Comparative Study of Sensorless Control Methods of PMSM Drives

Transcription

1 Compaative Study of Senole Contol Method of PMSM Dive Aafa S. Mohamed, Mohamed S. Zaky, Ahaf S. Zein El Din and Huain A. Yain Electical Engineeing Dept., Faculty of Engineeing, Minoufiya Univeity, Shebin El-Kom (3511), Egypt Abtact Recently, pemanent magnet ynchonou moto (PMSM) ae inceaingly ued in high pefomance vaiable peed dive of many indutial application. Thi i becaue the PMSM ha many featue, like high efficiency, compactne, high toque to inetia atio, apid dynamic epone, imple modeling and contol, and maintenance-fee opeation. In mot application, the peence of uch a poition eno peent eveal diadvantage, uch a educed eliability, uceptibility to noie, additional cot and weight and inceaed complexity of the dive ytem. Fo thee eaon, the development of altenative indiect method fo peed and poition contol become an impotant eeach topic. Many advantage of enole contol uch a educed hadwae complexity, low cot, educed ize, cable elimination, inceaed noie immunity, inceaed eliability and deceaed maintenance. The key poblem in enole vecto contol of ac dive i the accuate dynamic etimation of the tato flux vecto ove a wide peed ange uing only teminal vaiable (cuent and voltage). The difficulty compie tate etimation at vey low peed whee the fundamental excitation i low and the obeve pefomance tend to be poo. The eaon ae the obeve enitivity to model paamete vaiation, unmodeled nonlineaitie and ditubance, limited accuacy of acquiition ignal, dift, and dc offet. Poo peed etimation at low peed i attibuted to data acquiition eo, voltage ditotion due the PWM invete and tato eitance dop which degading the pefomance of enole dive. Moeove, the noie of ytem and meauement ae conideed othe main poblem. Thi pape peent a compehenive tudy of the diffeent method of peed and poition etimation fo enole PMSM dive. A deep inight of the advantage and diadvantage of each method i invetigated. Futhemoe, the difficultie faced enole PMSM dive at low peed a well a the eaon ae highly demontated. Keywod: pemanent magnet, ynchonou moto, enole contol, peed etimation, poition etimation, paamete adaptation. 1. Intoduction Pemanent magnet ynchonou moto (PMSM) dive ae eplacing claic dc and induction moto dive in a vaiety of indutial application, uch a indutial obot and machine tool [1-3]. Advantage of PMSM include high efficiency, compactne, high toque to inetia atio, apid dynamic epone, and imple modeling and contol [4]. Becaue of thee advantage, PMSMS ae indeed excellent fo ue in high-pefomance evo dive whee a fat and accuate toque epone i equied [5, 6]. Pemanent magnet machine can be divided in two categoie which ae baed on the aembly of the pemanent magnet. The pemanent magnet can be mounted on the uface of the oto (uface pemanent magnet ynchonou moto - SPMSM) o inide of the oto (inteio pemanent magnet ynchonou moto - IPMSM). Thee two configuation have an influence on the hape of the back electomotive foce (back- EMF) and on the inductance vaiation. In geneal, thee ae two main technique fo the intantaneou toque contol of high-pefomance vaiable peed dive: field oiented contol (FOC) and diect toque contol (DTC) [7, 8]. They have been invented epectively in the 70 and in the 80. Thee contol tategie ae diffeent on the opeation pinciple but thei objective ae the ame. They aim both to contol effectively the moto toque and flux in ode to foce the moto to accuately tack the command tajectoy 44

2 egadle of the machine and load paamete vaiation o any extaneou ditubance. The main advantage of DTC ae: the abence of coodinate tanfomation, the abence of a epaate voltage modulation block and of a voltage decoupling cicuit and a educed numbe of contolle. Howeve, on the othe hand, thi olution equie knowledge of the tato flux, electomagnetic toque, angula peed and poition of the oto [9]. Both contol tategie have been uccefully implemented in indutial poduct. The main dawback of a PMSM i the poition eno. The ue of uch diect peed/poition eno implie additional electonic, exta wiing, exta pace, fequent maintenance and caeful mounting which detact fom the inheent obutne and eliability of the dive. Fo thee eaon, the development of altenative indiect method become an impotant eeach topic [10, 11]. PMSM dive eeach ha been concentated on the elimination of the mechanical eno at the moto haft (encode, eolve, Hall-effect eno, etc.) without deteioating the dynamic pefomance of the dive. Many advantage of enole ac dive uch a educed hadwae complexity, low cot, educed ize, cable elimination, inceaed noie immunity, inceaed eliability and deceaed maintenance. Speed enole moto dive ae alo pefeed in hotile envionment, and high peed application [1, 13]. The main objective of thi pape i to peent a compaative tudy of the diffeent peed etimation method of enole PMSM dive with emphaizing of the advantage and diadvantage of each method. Futhemoe, the poblem of enole PMSM dive at low peed ae demontated.. PMSM Model The PMSM model can be deived by taken the following aumption into conideation: The induced EMF i inuoidal Eddy cuent and hyteei loe ae negligible Thee i no cage on the oto The voltage and flux equation fo a PMSM in the oto efeence (d-q) fame can be expeed a [8]: d d d Ri d dt (1) d Ri d dt () Li (3) d d d Li (4) q The toque equation can be decibed a: 3 T P [ i e ( L L q d ) i i d ] (5) The equation fo the moto dynamic can be expeed a: d 1 ( Te T L F ) (6) dt J whee the angula fequency i elated to the oto peed a follow: d P (7) dt whee P i the numbe of pole pai, R, i the tato winding eitance, i the angula fequency,, d, and i d, i ae d-q component of the tato winding cuent and voltage, d and ae d-q component of the tato flux linkage, L d and Lq ae d and q axi inductance, and 45 i the oto flux

3 linkage. F i the fiction coefficient elating to the oto peed; J i the moment of inetia of the oto; i the electical angula poition of the oto; and T and T ae the electical and load toque of the PMSM. e L 3. Speed Etimation Scheme of Senole PMSM Dive Seveal peed and poition etimation algoithm of PMSM dive have been popoed [14]. Thee method can be claified into thee main categoie. The fit categoy i baed on fundamental excitation method which ae divided into two main goup; non-adaptive o adaptive method. The econd categoy i baed on aliency and ignal injection method. The thid done i baed on atificial intelligence method. Thee method of peed and poition etimation can be demontated in Figue 1. Senole Contol of PMSM Fundamental excitation method Saliency & ignal injection method Atificial intelligence method Non-adaptive method Adaptive method 3.1. Fundamental Excitation Method Non-adaptive Method Figue 1. Speed etimation cheme of enole PMSM dive. Non-adaptive method ue meaued cuent and voltage a well a fundamental machine equation of the PMSM. The chaacteitic of thi method i eay to be computed, eponded quickly and almot no delay. But it equied high accuate Moto paamete, moe uitable fo Moto paamete online identification []. A. Etimato uing monitoed tato voltage, o cuent Fo etimating the oto angle uing meaued tato voltage and cuent diffeent autho follow diffeent appoache egading to the ued efeence fame. Thi ection how example fo the pepective in thee axi and γ-δ coodinate. [15, 16] popoe the appoach with the thee axi model. Fitly tanfomation fom the d-q coodinate to the α-β coodinate have to be done. The tanfomation matix a follow: 46

4 co in Tdq inco (8) The tanfomation matix fom the α-β coodinate to the thee axi model i illutated in equation: T 3 (9) The final equation fo the oto poition angle can be found a: 1 A tan ( ) (10) B Whee A b c R ( ib ic ) Ld p( ib ic ) (11) 3 ( L L ) i q d a B 3( R i L pi ) a a d a ( L L )( i i ) q d b c The poition of oto can thu be obtained in tem of machine voltage and cuent in the tato fame povided in equation can be evaluated in tem of voltage and cuent. [17] Popoe a voltage model and cuent model baed contol which wok in the γ-δ efeence fame with the aumption that Ld Lq L can be calculated a follow:. The equied peed 47 (1) C (13) D C ( a Ria L pi a ) (14) 1 ( ( ) ( )) b c R ib ic L p ib ic 3 D (15) The initial poition of the oto at t=0 can be detemined by ubtitution Whee: E F 1 o tan ( ) (16) 1 E ( b c R ( ib ic ) Ld p ( ib ic )) (17) 3 F R i L pi (18) a a d a =0 in above equation: The cuent ae detected by a cuent eno and the voltage ae obtained by calculation which uing infomation on PWM patten, dc voltage and dead time. The calculation i diect and eay with a vey quick dynamic epone, and no complicated obeve i needed. Howeve, the tato cuent deviation ued in above equation will intoduce calculation eo due

5 to meauement noie. And any uncetainty of moto paamete will caue touble to the moto poition etimation, which i the bigget poblem of thi method [18, 19]. B. Flux baed poition etimato In thi method, the flux linkage i etimated fom meaued voltage and cuent and then the poition i pedicted by ue of polynomial cuve fitting [0, 1]. The fundamental idea i to take the voltage equation of the machine, V d Ri (19) dt t ( V Ri ) dt (0) 0 Whee, V i the input voltage, i i the cuent, R i the eitance, and ψ i the flux linkage, epectively. Baed on the initial poition, machine paamete, and elationhip between the flux linkage and oto poition, the oto poition can be etimated. At the vey beginning of the integation the initial flux linkage ha to be known peciely to etimate the next tep flux linkage. Thi mean that the oto ha to be at a known poition at the tat [14, 16, and 0]. Lat equation (0) witten in α-β coodinate depend on the teminal voltage and the tato cuent. Uing the α-β fame the equation fo the oto angle can be witten a follow [14, ]: 1 tan ( ) Li Li whee L i the winding inductance. The actual oto angle uing the d-q fame can be calculated with [14, ]: (1) 1 d tan ( ) () Thi method alo ha an eo accumulation poblem fo integation at low peed. The method involve lot of computation and i enitive to the paamete vaiation. An expenive floating-point poceo would be equied to handle the complex algoithm [0]. Becaue of the noie, in the lat decade a pue invetigation of the oto poition ha gained le attention. Solution with adaptive o obeve method ae moe common [3, 4]. C. Poition etimato baed on back-emf In PM machine, the movement of magnet elative to the amatue winding caue a motional EMF. The EMF i a function of oto poition elative to winding, infomation about poition i contained in the EMF wavefom [14]. Pape [5] popagate the detemination of the back EMF without the aid of voltage pobe which educe the cot of the ytem and impove it eliability. Intead of the meaued voltage efeence voltage ae ued. The back EMF i not calculated by the integation of the total flux linkage of the tato phae cicuit becaue of the integato dift poblem. The etimation of the oto poition i given by the diffeence of the agument of the back EMF in the α-β efeence fame and the agument of the ame one in the otating d- q fame: e 1 1 tan ( ) tan ( ) (3) e L i q Peviou equation how, that thee i only a quadatue cuent dependency of the oto poition. Futhemoe the back-emf in ubject to the efeence voltage in α-β coodinate can be decibed a following function: 48

6 1 Ri ƒ (, ) tan ( ) (4) Ri The elation between the actual and efeence voltage may be witten in the fom in which the vaiation and ae due to the phae diffeence. * (5) * (6) Subtituting fom peviou equation into equation (4), one get: 儍 儍 * * (, ) (, ) = * Ri 1 tan ( ) * Ri 49 V T E The econd tem in thi equation i the dependent of the back EMF on the oto peed. V, E and T ae the m value of the tato voltage, the back EMF and the lag time intoduced by the invete epectively. Thu, we get fo the etimated poition : * * 1 1 * E Lqi Ri (7) * Ri V tan ( ) T tan ( ) (8) The popoed algoithm in [5] appea to be obut againt paamete vaiation. Futhemoe the electical dive ha a good dynamic pefomance. Many contol method uitable fo SPMSM cannot be ued diectly to IPM. In the mathematical model of the IPM, poition infomation i included not only in the flux o EMF tem but alo in the changing inductance becaue of it aliency. The model of SPMSM i a pecial ymmetical cae of IPM, which i elatively eay fo mathematical poceion. In ode to apply the method uitable fo SPM to a wide cla of moto, i.e. the IPM, in [6-8] a novel IPM model ae uggeted with an extended EMF (EEMF). By ewiting moto voltage equation into a matix fom: d R pld - Lq i d = i Ld R plq (9) 0 Thee ae two tigonometic function of θ, which eult fom changing tato inductance. A eaon why θ tem appea can be concluded a that the impedance matix i aymmetical. If the impedance matix i ewitten ymmetically a: d R pld - Lq i d = i Lq R pld (30) 0 ( Ld Lq )( i d pi ) The cicuit equation on α-β coodinate can be deived a follow, in which thee i no θ tem.

7 R pl ( L L ) d d q i = ( L L ) R pl i - d q d (31) in {( L L )( i pi ) } d q d co The econd tem on the ight ide of (31) i defined a the extended EMF (EEMF). In thi tem, beide the taditionally defined EMF geneated by pemanent magnet, thee i a kind of voltage elated to aliency of IPMSM. It include poition infomation fom both the EMF and the tato inductance. If the EEMF can be etimated, the poition of magnet can be obtained fom it phae jut like EMF in SPMSM. Geneally the poition etimation calculated fom the EEMF [14, 18]: e e e in {( Ld Lq )( i d pi ) } co e 1 tan ( ) e ( R pld ) i ( Ld Lq ) i ( ) ( R pl ) i ( L L ) i d d q The poblem i that, the EEMF i influenced by tato cuent id and i, which vay duing moto tanient tate. Thi will caue touble to the peed etimation. In the low peed ange, the ignal to noie atio of the EEMF i elatively mall and the peed etimation eult i till not o good. To ovecome thi difficulty eveal autho ue obeve and adaptive method [14] Adaptive Method In thi categoy, vaiou type of obeve ae ued to etimate oto poition. The fundamental idea i that a mathematical model of the machine i utilized and it take meaued input of the actual ytem and poduce etimated output. The eo between the etimated output and meaued quantitie i then fed back into the ytem model to coect the etimated value adaptation mechanim. The bigget advantage of uing obeve i that all of the tate in the ytem model can be etimated including tate that ae had to obtain by meauement. Alo, in the obeve baed method, the eo accumulation poblem in the flux calculation method do not exit [0], but the weakne i poo peed adjutable at low peed, complicated algoithm and huge calculation []. Obeve have been implemented in enole PM moto dive ytem. The adaption mechanim bae on the following thee method citeia of upe tability theoy (Popov), kalman filte, and method of leat eo quae [9]. Method uing the Popov ae citeia model efeence adaptive ytem and luenbege obeve. A. Etimato Baed on Model Refeence Adaptive Sytem A model efeence adaptive ytem (MRAS) can be epeented by an equivalent feedback ytem a hown in Figue. (3) (33) 50

8 u i Refeence Model x + - Adaptive Model ŷ Adaptation mechanim Figue. Roto peed etimation tuctue uing MRAS. Whee epeent the eo between the efeence model and the adaptive model. The diffeence between eal and etimated value can be expeed with the dynamic eo equation [9]: d d ( x x 垐 ) Ax Ax ˆ K ( Cx Cx?) dt dt ( A - KC ) ( A - Aˆ ) xˆ Whee x i the tate vecto, u the ytem input vecto, y the output vecto, the matice A, B and C the paamete of the PMSM and the matix K a gain coefficient epectively. All element with ^ ae the etimated vecto and matice. It hould be noted that, peed etimation method uing MRAS can claified into vaiou type accoding to the tate vaiable. The mot commonly ued ae the oto flux baed MRAS, back-emf baed MRAS, and tato cuent baed MRAS. Fo all mentioned tate can be applied one adaption model [9]: p q d q d i q d q d 0 (34) T y垐 k ( x x x垐 x ) k ( x x x? x ) dt (35) Stability and peed of the calculation of ŷ depend on the popotional and integal pat of (35). x and x d epeent the tate of the PMSM in quadatue and diect coodinate. A the oto peed i included in cuent equation, we can chooe the cuent model of the PMSM a the adaptive model, and the moto itelf a the efeence model. Thee two model both have the output d i and, Accoding to the diffeence between the output of the two model, though a cetain adaptive mechanim, we can get the etimated value of the oto peed. Then the poition can be obtained by integating the peed [30]. The equation (1) to (4) can be witten a below fom: di d Ld -Ri d Lqi d dt (36) di Lq -Ri -Ldi d - dt (37) q i 51

9 The d-q axi cuent i d, i ae the tate vaiable of the cuent model of the PMSM, which i decibed by (36) and (37). By ewiting equation (36) and (37) into a matix fom a below: R L q i d Ld L d i d d L d L d dt Ld R i - i Lq L q d R Ld L d Lq Fo the convenience of tability analyi, the peed ha been confined to the ytem matix: To be implified, define: R L Ld L A Ld R - Lq L x i q d q x 1 d L d x i d R u L 1 d L d u u Lq Then the efeence model can be ewitten a: 5 (38) (39) (40) (41) d x Ax u (4) dt The adaptation mechanim ue the oto peed a coective infomation to obtain the adjutable paamete cuent eo between two model in ode to dive the cuent eo to zeo, when we can take the etimation value a a coect peed. The poce of peed etimation can be decibed a follow: R Lq ˆ 垐 d x? 1 Ld Ld x 1 u 1 dt x垐? Ld R x u - ˆ Lq Lq (43)

10 Whee ˆ i to be etimated, (43) can be implified a below: d x 垐 Ax ˆ u? (44) dt The eo of the tate vaiable i: e x xˆ (45) Accoding to equation (4) and (44), etimation equation can be witten a: d e Ae Iw (46) dt De (47) Whee w ( Aˆ A) xˆ, chooe D I, then Ie e (48) Accoding to Popov upe tability theoy, if 1 (1) H ( ) D( SI - A) i a tictly poitive matix, () t0 T (0, t 0) wdt, t 0 0 The MARS ytem will be table. Finally, the equation of ˆ can be achieved a: Whee k 1, k 0 Replacing x with i : 0 ˆ, whee i a limited poitive numbe, then lim et ( ) 0. 0 t k 1( x 垐 1x x x 1) dt 0 k ( x x垐 x x ) ˆ t (0) 垐 ˆ? k 1( i di i i d ( i i )) dt L 垐 k ( i i i i ( i i? )) ˆ d d d (0) Ld In the equation (50), i ˆd, i ˆ can be calculated though the adjutable model, d the tanfomation of the meaued tato cuent. The oto poition can be obtained by integating the etimated peed: The MRAS cheme i illutated in Figue 3. t 0 (49) (50) ˆ ˆ dt (51) i, i t can be obtained by 53

11 u α u β PMSM i α i β Coodinate Tanfom i d i Coodinate Tanfom u d u Adjutable Model iˆd iˆ ˆ ˆ t ˆ ˆ ˆ ˆ k 1( i di i i d ( i i )) dt L 0 ˆ ˆ k ( i i i i ( i iˆ )) ˆ d d d (0) Ld Figue 3. Contol block cheme of MRAS B. Obeve-Baed Etimato Obeve method ue intead of the efeence model the eal moto. The obeve i the adaptive model with a contantly updated gain matix K which i elected by chooing the eigenvalue in that way, that the ytem will be table and that the tanient of the ytem will be dynamically fate than the PM machine [9]. 1) Luenbege Obeve A full ode tate obeve with meaueable etimated tate vaiable, geneally tato cuent, and not meauable vaiable like oto flux linkage, back-emf and oto peed can be decibed in the fom of tate pace equation fo contol of time invaiant ytem [9]: x Ax Bu y Cx whee A i the tate matix of the obeve a function of the etimated oto peed, B the input matix and C output matix. In the following example the etimation algoithm obeve baed on back-emf in α-β fame i conideed. With the aumption that the back-emf vecto ha the following fom: e e e in {( Ld Lq )( i d pi ) } co and that electical ytem time contant i much malle than the mechanical one. contant paamete. The linea tate equation can be decibed a follow [6, 8, and 9]: (5) (53) i egaded a a 54

12 d i i A B u W (54) dt e e Whee, i i C. e i [ i i ] T, e [ e e ] T (55) A 1 L d R - ( L L ) -1 0 d q ( L L ) R 0-1 d q B 1 L d , C 晻? in W ( Ld Lq )( i d i ) co i The tem W i the unknown lineaization eo and appea only, when d The tate equation of the Luenbege obeve can be witten a: d i垐 ˆ i u A B dt e垐 e u K ( i iˆ ) ˆ ˆ i i C. e ˆ can be een, that the dynamic ae decibed by the eigenvalue of A - KC. To detemine the tability of the eo dynamic of the obeve it can be ued Popov upe tability theoem o Lyapunov tability 55 oi (56) (57) i changing. Whee ^ denote etimated value. A ˆ i a function of the oto peed. Theefoe the peed mut alo be etimated. The etimated peed can be calculated with a PI-contolle which ha the fom of equation (58). 垐 ( 垐 ) (? k p e e k i e e ) dt (58) Whee k and k ae popotional and integal gain contant epectively, i iˆ and p i i iˆ ae the α-β axi cuent eo epectively. Fo obtaining eo dynamic (34) can be ued. It

13 theoem which give a ufficient condition fo the unifom aymptotic tability of non-linea ytem by uing the Lyapunov function V. A ufficient condition fo the unifom aymptotic tability i that the deivate of V i negative definite. If the obeve gain K i choen that ( A - KC ) T i negative emidefinite, then the peed obeve will be table [9]. Futhe liteatue in flux-baed obeve can be found in [31, 3]. Sytem with a Luenbege obeve geneally have a bette pefomance than MRAS baed Sytem. MRAS baed ytem have a highe eo in the etimated value. Futhemoe, the Luenbege appoach ha a le tendency to ocillate in the ange of low peed and need in compaion with the kalman Filte method le computation time and memoy equiement [9, 33]. ) Reduced Ode Obeve Pape [34] i included on the idea of the educed ode obeve. The deign method conide a geneal dynamic ytem in the fom of equation (5). Whee the pai (C, A) i obevable. If the output y can be witten a a combination of the tate vecto a: y C1x 1 C x ; det ( C ) 0 (59) Then, it i ufficient to deign an obeve fo the patial tate x 1. If xˆ 1 i the etimate of x 1, the patition x of the tate vecto can be calculated a: x垐 C ( y C x ) (60) The educed ode obeve allow fo ode eduction, i imple to implement and the tate patition x i found uing the algebaic equation (60). The deign methodology of the educed ode obeve equie tanfomation of the oiginal ytem to the fom: x 1 A11x 1 A1 y B1u (61) y A x A y B u (6) 1 1 A new vaiable x i intoduced: x x L y (63) 1 1 whee L 1 i a noningula gain matix. Afte the diffeentiation and algebaic manipulation of (63), the following fom i obtained: x ( A L A ) x ( A L A A L L A L ) y (64) ( B L B ) u 1 1 An obeve fo x i deigned in the fom: xˆ ( A L A ) xˆ ( A L A A L L A L ) y ( B L B ) u 1 1 Afte ubtaction, the dynamic of the mimatch i: (65) x ( A L A ) x (66) With the known matice A 11 and A 1, the gain in L 1 can be elected to obtain deied eigenvalue. Theefoe, the mimatch tend to zeo with the deied ate of convegence. Once xˆ ' ha been etimated, the tate patition x 1 follow fom (63) and x i calculated uing (60). Futhe liteatue in educed ode obeve can be found in [35-37]. 3) Sliding Mode Obeve 56

14 In [38, 39] peent a liding mode obeve (SMO) fo the etimation of the EMF and the oto poition of the PMSM. The obeve i contucted baed on the full PMSM model in the tationay efeence fame. The popoed liding mode obeve i developed baed on the equation of the PMSM with epect to the cuent and EMF: pe pe e (67) e (68) R 1 1 pi i e L L L (69) R 1 1 pi i e L L L (70) The voltage, and cuent i, i ae meaued and conideed known. In the obeve, a peed etimate i ued accoding to (71); the peed etimate i conideed diffeent than the eal peed (note that i unknown). ˆ (71) The obeve equation ae: whee the witch (liding mode) contol pe垐 ( ) e l u (7) 11 pe垐 ( ) e l u (73) 垐 R pi ˆ i e u L L L L (74) 垐 R pi ˆ i e u L L L L (75) u M. ign( ) u M. ign( ) u, ae: u ; iˆ i iˆ i 57 Note that M i a deign gain, M> 0; l 11 and l ae deign paamete. Afte the oiginal equation (67) to (70) ae ubtacted fom (7) to (75), ytem i obtained by following equation: 11 (76) pe e e ˆ l u (77) pe e e ˆ l u (78) R 1 1 e u L L L (79) R 1 1 e u L L L (80) In the lat two equation (79) and (80), note that if the liding mode gain M i high enough, the manifold, and thei time deivative have oppoite ign. A a eult, the manifold tend to zeo and liding mode occu; i.e. 0 and 0. Once liding mode tat,, and thei deivative ae identically equal to zeo. The equivalent contol ae: u u, eq, eq e e (81)

15 In ode to tudy the behavio of the mimatche e, e, the tem u and u ae eplaced with the equivalent contol in the fit two equation of (77) and (78). The eulting dynamic of the EMF mimatche i: pe e e ˆ l e (8) 11 pe e e ˆ l e (83) Next, elect the candidate Lyapunov function which i poitive definite, V> 0. 1 ( ) Afte diffeentiation, the expeion of V i: V e e (84) V e e e e (85) Afte eplacing the deivative fom (8) and (83), thi become: V l e l e e e e e (86) 垐 11 If l 11 l k whee k 0, the deivative of V i: V k ( e e ) ( e e e e ) (87) 垐 Equation (87) will be ued to tudy the convegence of the obeve. Note that V 0 If 0 and the obeve i aymptotically table. Thee ae two tem in (87): the fit one i alway negative (and can be inceaed uing the deign paamete k) while the econd one ha unknown ign. A long a the mimatche e and e ae ignificant, the fit tem ovecome the econd and V i negative (a a eult, function V decay). The Lyapunov function top decaying when V 0 and thi i equivalent to: k ( e e ) ( e e e e ) (88) 垐 Since the mimatche e, e hould be of the ame ode of magnitude, uing the notation me e (whee m i unknown), equation (88) i manipulated to give the value of the mimatch e at which the function V top decaying: m e垐 e e k (1 m ) The Lyapunov function ettle to the vicinity given by the mimatch in (89), and the ize of thi vicinity (and the mimatch) can be educed by inceaing k (which i a deign paamete). The analyi how that the influence of the peed mimatch (caued by the peed obeve) can be made ielevant by pope deign of the SM obeve gain; the mimatch between the eal and etimated EMF can be made a mall a deied accoding to (89). Once the EMF have been found, the oto poition i computed diectly with: 1 eˆ (89) ˆ tan ( ) (90) eˆ Futhe liteatue in liding mode obeve (SMO) can be found in [40-43]. The main diffeence between the Luenbege and the Sliding mode obeve (SMO) lie in the obeve tuctue. The SMO ue a ign-function of the etimation eo intead of the linea value a coection feedback [44]. 4) Kalman Filte 58

16 The kalman filte i in pinciple a tate obeve that etablihe the appoximation fo the tate vaiable of a ytem, by minimization of the quae eo, ubjected at both it input and output to andom ditubance. If the dynamic ytem of which the tate i being obeved i non-linea, then the kalman filte i called an extended kalman filte (EKF). The EKF i baically a full-ode tochatic obeve fo the ecuive optimum tate etimation of a nonlinea dynamical ytem in eal time by uing ignal that ae in noiy envionment. The EKF can alo be ued fo unknown paamete etimation o joint tate [45]. The linea tochatic ytem ae decibed by elation [7]: x ( t ) Ax ( t ) Bu( t ) w ( t ) ; x ( to) x o (91) y ( t ) Cx ( t ) (9) z ( t ) y ( t ) ( t ) (93) Whee: x, y,u, A, B,C have the ignificance known fom deteminitic ytem; w () t epeent the vecto of ditubance applied at the ytem input; z() t i the vecto of the meauable output, affected by the andom noie () t. It can be conideed that, beide the input ditubance, vecto w () t include ome uncetaintie efeing to the poce model. It will be aumed that the vecto function w () t and () t ae not coelated and zeo-mean tochatic pocee. Fom tatitic point of view, the tochatic pocee w () t and () t ae chaacteized by the covaiance matice Q and R, epectively. It i futhe aumed that the initial tate x o i a vecto of andom vaiable, of mean x o and covaiance P 0, not coelated with the tochatic pocee w () t and () t ove the entie inteval of etimation. The covaiance matice Q, R, P0 chaacteizing the noie ouce of ytem (94)-(96) ae, by definition, ymmetical and poitively emi-definite, of dimenion (n x n), (m x m) and (n x n) epectively, whee n and m epeent the numbe of tate and output vaiable, epectively. Fo linea time invaiant ytem, the following elation of ecuent computation decibe the geneal fom of the kalman filte implementation algoithm: K P C CP C R T T 1 k ( ) (94) k k 1 k k 1 x垐 x K ( y Cx? ) (95) k k k k 1 k k k k 1 P ( I n - K kc ) P k k k k 1 (96) x垐 A k 1k d x T k k Bu k (97) T P A k 1k dp A k k d Q (98) Whee T epeent the ampling peiod and A d i the matix of the dicete lineaized ytem: A I T A (99) d n In thee elationhip, the (n x m) matix K epeent the kalman gain; P epeent the covaiance tate matix and I n i the (n x n) unit matix. In the ecuent computation elationhip, the ubcipt index notation of type k/k-1 how that the epective quantitie (tate vecto o thei covaiance matice) ae computed fo ample k, uing the value of imila quantitie fom the peviou ample. Fo non-linea tochatic ytem, the dynamic tate model i decibed by the following expeion: x ( t ) f ( x ( t ), u( t ), t ) w ( t ) (100) y ( t ) h( x ( t ), t ) (101) z ( t ) h( x ( t ), t ) ( t ) (10) 59

17 whee f and h ae (n x 1) and (m x 1) function vecto, epectively. The A and C matice of the EKF tuctue ae dependent now upon the tate of the ytem and ae detemined by: f ( x ( t ), u( t ), t ) A( xˆ ( t ), t ) T x ( t ) xˆ ( t ) x () t (103) h( x ( t ), t ) C ( xˆ ( t ), t ) T x ( t ) xˆ ( t ) x () t (104) Additionally to the fact that matice A and c have now become dependent on the tate of the ytem, the algoithm uffe ome futhe change, which affect elationhip (95) and (97), now expeed a: x垐 x K [ y h( x? )] (105) k k k k 1 k k k k 1 x垐 x T (?( ), ( )) k 1k k k f x t u t (106) The kalman filte algoithm i initiated by adopting adequate value fo the covaiance matix of the initial P P tate 0 0 1, a well a fo the weighting matice Q and R, the latte two being contant duing the etimation. EKF i known fo it high convegence ate, which ignificantly impove tanient pefomance. Howeve, the long computation time i a main dawback of the EKF [45]. Although lat-geneation floating-point digital ignal poceo can eaily ovecome the EKF eal-time calculation [46], thi i not uitable fo low-cot PMSM application. Moeove, long computation equiement ditub othe pogam evice outine uch a fault diagnoi o cutom pogam intalled in poduct. [47] peent the optimal twotage kalman etimato (OTSKE) which i compoed of two paallel filte: a full ode filte and anothe one fo the augmented tate. Thi etimato ha the advantage of educing the computational complexity compaed to the claical EKF. The application of the EKF in the enole PMSM dive ytem will be inceaed a lot [9, 48]. The main tep fo a peed and poition enole PMSM dive implementation uing a dicedited EKF algoithm can be found in [45, 48-51]. 3. Saliency and Signal Injection Method In ignal injection method, the featue of alient-pole PMSM uch that the inductance vaie with the oto poition i ued. High fequency voltage o cuent ignal i injected on the top of the fundamental, and ignal poceing (vecto filte with inevitable time delay) i employed to extact cuent hamonic that contain oto poition. Thu, the poition can be etimated even at tandtill and low peed, obutly to paamete vaiation [5]. Fo wide peed ange, hybid method ae ued [53]. High fequency ignal injection technique, Figue 4, ae conideed to be upeio to othe enole contol cheme of ac machine fo low and zeo peed opeation. Fundamental excitation High fequency ignal PWM Invete AC Machine Band pa filte Heteodyning demodulation Figue 4. High fequency ignal injection block diagam Speed etimation Poition etimation ˆ ˆ 60

18 Baed on the injection diection of the excitation ignal, the high fequency injection cheme could be claified a otating injection method, in which the caie ignal i a otating inuoidal ignal in the tationay efeence fame; pulating injection method, in which an ac voltage ignal i injected on the etimated oto d-axi, otating with the oto and the oto poition offet could be obeved fom the high fequency component of the etimated q-axi cuent. Howeve, the dive efficiency of the cheme i had to be acceed and the development of the enole tategie uffe the unknown nonlineaity of the model [54]. Othe method ae baed on the ignal poceing of PWM excitation without ignal injection. The SV- PWM wavefom povide ufficient excitation to extact the poition ignal fom the tato cuent. Thee method ae: Indiect Flux detection by On-line Reactance Meauement (INFORM) method, and method baed on the meauement of di/dt of the tato cuent induced by SV-PWM. Typically, the injected ignal i a inuoidal type. To eliminate the time delay intoduced by filte, a new quae wave ignal injection method i popoed, baed only on the meauement of the coeponding induced tato cuent vaiation, which lead to high dynamic and obut poition etimation [5]. Magnetic aliency method ae elatively complicated fo eal time implementation and ae le potable fom one machine to anothe; howeve, they wok well at low peed. The oto poition of the PMSM can alo be etimated at tandtill; a a eult, the moto can be tated with the coect oto poition fom the beginning of the motion [38]. Futhe liteatue which ue the magnetic aliency method can be found in [55-58]. 3.3 Atificial Intelligence Method Atificial intelligence decibe neual netwok (NN), fuzzy logic baed ytem (FLS) and fuzzy neual netwok (FNN). The ue of atificial intelligence (AI) to identify and contol nonlinea dynamic ytem ha been popoed becaue they can appoximate a wide ange of nonlinea function to any deied degee of accuacy [59]. Moeove, they have been the advantage of immunity fom input hamonic ipple and obutne to paamete vaiation. Howeve, ANN contolle ynthei equie deign of the contol tuctue which include electing the neual netwok tuctue, weight coefficient and activation function. The election of neual tuctue a the initial tep i done by tial and eo method ince thee i no pope pocedue fo thi [60]. The complex of the elected neual netwok tuctue i a compomie between the high quality of contol obutne and the poibility of contol algoithm calculation in eal time. Thi give ie to inaccuacie [60]. Recently, thee have been ome invetigation into the application of AI to powe electonic and ac dive, including peed etimation [60-63]. Pape [64] peent a obut contol tategy with NN flux etimato fo a poition enole SPMSM dive. In the popoed algoithm tato flux i etimated fom tationay α-β axi tato cuent and peed eo, E ω. An equivalent Recuent Neual Netwok (RNN) i then popoed which eult in the following matix equation: ( k 1) W 0 ( k ) W i ( k 1) 0 W ( k ) W 3 W W i ( ) ( ) k E w k W W 4 5 whee, W11, W13,W, W3, W14 etc. ae the weight of the RNN. ( k ) (107) The etimated tato flux uing RNN i ued to find out the oto poition a following: (108) 61

19 1 Whee, i the flux angle, and i the toque angle. Whee tan ( ) 4. Paamete Adaptation Motion-enole PMSM dive may have an untable opeating egion at low peed. Since the back electomotive foce (EMF) i popotional to the otational peed of the moto, paamete eo have a elatively high effect on the accuacy of the etimated back EMF at low peed [65]. Impope obeve gain election may caue untable opeation of the dive even if the paamete ae accuately known [66]. In pactice, the tato eitance vaie with the winding tempeatue duing the opeation of the moto, o thee i often a mimatch between the actual winding eitance and it coeponding value in the model ued fo peed etimation. Thi may lead not only to a ubtantial peed etimation eo but to intability a well. Paamete vaiation not only degade the contol pefomance but alo caue an eo in the etimated poition [67]. A conequence, numeou online cheme fo paamete identification have been popoed, ecently [65-69]. 5. Concluion Recently, pemanent magnet ynchonou moto (PMSM) dive ae eplacing claic dc and induction machine dive in a vaiety of indutial application. PMSM dive eeach ha been concentated on the elimination of the mechanical eno at the moto haft without deteioating the dynamic pefomance of the dive. Many advantage of enole ac dive uch a educed hadwae complexity, low cot, educed ize, cable elimination, inceaed noie immunity, inceaed eliability and deceaed maintenance.in thi pape, a eview of diffeent peed and oto poition etimation cheme of PMSM dive ha been intoduced. Each method ha it advantage and diadvantage. Although numeou cheme have been popoed fo peed and oto poition etimation, many facto emain impotant to evaluate thei effectivene. Among them ae teady tate eo, dynamic behavio, noie enitivity, low peed opeation, paamete enitivity, complexity, and computation time. In paticula, zeo-peed opeation with obutne againt paamete vaiation yet emain an aea of eeach fo peed enole contol. A a final comment, each peed etimation method of enole application equie a pecific deign, which take into conideation the equied pefomance, the available hadwae and the deigne kill. Refeence: [1] S. Yu, Z. Yang, S. Wang and K. Zheng, "Senole Adaptive Backtepping Speed Tacking Contol of Uncetain Pemanent Magnet Synchonou Moto", in Conf. Rec., IEEE-ISCAA, June 010, pp [] Q. Gao, S. Shen, and T. Wang, "A Novel Dive Stategy fo PMSM Compeo", in Conf. Rec., IEEE- ICECE, June 010, pp [3] Z. Peoutka, K. Zeman, F. Ku, and F. Koten, "New Geneation of Tam with Geale Wheel PMSM Dive: Fom Simple Diagnotic to Senole Contol", in IEEE Conf. Rec., 14th Intenational Powe Electonic and Motion Contol Confeence EPE-PEMC, Septembe 010, pp [4] H. Peng, H. Lei, and M. Chang-yun, "Reeach on Speed Senole Backtepping Contol of Pemanent Magnet Synchonou Moto", in Conf. Rec., IEEE-ICCASM, Octobe 010, Vol. 15, pp [5] J. Sung Pak, S. Hun Lee, C. Moon, and Y. Ahn Kwon, "State Obeve with Stato Reitance and Back-EMF Contant Etimation fo Senole PMSM", IEEE Region 10 Confeence, TENCON 010, Novembe 010, pp [6] T. J. Vyncke, R. K. Boel and J. A. A. Melkebeek, "Diect Toque Contol of Pemanent Magnet Synchonou Moto An Oveview", 3d IEEE Benelux Young Reeache Sympoium in Electical Powe Engineeing, Apil 006, pp

20 [7] V. Comnac, M. N. Citea, F. Moldoveanu, D. N. Ilea, and R. M. Cenat, "Senole Speed and Diect Toque Contol of Inteio Pemanent Magnet Synchonou Machine Baed on Extended Kalman Filte", in Poc. of the IEEE-ISIE Conf., Vol. 4, Novembe 00, pp [8] M. S. Mezoug, and F. Nacei, "Compaion of Field-Oiented Contol and Diect Toque Contol fo Pemanent Magnet Synchonou Moto (PMSM)", in Wold Academy of Science, Engineeing and Technology, Vol. 48, 008, pp [9] Y. Xu, and Y. Zhong, "Speed Senole Diect Toque Contol of Inteio Pemanent Magnet Synchonou Moto Dive Baed on Space Vecto Modulation", in Conf. Rec., IEEE-ICECE, June 010, pp [10] J. Aellano-Padilla, C. Geada, G. Ahe, and M. Sumne, "Inductance Chaacteitic of PMSM and thei Impact on Saliency-baed Senole Contol", in IEEE Conf. Rec., 14th Intenational Powe Electonic and Motion Contol Confeence EPE-PEMC, Septembe 010, pp [11] K. Jezenik, R. Hovat, "High Pefomance Contol of PMSM ", in Conf. Rec., IEEE-SLED, July 010, pp [1] S. Sumita, K. Tobai, S. Aoyagi, and D. Maeda, "A Simplified Senole Vecto Contol Baed on the Aveage of the DC Bu Cuent", in Conf. Rec., IEEE-IPEC, June 010, pp [13] R. Mutafa, Z. Ibahim and J. Mat Lazi, "Senole Adaptive Speed Contol fo PMSM Dive", in IEEE Conf. Rec., 4th Intenational Powe Engineeing and Optimization Conf., PEOCO'10, June 010, pp [14] O. Benjak, and D. Geling, "Review of Poition Etimation Method fo IPMSM Dive Without a Poition Seno Pat I: Nonadaptive Method", in Conf. Rec., IEEE-ICEM, Septembe 010, pp [15] M. A. Jabba, M. A. Hoque, and M. A. Rahman, "Senole Pemanent Magnet Synchonou Moto Dive", IEEE Canadian Confeence on Electical and Compute Engineeing, CCECE'97, Vol., May 1997, pp [16] J. P. Johnon, M. Ehani, and Y. Guzelgunle, "Review of Senole Method fo Buhle DC", in Conf. Rec., IEEE-IAS'99, Annual Meeting, Vol. 1, Octobe 1999, pp [17] S. Kondo, A. Takahahi and T. Nihida, "Amatue Cuent Locu Baed Etimation Method of Roto Poition of Pemanent Magnet Synchonou Moto without Mechanical Seno", in Conf. Rec., IEEE- IAS'95, Annual Meeting, Vol. 1, Octobe 1995, pp [18] L. Yongdong, and Z. Hao, "Senole Contol of Pemanent Magnet Synchonou Moto A Suvey", in Conf. Rec., IEEE-VPPC'08, Septembe 008, pp [19] T. D. Batzel, and K. Y. Lee, "Electic Populion with the Senole Pemanent Magnet Synchonou Moto: Model and Appoach", IEEE Tanaction on Enegy Conveion, Vol. 0, No. 4, Decembe 005, pp [0] T. Kim, H. Lee, and M. Ehani, "State of the At and Futue Tend in Poition Senole Buhle DC Moto/Geneato Dive", Poc. of the 31th Annual Confeence of the IEEE-IECON, Novembe 005, pp [1] N. Bekioglu, S. Ozcia, "Obevele Scheme fo Senole Speed Contol of PMSM Uing Diect Toque Contol Method with LP Filte", Advance in Electical and Compute Engineeing (AECE), Vol. 10, No. 3, Augut 010, pp [] D. Youfi, A. Halelfadl, and M. EI Kad, "Senole Contol of Pemanent Magnet Synchonou Moto", in Conf. Rec., IEEE-ICMCS'09, Apil 009, pp [3] D. Paulu, J.-F. Stumpe, P. Landmann, and R. Kennel, "Robut Encodele Speed Contol of a Synchonou Machine by diect Evaluation of the Back-EMF Angle without Obeve", in Conf. Rec., IEEE-SLED, July 010, pp [4] S. Shimizu, S. Moimoto, and M. Sanada, "Senole Contol Pefomance of IPMSM with Ovemodulation Range at High Speed", in Conf. Rec., IEEE-ICEMS'09, Novembe 009, pp [5] F. Genduo, R. Miceli, C. Rando, and G. R. Galluzzo, "Back EMF Senole-Contol Algoithm fo High-Dynamic Pefomance PMSM", IEEE Tanaction on Indutial Electonic, Vol. 57, No. 6, June 010, pp [6] Z. Chen, M. Tomita, S. Doki, and S. Okuma, "An Extended Electomotive Foce Model fo Senole Contol of Inteio Pemanent Magnet Synchonou Moto", IEEE Tanaction on Indutial Electonic, Vol. 50, No., Apil 003, pp

21 [7] S. Moimoto, K. Kawamoto, M. Sanada, and Y. Takeda, "Senole Contol Stategy fo Salient- Pole PMSM Baed on Extended EMF in Rotating Refeence Fame", IEEE Tanaction on Induty Application, Vol. 38, No. 4, July/Augut 00, pp [8] S. Ichikawa, Z. Chen, M. Tomita, S. Doki, and S. Okuma, "Senole Contol of an Inteio Pemanent Magnet Synchonou Moto on the Rotating Coodinate Uing an Extended Electomotive Foce", Poc. of the 7th Annual Confeence of the IEEE-IECON, Vol. 3, Novembe/Decembe 001, pp [9] O. Benjak, D. Geling, "Review of Poition Etimation Method fo IPMSM Dive without a Poition Seno Pat II: Adaptive Method", in Conf. Rec., IEEE-ICEM, Septembe 010, pp [30] Y. Shi, K. Sun, H. Ma, and L. Huang, "Pemanent Magnet Flux Identification of IPMSM baed on EKF with Speed Senole Contol", Poc. of the 36th Annual Confeence of the IEEE-IECON, Novembe 010, pp [31] T. F. Chan, W. Wang, P. Boje, Y. K. Wong, and S. L. Ho, "Senole pemanent-magnet ynchonou moto dive uing a educed-ode oto flux obeve", Electic Powe Application, IET, Vol., No., Mach 008, pp [3] P. Vaclavek, and P. Blaha, "PMSM Poition Etimation Algoithm Deign baed on the Etimate Stability Analyi", in Conf. Rec., IEEE-ICEMS'09, Novembe 009, pp [33] B. S. Bhangu, and C. M. Bingham, "GA-tuning of Nonlinea Obeve fo Senole Contol of Automotive Powe Steeing IPMSM", in Conf. Rec., IEEE-VPPC, Septembe 005, pp [34] M. Comanecu, and T. D. Batzel, "Reduced Ode Obeve fo Roto Poition Etimation of Nonalient PMSM", in Conf. Rec., IEEE-IEMDC'09, May 009, pp [35] D. Youfi, A. Halelfadl, and M. EI Kad, "Review and Evaluation of Some Poition and Speed Etimation Method fo PMSM Senole Dive ", in Conf. Rec., IEEE-ICMCS'09, Apil 009, pp [36] C. H. De Angelo, G. R. Boio, J. A. Solona, G. O. Gacia, and M. I. Valla, "Senole Speed Contol of Pemanent Magnet Moto Diving an Unknown Load", in Conf. Rec., IEEE-ISIE'03, Vol. 1, June 003, pp [37] S. Ichikawa, C. Zhiqian, M. Tomita, S. Doki, and S. Okuma, "Senole Contol of an Inteio Pemanent Magnet Synchonou Moto on the Rotating Coodinate Uing an Extended Electomotive Foce", Poc. of the 7th Annual Confeence of the IEEE-IECON, Vol. 3, Novembe/Decembe 001, pp [38] M. Comanecu, "Roto Poition Etimation of PMSM by Sliding Mode EMF Obeve unde impope peed", in Poc. of the IEEE-ISIE Conf., July 010, pp [39] M. Comanecu, "Cacaded EMF and Speed Sliding Mode Obeve fo the Nonalient PMSM", Poc. of the 36th Annual Confeence of the IEEE-IECON, Novembe 010, pp [40] M. Ezzat, J. de Leon, N. Gonzalez, and A. Gluminea, "Obeve-Contolle Scheme uing High Ode Sliding Mode Technique fo Senole Speed Contol of Pemanent Magnet Synchonou Moto", Poc. of the 49th Confeence of the IEEE-CDC, Decembe 010, pp [41] Y. Nan, and T. Zhang, "Reeach of Poition Senole Contol fo PMSM Baed on Sliding Mode Obeve", nd intenational confeence of the IEEE-ICISE, Decembe 010, pp [4] L. Jun, W. Gang, and Y. JinShou, "A Study of SMO Buffeting Elimination in Senole Contol of PMSM", in Poc. of the IEEE-WCICA Conf., July 010, pp [43] Zhang Niaona, Guo yibo and Zhang Dejiang, "Sliding Obeve Appoach fo Senole Opeation of PMSM Dive", in Poc. of the IEEE-WCICA Conf., July 010, pp [44] L. Jiaxi, Y. Guijie, and L. Tiecai, "A New appoach to Etimated Roto Poition fo PMSM Baed on Sliding Mode Obeve", in Conf. Rec., IEEE-ICEMS'07, Octobe 007, pp [45] J. Jang, B. Pak, T. Kim, D. M. Lee, and D. Hyun, "Paallel Reduced-Ode Extended Kalman Filte fo PMSM Senole Dive", Poc. of the 34th Annual Confeence of the IEEE-IECON, Novembe 008, pp [46] S. Bolognani, R. Oboe, and M. Zigliotto, "Senole Full-Digital PMSM Dive with EKF Etimation of Speed and Roto Poition", IEEE Tanaction on Indutial Electonic, Vol. 46, No. 1, Febuay 1999, PP

22 [47] A. Akad, M. Hilaiet, and D. Diallo, "Pefomance Enhancement of a Senole PMSM dive with Load Toque Etimation", Poc. of the 36th Annual Confeence of the IEEE-IECON, Novembe 010, pp [48] T. J. Vyncke, R. K. Boel, and J. A. A. Melkebeek, "On Extended Kalman Filte with Augmented State Vecto fo the Stato Flux Etimation in SPMSM", in Poc. of the Twenty-Fifth Annual IEEE- APEC Conf., Febuay 010, pp [49] A. Titaouinen, F. Benchabane, o. Benni, K. Yahia, and D. Taibi, "Application of AC/DC/AC Convete fo Senole Nonlinea Contol of Pemanent Magnet Synchonou Moto", in Conf. Rec., IEEE-SMC, Octobe 010, pp [50] F. Benchabane, A. Titaouine, o. Benni, K. Yahia, and D. Taibi, "Sytematic Fuzzy Sliding Mode Appoach Combined With Extented Kalman Filte fo Pemanent Magnet Synchonou Moto contol", in Conf. Rec., IEEE-SMC, Octobe 010, pp [51] S. Caiee, S. Caux, M. Fadel, and F. Alonge, "Velocity enole contol of a PMSM actuato diectly diven an uncetain two-ma ytem uing RKF tuned with an evolutionay algoithm", in Poc. of the IEEE-(EPE/PEMC) Conf., Septembe 010, pp [5] G.-D. Andeecu and C. Schlezinge, "Enhancement Senole Contol Sytem fo PMSM Dive Uing Squae-Wave Signal Injection", Poceeding of the Intenational Sympoium on Powe Electonic, Electical Dive, Automation and Motion (SPEEDAM), June 010, pp [53] D. Xiao, G. Foo, and M. F. Rahman, "A New Combined Adaptive Flux Obeve with HF Signal Injection fo Senole Diect Toque and Flux Contol of Matix Convete Fed IPMSM ove a Wide Speed Range", IEEE Enegy Conveion Conge and Expoition, ECCE 10, Septembe 010, pp [54] Y. Wang, J. Zhu, Y. Guo, Y. Li, and W. Xu, "Toque Ripple and Etimation Pefomance of High Fequency Signal Injection baed Senole PMSM Dive Stategie", IEEE Enegy Conveion Conge and Expoition, ECCE 10, Septembe 010, pp [55] Z. Anping, and W. Jian, "Obevation Method fo PMSM Roto Poition Baed on High Fequency Signal Injection", in Conf. Rec., IEEE-ICECE, June 010, pp [56] D. Baic, F. Malait, and P. Rouchon, "Initial Roto Poition Detection in PMSM baed on Low Fequency Hamonic Cuent Injection", in IEEE Conf. Rec., 14th Intenational Powe Electonic and Motion Contol Confeence EPE-PEMC, Septembe 010, pp [57] W. Staffle, and M. Schödl, "Extended mechanical obeve tuctue with load toque etimation fo enole dynamic contol of pemanent magnet ynchonou machine", in IEEE Conf. Rec., 14th Intenational Powe Electonic and Motion Contol Confeence EPE-PEMC, Septembe 010, pp [58] F. De Belie, P. Segeant, and J. A. Melkebeek, "A Senole Dive by Applying Tet Pule Without Affecting the Aveage-Cuent Sample", IEEE Tanaction on Powe Electonic, Vol. 5, No. 4, Apil 010, pp [59] H. Chaoui, W. Gueaieb, and M. C.E. Yagoub, "Neual Netwok Baed Speed Obeve fo Inteio Pemanent Magnet Synchonou Moto Dive", in Conf. Rec., IEEE-EPEC, Octobe 009, pp [60] J. L. F. Daya, V. Subbiah, "Robut Contol of Senole Pemanent Magnet Synchonou Moto Dive uing Fuzzy Logic", in Conf. Rec., IEEE-ICACC, June 010, pp [61] H. Chaoui, and P. Sicad, "Senole Neual Netwok Speed Contol of Pemanent Magnet Synchonou Machine with Nonlinea Stibeck Fiction", IEEE/ASME Intenational Confeence on Advanced Intelligent Mechatonic (AIM), July 010, pp [6] A. Accetta, M. Ciincione, and M. Pucci, "Senole Contol of PMSM by a Linea Neual Netwok: TLS EXIN Neuon", Poc. of the 36th Annual Confeence of the IEEE-IECON, Novembe 010, pp [63] C. B. Butt, M. A. Hoque, and M. A. Rahman, "Simplified Fuzzy-Logic-Baed MTPA Speed Contol of IPMSM Dive", IEEE Tanaction on Induty Application, Vol. 40, No. 6, Novembe/Decembe 004, pp [64] K. K. Halde, N. K. Roy, and B. C. Ghoh, "A High Pefomance Poition Senole Suface Pemanent Magnet Synchonou Moto Dive Baed on Flux Angle", in Conf. Rec., IEEE-ICECE, Decembe 010, pp

23 [65] M. Hinkkanen, T. Tuovinen, L. Hanefo, and J. Luomi, "Analyi and Deign of a Poition Obeve with Stato-Reitance Adaptation fo PMSM Dive", in Conf. Rec., IEEE-ICEM, Septembe 010, pp [66] S. Koonlaboon, and S. Sangwongwanich, "Senole Contol of Inteio Pemanent Magnet Synchonou Moto Baed on A Fictitiou Pemanent Magnet Flux Model", in Conf. Rec., IEEE- IAS'05, Vol. 1, Octobe 005, pp [67] Y. Inoue, Y. Kawaguchi, S. Moimoto, and M. Sanada, "Pefomance Impovement of Senole IPMSM Dive in a Low-Speed Region Uing Online Paamete Identification", IEEE Tanaction on Induty Application, Vol. 47, No., Mach/Apil 011, pp [68] M. Hinkkanen, T. Tuovinen, L. Hanefo, and J. Luomi, "A Reduced-Ode Poition Obeve With Stato-Reitance Adaptation fo PMSM Dive", in Poc. of the IEEE-ISIE Conf., July 010, pp [69] Magnu Janon, Lennat Hanefo, Oka Wallmak, and Mat Lekell, "Synchonization at Statup and Stable Rotation Reveal of Senole Nonalient PMSM Dive", IEEE Tanaction on Indutial Electonic, Vol. 53, No., Apil 006, pp

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