances of the technue use (Fg.4 an 5) but n stato esstance vaaton the oto flux s evate clockwse fom the ect axs. Fnally estmaton of the stato esstance s eue. Fgue 4. Test of obustness fo moment of neta vaaton Fgue 5. Test of obustness fo stato esstance vaaton an zoom VIII. Concluson A fuzzy-mras base synchonous spee estmaton metho s popose fo the sensoless slng moe contolle IPMSM ve. The popose fuzzy-mras on-lne synchonous spee estmaton skll s base on stato cuent obseve n whch the tatonal PI aaptve mechansm s eplace by aaptve fuzzy ones n MRAS confguaton. The system was esgne an the pefomance of ths new appoach was smulate an analyze such as ynamc/statc an obust popety. Smulaton esults shows that the esgne sensoless slng moe contol usng fuzzy-mras ealzes a goo ynamc behavou of the moto wth a ap settlng tme no oveshoot an has bette pefomance than sensoless vecto contol usng MRAS obseve. Acknowlegment The authos gatefully appecate the suppot of Taet Unvesty Algea. Appenx Table. Inteo pemanent magnet synchonous moto. Paametes Specfcaton Rs.8 ate powe Kw.H J 6.6*-Kg.m.4mH B.4N.m/a- P 4 Te 8.5N.m ψ.wb Rate Quaatue cuent A Refeences [] N. Vaslos Katsks MATAB A Funamental Tool fo Scentfc Computng an Engneeng Applcatons Volume Septembe. [] F. Benchabane A. Ttaoune O. Benns A. Guettaf K. Yaha D. Tab Robust Poston an Spee Estmaton Algothms fo Pemanent Magnet Synchonous Dves Euopean Jounal of Scentfc Reseach vol.57 no. pp.6-4. [] W. Yan H. n H. Hu. an J. u A MRAS base Spee Ientfcaton Scheme fo a PM Synchonous Moto Dve Usng the Slng Moe Technue Intenatonal Confeence on Mechatoncs an Automaton IEEE 9. [4] W. Wenje Z. Mn W. Qngha Applcaton of Reuce-Oe extene Kalman Flte n pemanent magnet synchonous moto sensoless egulatng system IEEE Intenatonal Confeence on Dgtal Manufactung & Automaton. [5] Y. ang an Y. Sensoless contol of PM synchonous motos base on MRAS metho an ntal poston estmaton In Poc. Int. Conf. Elect. Mach. Syst. vol. pp [6] A. Khlaef M. Benjea M. Boussak A. Châa Nonlnea Obseve fo Sensoless Spee Contol of IPMSM Dve wth Stato Resstance Aaptaton n Intenatonal Confeence on Communcatons Computng an Contol Applcatons (CCCA) pp Dec. [7] X Xao Yongong A sensoless contol base on MRAS metho n nteo pemanent-magnet machne ve Poceengs of the Intenatonal Confeence on Powe Electoncs an Dve Systems vol. pp [8] G. K. Nsha S. Ushakuma an Z. V. akapaampl Hamonc Elmnaton of Space Vecto Moulate Thee Phase Invete In Poc. IMECS pp. 9-5 Ma.. [9] H. W. Van e Boeck H. C. Skuelny an G.V. Stanke" Analyss an ealsaton of a pulse wth moulato base on voltage space vectos" IEEE Tans. In. Appl. vol. 4 pp. 4-5 Jan./Feb [] D. G. Holmes an T. A. po Pulse Wth Moulaton fo Powe Convetes: Pncples an Pactce New Jesey: Wley IEEE Pess. [] Kshnan R. Electonc Moto Dves: Moelng Analyss an Contol Uppe Sale Rve New Jesey USA: Pentce Hall Feb.. [] V. I. Utkn Vaable stuctue system wth slng moes IEEE Tans. on Automatc Contol vol. AC- Apl 977. [] J. J. E. Slotne W. Apple nonlnea contol Pentce Hall USA 998.

8 A New Appoach Fuzzy-MRAS Spee Sensoless Slng moe Contol fo Inteo Pemanent-Magnet Machne Dve 65 [4] A. G. Assaou M. Ab H. Ab A. Tahou an A. Tlmatne Slng Moe Applcaton fo Synchonous Moto Dve Acta Elecotehnca Vol. 47 no. 6. [5] Yuchao Sh Ka Sun Hongyan Ma pe Huang Pemanent Magnet Flux Ientfcaton of IPMSM base on EKF wth Spee Sensoless Contol -6th Annual Confeence on IEEE Inustal Electoncs Socety pp Nov. [6] W. Huau Z. Y. Chen W. P. Cao Smulaton eseach on optmzaton of pemanent magnet synchonous moto sensoless vecto contol base on MRAS. IEEE. Autho Bogaphes Khalfallah Tah s PhD stuent n the Depatment of Electcal Engneeng n at the D Moulay Taha Unvesty of Saa AGERIA. He eceve a MASTER egee n Actuato an nustal contol fom the UDMT of Saa. Hs eseach actvtes nclue the Renewable Eneges an the Contol of Electcal Systems. He s a membe n Enegetc Engneeng an Compute Engneeng aboatoy (GEGI). M Hame Doum s PhD stuent n the Depatment of Electcal Engneeng n at the D Moulay Taha Unvesty of Saa AGERIA. He eceve a MASTER egee n Actuato an nustal contol fom the UIK of Saa. Hs eseach actvtes nclue the Renewable Eneges an the Contol of Electcal Systems. He s a membe n Enegetc Engneeng an Compute Engneeng aboatoy (CAOSEE). Chekh Belfeal eceve the Magste egee n electcal engneeng fom Taet Unvesty Algea n 996. Cuently he s wth the Depatment of Electcal Engneeng Taet Unvesty. Hs fels of nteest ae contol of electcal machnes powe convetes moellng an contol of wn tubnes. He s a membe n Enegetc Engneeng an Compute Engneeng aboatoy (GEGI) Tayeb Allaou eceve hs engnee egee n electcal engneeng fom the Ibn Khaloun Unvesty of Taet n 996 an hs maste egee fom the Unvesty of Scence an Technology of Oan n.hs eseach nteests nclues ntellgent contol of powe systems an FACTS Actve flte an enewable eneges. He s a Decto of Enegetc Engneeng an Compute Engneeng aboatoy (GEGI). Abel Ghan Assaou s a full Pofesso of electcal engneeng at Unvesty of Becha (AGERIA). He eceve hs BS egee n 99 the MS egee n 997 the PhD egee n 7 fom the Electcal Engneeng Insttute of Djlal abes Unvesty of S Bel Abbes (AGERIA). He s an actve membe of IRECOM (Inteacton Réseaux Electue - Convetsseus Machnes) aboatoy an IEEE seno membe. He s an eto membe fo many ntenatonal jounals (MER JECE IJECE EEG ) he seves as evewe at ntenatonal jounals (IJAC ECPS ). He seves as membe n techncal commttee (TPC) an evewe n ntenatonal confeences: CHUSER SHUSER PECON SAI SCSE SDM4 SEB4 an PEMC4. Hs cuent eseach nteest nclues powe electoncs contol of electcal machnes atfcal ntellgence an Renewable eneges. Aballah Mlou was bon n Saa Algea n Octobe 958. He eceve a BSc egee n Mechancal Engneeng an hs MSc egee n Contol Engneeng fom Bafo Unvesty Englan n 98 an 98 espectvely. He eceve hs PhD n Electcal Engneeng n 6 fom USTO n Algea. Hs man eseach nteests ae n the fel of analyss an ntellgent contol of electcal ves an DSP pogammng. He s now a seno lectue at the Depatment of Electcal Engneeng at the Unvesty of Saa Algea.