Direct Torque Control Strategy (DTC) Based on Fuzzy Logic Controller for a Permanent Magnet Synchronous Machine Drive

Journal of Electrcal Engneerng & Technology, Vol., o., pp. ~78, 9 Drect Torque Control trategy (DTC) Based on Fuzzy Logc Controller for a Permanent Magnet ynchronous Machne Drve A. Tlemcan, O. Bouchhda, K. Benmansour, D. Boudana and M.. Bouchert Abstract Ths paper ntroduces the desgn of a fuzzy logc controller n conjuncton wth drect torque control strategy for a Permanent Magnet synchronous machne. A stator flux angle mappng technque s proposed to reduce sgnfcantly the sze of the rule base to a great extent so that the fuzzy reasonng speed ncreases. Also, a fuzzy resstance estmator s developed to estmate the change n the stator resstance. The change n the steady state value of stator current for a constant torque and flux reference s used to change the value of stator resstance used by the controller to match the machne resstance. Keywords: Drect torque control, fuzzy logc, fuzz resstance estmator, permanent magnet synchronous machne drve, stator resstance, swtchng tables. Introducton Permanent magnet synchronous motors (PMM) are wdely used n hghperformance drves such as ndustral robots and machne tools thanks to ther known advantages of: hgh power densty, hghtorque/nerta rato, and free mantenance. In recent years, the magnetc and thermal capabltes of the PMM have been consderably ncreased by employng hghcoercve PMM materals. The Drect Torque Control (DTC) method was frst proposed for nducton machnes n the md98s (Takahash and oguch [], [], Depenbrock), and then extended to PMM motors [], []. Ths technque s becomng more and more accepted nowadays snce the basc dea of DTC for motors s to control the torque and flux lnkage by selectng the voltage space vectors properly, whch s based on the relatonshp between the slp frequency and torque. In the late 99s, DTC technques for PMM machnes have appeared [], []. Fgure shows a DTC system for an Interor Permanent Magnet motor. It s seen that no extra sensors are needed to mplement DTC when compared wth vector control except for the use of a voltage sensor. The rotor poston, whch s essental for torque control n a vector control scheme, s not requred n DTC provded the ntal rotor poston s known. Ths makes the sensorless PMM drve easer to mplement []. Correspondng Author: Laboratore de Commande des Processus, Département du Géne Electrque, Ecole atonale Polytechnque,, ave Hassen Bad, BP. 8, ElHarrach, Alger, Algére (h_tlemcan@yahoo.fr) Laboratore de Commande des Processus, Département du Géne Electrque, Ecole atonale Polytechnque,, ave Hassen Bad, BP. 8, ElHarrach, Alger, Algére Equpe Commande des ystèmes, EEA., 9 CergyPontose Cedex, France (benmansour@ensea.fr) Receved Aprl, 8 ; Accepted 9 January, 9 Bascally, drect torque control employs two hysteress controllers to regulate the stator flux and the torque respectvely, whch results n approxmate decouplng between the flux and the torque control. The key ssue of desgnng the DTC les n the strategy of how to choose a proper stator voltage vector to keep the stator flux and the torque n ther prescrbed band [7]. In most DTC schemes, a hysteress controller s used. The latter s usually a twovalue bangbang type controller, whch naturally leads to takng the same acton for the bg torque error and the small one. As a consequence, the above scheme gves poor performances n response to step changes and large torque rpple. In order to mprove the performance of the DTC, t s natural to dvde the torque error nto several ntervals on whch dfferent control acton s taken; snce the DTC control strategy s not based on a motor mathematcal model, t s not easy to gve an apparent boundary to the dvson of the torque error. Besdes, fuzzy control s a way of controllng a system wthout knowng ts mathematc model and whch uses the experence of people knowledge to form ts control rule base. Many applcatons of fuzzy control have appeared n power electroncs and drve controls n the past few years [8]. A fuzzy logc controller was reported n [9] beng used wth DTC []. However, there arses the problem that the rule numbers used s very large (8 rules) and wll slow down the speed of the fuzzy reasonng. Ths paper ntroduces the desgn of a fuzzy logc controller n conjuncton wth a drect torque control strategy for a Permanent Magnet synchronous machne. A stator flux angle mappng technque s proposed to reduce sgnfcantly the sze of the rule base to a great extent so that the fuzzy reasonng speed ncreases. Also, a fuzzy resstance estmator s developed to estmate the change n the stator resstance. The

A. Tlemcan, O. Bouchhda, K. Benmansour, D. Boudana and M.. Bouchert 7 change n the steady state value of stator current for a constant torque and flux reference s used to change the value of stator resstance used by the controller to match the machne resstance. The paper s organzed as follows. In secton, the PMM motor model s dscussed. In secton, the DTC scheme s gven. The fuzzy controller s proposed n secton, where three approaches for the optmzaton of fuzzy rules are dscussed. ecton s devoted to the stator resstance estmator whch s based on fuzzy logc. Mathematcal model of PMM The electrcal and mechancal equatons of the PMM motor n the rotor dq reference frame can be expressed as: v d q = R s d v = R s q dω J = T dt + L + L em d q T dd plqωq dt dq + pld Ωd dt r F Ω c + pωφ f () P s T em = [Φ f Lq sn γ s ( Lq Ld )sn γ] () L L d q Where: R s : tator armature resstance; L d,l q : Drect and quadrature nductance; Ω : Rotor speed; p: Pole pars; v, : tator voltage n dqaxs; d v q d, q : tator current n dqaxs; Φ f : Flux created by the rotor magnets; s : tator flux; T, : Electromagnetc torque and load torque; em T r F : Vscous frcton coeffcent; c J : Total moment of nerta of the motor and load; γ : Angle between rotor and stator flux lnkage; The state vector s composed by the (dq) current components ( d q ), and the rotor speed Ω, whereas a vector control s composed of the rotor voltage components (v d, v q ) and the external dsturbance s represented by the load torque T r []. Under the condton of constant ampltude of s, by dfferentatng equaton () wth respect to tme, the rate of ncreasng of torque can be obtaned. dt P em = [rlq γ cosγ s ( Lq Ld ) γ cosγ] () dt L L d q The dervatve of torque s always postve provded that γ s wthn the range of [ π/ π/] whch mples that the ncrease of torque s proportonal to the ncrease of angle γ. In other words, the stator flux lnkage should be controlled n such a way that flux ampltude s kept constant and the rotatng speed s controlled as fast as possble to obtan the maxmum change n actual torque []. Therefore, for PMMs, the ampltude of the stator flux lnkage should also be changed wth the change of actual torque for mantanng a postve dt/dγ. Wth constant stator flux lnkage, the condton for postve dt/dγ around γ= s gven by: q s < Φ () f Lq Ld DC voltag e L By dfferentatng () wth respect to γ and equalzng t to zero, the condton for maxmum allowable angle γ m can be found, as: γ m Where: a / = cos ccpl Τ ref Voltag e Inverter a Τ em ( a / b c wtchng Table cflx ) Φ f Lq a = L L q + 8 In mantanng postve dt em /dγ the torque angle γ should be also controlled to not exceed γ m whch s correspondng to the maxmum torque []. Hence, the applcaton of DTC n PMM drves, the ampltude of the stator flux lnkage should be controlled to satsfy (), and γ must also be lmted to γ m.. Implementaton of DTC for a PMM Drve The DTC scheme for a PMM drve s shown n Fg.. d U dc ref I c I b V V β I a Concorda Transform aton Fg.. DTC scheme for PMM drve I I β Flux Estmator β PMM Torque Estmator () I I β

8 Drect Torque Control trategy (DTC) Based on Fuzzy Logc Controller for a Permanent Magnet ynchronous Machne Drve. Control Algorthm Between swtchng ntervals, each voltage vector s constant and the stator flux lnkage of a PMM can be expressed n the statonary reference frame as: = V t R I dt + s () t= eglectng the stator resstance, () mples that the tp of the stator flux vector, φ s wll move n the drecton of the appled voltage vector. t= s the ntal stator flux lnkage at the nstant of swtchng. To select the voltage vectors for controllng the ampltude of φ s, the voltage vector plane s dvded nto sx regons. In each regon, two adjacent voltage vectors, whch gve the mnmum swtchng frequency, are selected to ncrease or decrease the ampltude φ s respectvely []. The torque ncreases wth the angle, not wth the slp frequency as n nducton motors. For controllng the ampltude of the stator flux lnkage and for changng the torque or angle quckly, zero voltage vectors are not used n PMM. For nducton motors, the applcaton of zero voltage vectors mmedately makes the slp frequency and torque negatve. For PMMs, the change of torque must occur through change n angle. The applcaton of zero voltage vectors wll make ths change subject to the rotor mechancal tme constant whch can be rather long. In other words, φ s should always be n moton wth respect to the rotor flux lnkage. The rotatng drecton of φ s s determned by the output of the torque controller.. Hystercs Controller Let the stator flux space vector be located n the k sector (k=,...,) of the dq plane as drawn n Fg.. In order to ncrease the ampltude of the stator flux, the nverter voltage space vectors V k, V k+, V k should be appled to the motor. Conversely, to decrease ts ampltude, V k+, V k, V k+ must be appled. The nverter voltage utlzed for the control of the stator flux ampltude acts also on the motor torque. From the prevous secton, t turns out that nverter voltage space vectors whch cause an ncrease n the slp speed of the stator flux produce a torque ncrease. The converse s true for the space vectors whch reduce the slp speed of the stator flux [], []. Table summarzes the combned acton of each nverter voltage space vector on both the stator flux ampltude and the motor torque. In ths table, a sngle arrow means a small varaton, whereas two arrows mean a larger varaton. As t appears from the table, an ncrement of torque ( ) s obtaned by applyng the space vectors V k+ and V k+, rrespectve of the motor speed drecton. Conversely, a decrement of torque ( ) s obtaned by applyng V k or V k. The space vectors V k, V k+ and the zero voltage space vectors alter the torque n accordance wth the motor speed drecton as specfed n Table. Table. Combned acton of each nverter voltage space vector V V V V V + V + V + V,V 7 T em ( > ) T ( < ) em Ω Ω Table. Four swtchng solutons T em T em st wtchng nd wtchng rd wtchng th wtchng T em T em V + V + V, V7 V, V7 V + V + V + V + V V,V7 V V + V + V + V V Wth hysteress controllers havng a two level output, there are four condtons regardng the stator flux and the motor torque voltage demands. For each condton t can be found at least one nverter voltage space vector whch acts n the way of reducng the error sgnals. Ths demonstrates that a voltage nverter s able to regulate n a drect manner the stator flux ampltude and the motor torque of a PMM or to force them so as to track any reference. everal swtchng solutons can be employed to control the torque accordng to whether the stator flux has to be reduced or ncreased. Each soluton nfluences the drve behavor n terms of torque and current rpple, swtchng frequency, and two or fourquadrant operaton capablty. In Table four swtchng solutons are gven. Upon each soluton, a swtchng table can be bult and mplemented n the block selector of Fg.. The swtchng table nputs are the twolevel demands of stator flux and torque, and the stator flux sector, whlst the swtchng table output s the nverter voltage space vector for the motor []. β, Γ V+ V+ V, Γ, Γ V+ Fg.. Inverter voltage and correspondng stator flux varatons V V, Γ

A. Tlemcan, O. Bouchhda, K. Benmansour, D. Boudana and M.. Bouchert 9 To use the swtchng table, rather than the poston of the flux, the zone where the flux s stuated s used. In the tables, Cflx and ccpl are the outputs of the hysteress controllers for flux lnkage and torque, respectvely. The flux lnkage (=: ), where ndcates the stuaton of the flux poston, can be obtaned by the followng equatons: ( ) π/ < θ < ( ) π/ (7) Fg.. gves flux trajectores for dfferent swtchng strateges, the most crcular trajectores are gven n Table and Table. One can see the hard trajectory oscllatons n Table. The torque responses to the dfferent swtchng algorthms are gven n Fg.. One can see the hard trajectory oscllatons n Table. The torque responses to the dfferent swtchng algorthms are gven n Fg.. Table gves the best performance wth respect to Tables, and. The latter exhbts hard torque oscllatons. The same conclusons for the currents responses can be obtaned from Fg.. Table. The st swtchng strategy Torque Flux = = = = = = ccpl = ccpl = Cflx = V V V V V V Cflx = V V V V V V Cflx = V 7 V V 7 V V 7 V Cflx = V V 7 V V 7 V V 7 Table. The nd swtchng strategy Torque Flux = = = = = = ccpl = ccpl = Cflx = V V V V V V Cflx = V V V V V V Cflx = V V V V V V Cflx = V V 7 V V 7 V V 7 Table. The rd swtchng strategy Torque Flux = = = = = = ccpl = ccpl = Cflx = V V V V V V Cflx = V V V V V V Cflx = V V V V V V Cflx = V V V V V V Table. The th swtchng strategy Torque Flux = = = = = = ccpl = Cflx = V V V V V V Cflx = V V V V V V β (Wb)... Table.. β (Wb)... Table.. (Wb) β (Wb)... Table.. β (Wb)... Table.. (Wb) (Wb) (Wb) Fg.. Flux trajectores for dfferent swtchng strateges T em (m).... T em (m) Table Table.... T em (m).... T em (m) Table Table.... Fg.. Torque responses to the dfferent swtchng algorthms 8 8 (A) I Table.... 8 8 (A) I Table.... I (A) Table I (A) 8 8 Table 8 8........ Fg.. Currents responses to the dfferent swtchng algorthms ccpl = Cflx = V V V V V V Cflx = V V V V V V The case of nvertng the torque s gven n Fg.. One can see that the nverson of the torque fals wth strateges of

7 Drect Torque Control trategy (DTC) Based on Fuzzy Logc Controller for a Permanent Magnet ynchronous Machne Drve Tables, and. However, wth the strategy of Table, the nverson s done and a good response s obtaned. In the sequel we wll us only Table for the smulatons snce t gves the best compromse between flux and torque. Torque (m) Torque (m) Table Table t (s).... t (s).... Torque (m) t (s).... Table Table Torque (m) t (s).... Fg.. Invertng the torque to the dfferent swtchng algorthms. Fuzzy logc controller From the dscusson n the prevous secton the controller adoptng DTC strategy s a type of hysteress, whch means the control acton wll be the same n the whole error range. To obtan better control effect a fuzzy logc controller has been ntroduced to replace the hysteress controller. The dagram of a drect torque control ncorporated wth a fuzzy logc controller s shown n Fg. 7. Generally speakng, a fuzzy logc controller conssts of three man parts: fuzzfcaton, fuzzy reasonng and defuzzfcaton. We wll dscuss three approaches: the frst approach developed [] was for nducton motors and adopted by us for PMM; the second was developed by []; and the thrd approach s proposed n ths paper.. Frst Approach.. Fuzzy state and control varables The fuzzfcaton s the process of a mappng from measured or estmated nput to the correspondng fuzzy set n the nput unverse of dscourse. In ths system there are three nputs, whch are E (error of stator flux), (error of torque) and θ (stator flux angle) respectvely. They are defned as: E E Te = θ = tg s = T e T ( β e ) s Where and Te are references of stator flux and torque respectvely, s s the magntude of stator flux, whch can be estmated. The fuzzfcaton s performed usng membershp functon wth a sngleton fuzzfer. There are three groups of membershp functon depcted n Fg. 8 correspondng to three nput varables. The unverse of dscourse of fuzzy angle varable s dvded nto fuzzy sets θ to θ. The control varable s the nverter swtchng state (). In a sx step nverter, seven dstnct swtchng states are possble [8]. The swtchng states are crsp thus do not need a fuzzy membershp dstrbuton. (8) V DC Inverter s a b PMM V ab Fuzzy Controller s Torque Torque reference e tator flux and torque estmator Fg. 7. Fuzzy controller for drect torque control of PMM Γ Flux angle Fg. 8. Membershp dstrbuton of fuzzy varables for frst approach.. Fuzzy rules for self control Each control rule can be descrbed usng the state varables E, and θ and the control varable. The rule R can be wrtten as:

A. Tlemcan, O. Bouchhda, K. Benmansour, D. Boudana and M.. Bouchert 7 R : f E E s B and θ s C then s (9) s A, Te Where A, B, C and represent the fuzzy segments. The control rules are formulated usng the vector dagram for drect self control as shown n Fg. 9. By fuzzy reasonng usng Mamdan s mnmum operaton rule as a fuzzy mplcaton functon, the th rule leads to the control decson: ( n) = mn(, ( n)) () ' β Δ Δ Δ Δ Δ Δ β Thus the membershp functon of the output n s pont wse gven by: ( n) = max( ' = ( n)) () I V I ΔI ΔI ΔI ΔI ΔI ΔI nce the output s crsp, the maxmum crteron method s used for defuzzfcaton. By ths method, the value of fuzzy output whch has the maxmum possblty dstrbuton s used as the control output. Fg. 9. Vector dagram used for knowledge base Lookng at the poston of the flux n Fg. 9 states, and wll ncrease the flux whle states, and wll decrease t. mlarly states, and wll ncrease the torque whle states, and wll decrease t. For a large ncrease n flux and a small ncrease n torque, state s selected. For a small ncrease n flux and a large ncrease n torque, state s selected. For a small decrease n flux and a small ncrease n torque, state s selected. For a large decrease n flux and a small decrease n torque, state s selected. For a small decrease n flux and a large decrease n torque, state s selected. For a small ncrease n flux and a large decrease n torque, state s selected. For a small decrease n torque and constant flux, state s selected. Ths selecton changes as the poston of the flux vector changes. The total number of rules s 8 as shown n Table. Each cell n ths dagram shows the best swtchng state for the gven angle. The total number of obtaned rules s nstead of 8 obtaned n [] snce we do not use the null voltage vectors for DTC n the PM motors. The latter s are represented n the tables shown below Tab. 7. Each table gves the best swtch state for a gven flux angle... Fuzzy Interface The nterface method used s basc and smple and s developed from the mnmum operaton rule as a fuzzy mplementaton functon [9]. The membershp functons of A, B, C and are gven by A, B, C and respectvely. The frng strength of th rule can be expressed as: = mn( A ( E), B ( Ete), C ( θ)) (). econd Approach In [] the flux angle has fuzzy subsets whch results n 8 rules n the rule base. Ths s too many to be ncorporated nto the fuzzy logc Toolbox and s dffcult to mplement n practce as well. For the purpose of reducng the total rule numbers the nput to the fuzzy controller n our case only π π covers the partal unverse [, ] not lke that of [,. π ] whch covers the whole unverse of dscourse []. Based on the symmetry of mpressed PMW voltage vectors and flux angle n dq coordnate, we defne a mappng to ' convert the θ n the range of [,. π ] nto a sector wth range π π : of [, ] ' ' π θ + π/ θ = θ Fx [ ] () π/ Where θ s the angle that goes nto the fuzzy logc controller. The operator Fx denotes roundng the varable to the nearest nferor nteger. It should be noted here after the fuzzy reasonng that the result acton should be converted to the correct voltage vector accordng to the real angle of the flux. The control varable obtaned by the fuzzy controller s then transformed to the correct value by takng nto account the number of the stator flux sector []. The Unverse of dscourse for the new fuzzy varable s dvded nto fuzzy sets ( θ, θ, θ ) as shown n Fg.. Usng fuzzy sets for the flux angle, we had an ncomplete table of rules reported n Table.

7 Drect Torque Control trategy (DTC) Based on Fuzzy Logc Controller for a Permanent Magnet ynchronous Machne Drve Table 7. et of fuzzy rules for frst approach E P θ E P θ θ E P θ E P θ E P θ E P θ 7 E P θ8 E P θ 9 E P θ E P θ E P θ E P

A. Tlemcan, O. Bouchhda, K. Benmansour, D. Boudana and M.. Bouchert 7 E E PE ETe E Te E Te Te ETe the correct voltage vector of the nverter confguraton.... Proposed Approach E x θ θ θ θ. θ Fg.. Membershp dstrbuton of fuzzy varables for second approach Table 8. et of fuzzy rules for second approach E P θ E θ E P P θ It s possble to reduce the sze of the precedents rules table by usng the symmetry of rules table gven n the frst approach Table and a heurstc repartton of the state flux angle. We see from Table that we can use only fuzzy sets for the flux angle θ ( θ and θ ). Ths allows elmnatng redundancy exstng n the fuzzy rules. We have also developed an nterestng technque to reduce the number of rules to. The thrd fuzzy controller nput (flux angle) actually cover the unverse [, π ] and not [,. π ] as n the frst approach. Based on the symmetry of the voltage vector and the stator flux angle, we defne the followng transformaton that converts the angle θ from [,. π ] to angle θ n [, π ] : ' θ = rem ( θ ' ) () Where θ s the nput angle of the fuzzy controller. The operator rem used above stands for "reman of dvson". Table 9. et of fuzzy rules for proposed approach E P θ E By usng fuzzy sets for flux angle, we obtan rules gven n Table 7. Fg. represents the dstrbuton of the underlyng fuzzy sets. P θ The fuzzy reasonng used s mandan s method Mamdan [9]. = mn( ' A ( E ( n) = mn(, ( n) = max( = ), ' B ( n)) ( E te ( n)) ), C ( θ)) () E. E PE ETe. E x θ θ θ Te The relaton gvng the number of the sector n whch the stator flux vector les s obtaned as: θ + π/ = Fx(( ) + ) () π/ We add to the fuzzy regulator output () n order to get. θ Fg.. Membershp dstrbuton of fuzzy varables for proposed approach

7 Drect Torque Control trategy (DTC) Based on Fuzzy Logc Controller for a Permanent Magnet ynchronous Machne Drve. mulaton of the ystem To study the performance of the fuzzy logc controller wth the drect torque control strategy, the system smulaton was conducted usng Matlab and a fuzzy logc toolbox. The parameters of the motor are gven n Table. Table. Parameters of the used motor ombre of pole pars P Armature resstance R.7 Ω Magnet flux lnkage Φ f.8 Wb daxs Inductance L d 8.7 mh qaxs Inductance L q.8 mh Phase voltage V V Phase current I 8. A Base speed Ω rpm a faster ncrease n torque. Fg. shows the response of the system for a step change n torque from m to m keepng the flux command constant. The response of the fuzzy controller s faster than the conventonal controller. The steady state torque and flux vector n Fg. and Fg. shows nearly a crcular path ndcatng a good flux regulaton. Torque (m)... Fuzzy DTC Conventonal DTC. Fuzzy DTC Conventonal DTC Torque (m)..........7.8.9. Fg.. Torque response of fuzzy controller and conventonal DTC durng startup Flux (Wb).8.7..... Fuzzy DTC Conventonal DTC....7.8.9...... Fg.. Torque response of fuzzy controller and conventonal DTC for step change n command torque Torque (m) Torque (m) Torque (m) Fuzzy DTC wth rules........ Fuzzy DTC wth rules........ Fuzzy DTC wth rules.......... Fg.. Torque response of fuzzy controller for three approaches Torque (m) Flux (Wb)...........7.8.9. Fg.. tator flux response of fuzzy controller and conventonal DTC durng startup I (A)..... (Wb)..... Fg. and shows the torque and the stator flux responses of the system durng startup for the conventonal DTC and the fuzzy controller. The response of the fuzzy controller s faster than the conventonal DTC. In the fuzzy controller the ntal stator flux error s very large. Thus the controller chooses the states gvng a hgher ncrease n the flux. The change n torque durng ths tme s small. Once the flux error becomes small, the controller chooses the states gvng.... peed (Rad/s) 8...... β (Wb).... (Wb) Fg.. Responses of the PMM wth the proposed approach

A. Tlemcan, O. Bouchhda, K. Benmansour, D. Boudana and M.. Bouchert 7. Fuzzy Resstance Estmator In drect torque control schemes, estmaton of stator flux s based upon the knowledge of stator resstance. Ths s especally true at low speeds where the resstve drop (I s R s ) s the major porton of the measured termnal voltage. The stator resstance error would cause mproper flux estmaton makng the controller perform poorly. The magntude of the stator current vector can be used to correct the stator resstance used by the controller durng any change n stator resstance of the machne. The magntude of the stator current vector n drect selfcontrol s a functon of torque and flux. It s not affected by any change n the nput DC voltage or a change n load. Also, the model used n the drect selfcontroller s ndependent of all machne parameters other than stator resstance. Change of any parameter other than stator resstance does not change the magntude of the stator current vector. For any change n the current vector, durng a change n the nput voltage or the motor parameters other than stator resstance, the controller chooses the swtchng states so that the stator current changes back to ts orgnal value to have constant flux and torque []. Durng a change n stator resstance the actual and the estmated stator flux are dfferent. Therefore, the swtchng states selected by the controller for constant flux and torque do not change the current to ts constant value. Thus, for a constant value of torque and stator flux, any change n the magntude of the stator current vector s due to the change n stator resstance. Wth knowledge of the magntude of current vector, for the gven values of stator flux and torque, a fuzzy resstance estmator can be developed for the correcton of changes n stator resstance. The fuzzy resstance estmator suggested s shown n Fg. 7. The estmator requres the magntude of the stator current vector to obtan the change n stator resstance. Ths magntude s obtaned by measurng the stator currents and calculatng the current vector. Ths s fltered and sent to the fuzzy resstance estmator. To estmate the error n stator resstance, the stator current vector error and the change n the current vector error are employed. The current vector error and the change n current vector error are defned as: e( k) = I ( k) I ( k) (7) Δe( k) = e( k) e( k ) Where I s (k) s the current vector correspondng to the flux and torque commands and I s (k) s the measured stator current vector gven by: ( k ) = + β I s (8) The unverse of dscourse of the two fuzzy nput varables and the output varable, whch s the change n stator resstance, ΔR s are dvded nto fve fuzzy sets each as shown n Fg. 9. The fuzzy rule appled can be wrtten as: R : f e s A and Δe s B then ΔR s C (9) The error n the stator current vector for a lnear change n stator resstance s shown n Fg. 9., shows the relaton between the error n the stator current vector and the error n stator resstance. Usng ths response we can formulate fuzzy Fg. 7. Fuzzy DTC Controller wth fuzzy resstance estmator tator Current Is 8 7. 7.. 8 Fg. 8. Error n stator current for lnear change n stator resstance e.... ΔR (a) V dc s T e Δ e Inverter Fuzzy DTC R s (k) ( k ) R s ΔR s..... (c) Current vector flter.... (b) Fg. 9. Membershp dstrbuton of fuzzy nput and output varables a b PMM Fuzzy resstance Estma

7 Drect Torque Control trategy (DTC) Based on Fuzzy Logc Controller for a Permanent Magnet ynchronous Machne Drve Table. Fuzzy rules for fuzzy resstance estmator e / Δe Torque wthout resstance estmator Torque wth resstance estmator Fg.. Torque response wth and wthout fuzzy resstance estmator rules to change the stator resstance used by the controller. There are rules as shown n Table. Mamdan s mnmum operaton rule s used as the nterface method and, fnally, the value of resstance error can be obtaned by the center of gravty method used for defuzzfcaton. The value of stator resstance used by the controller s then gven by: R s ( k) Rs ( k ) + ΔRs = (). mulaton Results The stator resstance varaton was smulated as well. The speed of the PMM s set at rad/s and torque reference. m. The stator resstance used by the controller follows very closely the actual stator resstance of the motor, and the smulaton results are shown n Fg.. Fg. shows the fltered electrc torque wth and wthout the fuzzy resstance estmator. There s very small error n actual electrc torque of the machne durng a change n resstance usng the fuzzy resstance estmator. Fg.. Fuzzy resstance estmator. Concluson A fuzzy logc controller usng the DTC strategy for PMM has been descrbed n ths paper. To make the fuzzy reasonng fast and the smulaton avalable wth the fuzzy logc toolbox, the number of rules was greatly reduced n terms of the flux angle mappng approach. The change n the steady state value of stator current for a constant torque and flux reference s used to change the value of stator resstance used by the controller to match the machne resstance. The smulaton results show the effectveness of the new control strateges. References [] L. Tang, L. hong and F. Rahman, Modellng and Expermental Approach of a ovel Drect Torque Control cheme for Interor Permanent Magnet ynchronous Machne Drve, n Proceedngs of IEEE IECO 8 th Annual Conference, pp., 8 ov.. [] I. Takahash and T. oguch, A ew QuckResponse and HghEffcency Control trategy of an Inducton Motor, IEEE Trans. Industral Applcaton, vol.ia, no., pp.887, ept\ October 98. [] L. hong and M. F. Rahman, Analyss of Drect Torque Control n Permanent Magnet ynchronous Motor Drves, IEEE Trans. Power Electroncs, vol., no., pp.8, May 997. [] M. F. Rahman and L. hong, A Drect Torque Controller for Permanent Magnet ynchronous Motor Drves, IEEE Trans. Energy Converson, vol., no., pp.7, ep. 999. [] M. F. Rahman and L. hong, A Drect TorqueControlled Interor Permanent Magnet ynchronous Motor Drve Incorporatng Feld Weakenng, IEEE Trans. Industral Applcaton, vol., no., pp., ov.\ Dec. 998. [] M. R. olghadr, Contrôle Drect du Couple des Actonneurs ynchrones: Phd Thess, IP Grenoble, France 997. [7] Y. La and J. Chen, A ew Approach to Drect Torque

A. Tlemcan, O. Bouchhda, K. Benmansour, D. Boudana and M.. Bouchert 77 Control of Inducton Motor Drves for Constant Inverter wtchng Frequency and Torque Rpple Reducton, IEEE Trans. Energy Converson, vol., no., pp. 7, ep.. [8]. A. Mr and D.. nger, Fuzzy Implementaton of Drect elf Control for Inducton Machnes, IEEE Trans. Industral Applcaton, vol., no., pp.797, May\Jun. 99. [9] K. Benmansour, H. Rezne and M.. Bouchert, ouvelle approche de la commande floue base sur DTC de la machne synchrone a amant permanent, CIFA, Tunse, July. [] J. Lu, P. Wu and H. Xpng, Applcaton of Fuzzy Control n Drect Torque Control of Permanent Magnet ynchronous Motor, Proceedng of th world congress on ntellgent Control and automaton, Hangzhou, Chna, June. [] M. Fu and L. Xu, A ensorless Drect Torque Control Technque for Permanent Magnet ynchronous motors, n Proceedngs of IEEE Power Electroncs n Transportaton, pp.7, Oct. 998. [] M. F. Rahman and L. hong, An Investgaton of Drect and Indrect Torque Controllers for PM ynchronous Motor Drves, n Proceedngs of IEEE PED 97 Conference, ngapore, pp. 9, 9 May 997. [] D. Casade, G. Grand and G. erra, Effects of Flux and Torque Hysteress Band Ampltude n Drect Torque Control of Inducton Machnes, n Proceedngs of IEEE IECO 9 th Internatonal Conference, pp.99, 9 ep. 99. [] G. Buja, D. Casade and G. erra, Drect tator Flux and Torque Control of Inducton Motor: Theoretcal Analyss and Expermental Results, n Proceedngs of IEEE Internatonal Conference, pp.tt, 998. [] D. O. eacsu, Comparatve Analyss of TorqueControlled IM Drves wth Applcatons n Electrc and Hybrd Vehcles, IEEE Trans. Power Electroncs, vol., no., pp.7, March. []. A. Mr and D.. nger, Fuzzy Controller for Inverter Fed Inducton Machnes, IEEE Trans. Industral Applcaton, vol., no., pp.788, Jan.\Fab. 99. [7] B. K. Bose, L. Fellow, Quas fuzzy Estmaton of tator Resstance of Inducton Motor, IEEE Trans. Power Electroncs, vol., no., pp.8, May 998. [8] H. Rezne and A. Derbane, Implémentaton du Contrôle Drect du Couple de la Machne ynchrone à Amants Permanents par la Logque Floue, Internatonal Conference CGE, Algers EMP, Algera,. [9] T. oguch, K. Yamada,. Konodo and I. Takahash, Intal Rotor Poston Estmaton Method ensorless PM ynchronous Motor wth no enstvty to Armature Resstance, IEEE Trans. Industral Applcaton, vol., no., pp.8, Fab. 998. []. Mr, E. Malk, D.. nger, PI and Fuzzy Estmaton for Tunng the tator Resstance n Drect Torque Control of Inducton Machnes, IEEE Trans. Power Electroncs, vol., no., pp.7987, March 998. [] Y. Xa, W. Oghanna, Fuzzy Drect Torque Control of Inducton Motor wth tator Flux Estmaton Compensaton, n Proceedngs of IEEE IECO 97 rd Internatonal Conference, pp., 9 ov. 997. Abdelhalm Tlemcan He receved hs engneerng degree and M.c. n power electroncs from the atonal Polytechnc chool of Algers (EP), Algera, n 997 and 999, respectvely. He receved hs Ph.D. degree n electrcal engneerng from EP n 7. nce he has held teachng and research postons n the Department of Electrcal Engneerng, UYFM, where he s currently Assocate Professor. He s member of Process Control Laboratory. Hs research nterests are n electrcal drves, power electroncs, robust and nonlnear control and fuzzy systems. Ouahd Bouchhda He receved hs Ingéneur d Etat degree (equv. Bc.+one year) n Electrotechncs and Magster degree (equv. MPhl) n electrcal engneerng from the Ecole atonale Polytechnque, Algers, Algera, n 99 and 998 respectvely. He receved hs Ph.D. degree n electrcal engneerng from EP n 8. nce 999 he has held teachng and research postons n the Department of Electrcal Engneerng, UYFM, where he s currently Assstant Professor. Hs current research nterests are ntegrated actuators, machne speed sensors and drves. Khelfa Benmansour He receved hs Engneer degree n Electrotechncs, and Magster degree n electrcal engneerng, from the Ecole atonale Polytechnque, (EP, EMP) Algers, Algera, n 997, 999 respectvely. He receved hs Ph.D. degree n electrcal engneerng from EP n. He s a member of the EC research group, EEA, Hs current research nterests are ntegrated actuators, machne speed sensors, drves, multcells nverter and hybrd system.

78 Drect Torque Control trategy (DTC) Based on Fuzzy Logc Controller for a Permanent Magnet ynchronous Machne Drve Djamel Boudana He receved hs Engneer degree n Electrotechncs, and Magster degree n electrcal engneerng, from UTHB Algers, Algera, n 99 and 999 respectvely. nce he has held teachng and research postons n the Department of Electrcal Engneerng, UYFM, where he s currently Assstant Professor. He s a member of Process Control Laboratory. Hs research nterests are n electrcal drves. Mohamed eghr Bouchert He receved hs Engneer degree n Electrotechncs, the Magster degree and the Doctorat d Etat (Ph.D. degree) n electrcal engneerng, from the atonal Polytechnc chool, Algers, Algera, n 98, 988 and 99 respectvely. Upon graduaton, he joned the Electrcal Engneerng Department of atonal Polytechnc chool. He s a Professor, a member of Process Control Laboratory and hs research nterests are n the area of electrcal drves and process control.