Direct Torque Control of 5-Phase 10/8 Switched Reluctance Motors

Transcription

1 Dwnladed fm ijeee.iust.ac.i at 18:19 IRST n Fiday Septembe 8th 18 Diect Tque Cntl f -Phase 1/8 Switched Reluctance Mts M. R. Feyzi* and Y. Ebahimi* Abstact: A switched Reluctance mt (SRM) has seveal desiable featues, including simple cnstuctin, high eliability and lw cst. Hweve, it suffes fm lage tque ipple, highly nn-unifm tque utput and magnetizatin chaacteistics and lage nise. Seveal studies have succeeded in tque ipple eductin f SRM using Diect Tque Cntl (DTC) technique. DTC methd has many advantages ve cnventinal vltage cntl and cuent chpping mde cntl such as simple algithm, less tque ipple and instantaneus espnse t the tque cmmand. In this pape, DTC methd is ppsed f a -phase 1/8 SRM. The pefmance f the mt is demnstated thugh the cmpute simulatin in Mtalab/Simulink. Then, the btained esults ae veified by cmpaisn with the cespnding esults f a 3-phase / mt pefmance. Keywds: Diect Tque Cntl, Electical Dives, Switched Reluctance Mt, Tque Ripple. 1 Intductin 1 A switched Reluctance mt (SRM) has numeus advantages ve the types f AC machines due t its simple and slid cnstuctin. The t has a simple laminated stuctue with neithe pemanent magnets n t windings, and tates by using the eluctance tque pduced fm magnetic saliency between stat ples and t ples. Thus, SRM can peate at high speed and is suitable f applicatins in hightempeatue and hazadus envinments. In additin, SRM has simila enugh high efficiency as cmpaed with pemanent magnet mts because it als nt need secnday windings. SRM is nw accepted f sme applicatins. Hweve, SRM has been limited t be used because it pduces lage tque ipples and lage nise due t nn-unifm tque utput chaacteistics and dubly salient stuctue. Additinally, the highly nnlinea magnetic chaacteistics f the mt make the cntl f the mt inticate. This is futhe cmplicated by the inteactin due t mutual cupling f mt phases and paametes vaiatin f the inductance chaacteistics [1], []. T vecme these pblems vaius studies have Ianian Junal f Electical & Electnic Engineeing, 9. Pape fist eceived 11 Ma. 9 and in evised fm 1 Ap. 9. * The Auths ae with the Depatment f Electical and Cmpute Engineeing, Tabiz Univesity, Tabiz, Ian. feyzi@tabizu.ac.i and ye@yah.cm been pefmed. The pevius wks have fallen in t tw main gups: thse which used the linea mdel f mt withut taking int accunt the satuatin [3-] and thse which used the nnlinea mdel which takes int accunt the mt satuatin [7-9]. Tayl [3] used an adaptive feedback lineaising cntlle f the SRM cnsideing a linea magnetic cicuit. Nagel et al. ppsed an analytical slutin in de t pduce a vltage pfile that pvides a smth mt tque []; they assumed a linea tque chaacteistic f the mt. In thei wks, Matsui and Ma [], [] expessed the inductance f the mt as a simple sinusidal functin vaying with psitin. Highly simplified mdels f a mt with the highly nnlinea tque and magnetizatin chaacteistics cause inaccuacy in mst pactical dives in the efeences abve. Ilic'-Spng et al. [7] ppsed a feedback lineaising cntl methd cmpensating the magnetic nnlineaities f the mt. This methd needs exact knwledge f the mt paametes, s it is difficult t be implemented as a pactical dive. In de t btain a smth tque [8], [9] geneated such a cuent pfile that enables the tque shaing between tw phases. Hweve, it equies a cmplex cuent wavefm that impses a time cnsuming cmputatin making the cntl system t cmplicated f eal-time implementatin. In geneal, mst implicit studies utilize the vltage Ianian Junal f Electical & Electnic Engineeing, Vl., N. 3, Sep. 9

2 Dwnladed fm ijeee.iust.ac.i at 18:19 IRST n Fiday Septembe 8th 18 cuent cmmand pfile in de t tque, speed psitin cntl tque ipple eductin. Sme studies have succeeded in tque ipple eductin f SR mts using DTC methd [1]. This methd used the cncept f sht flux patten that links tw sepaate ples f the stat. This needed a new type f winding cnfiguatin that is a dminant disadvantage, because changing f the mt winding cnfiguatin is bth expensive and incnvenient. An excellent study f DTC methd applied t 3phase / SRM with clsest cncept t the cnventinal DTC f ac machines was fulfilled in [11]. Auths intduced cmpaable they with cnventinal DTC f ac machines by using mt flux and tque defining equatins that will be mentined summaily in the fllwing sectins. In this methd n winding cnfiguatin changing is equied, thus the scheme can be cnveniently implemented n any nmal type f SRM dive. Since tque ipple minimizatin is ne f the main bjectives f DTC methd, it seems that applying this methd t a SRM with me ple numbes can intensify the tque ipple eductin. Mts with a lw phase numbe have sme disadvantages that ntably incease tque ipple [1]. On the the hand, ple numbe incement impses sme disadvantages n the the pefmance citeia that shuld be nticed. If in tw SRM with diffeent ple numbes, the in t ai ati and excitatin ampee-tun assumed t be cnstant, in de t achieve high inductance and flux density, the mt with the fewe ple numbe is pefeable. In pesent study, DTC methd is applied t a phase 1/8 SRM, whee a significant mdificatin shuld be exeted n mentined methd in [11]. This ccus due t discepancy f ples and phases numbe f tw mts. Main Cncepts f DTC Methd in -Phase SRM The pape ppsed in [11] is a cmpehensive efeence t peceive DTC scheme in 3-phase / SRM. Detailed illustatins have been ppsed abut the electmagnetic tque extactin by using the enegy cncept instead f c-enegy, the stat flux calculatin, the vltage space vects definitin and thei elatin with mt tque and flux cntl. The pwe cnvete cnfiguatins, its peatin in diffeent states f the switching elements and the vltage space vects fmatin then have been pesented f 3-phase / SRM. In the pesent pape mentined cncepts ae expanded f a -phase 1/8 SRM summaily..1 Flux Equatin and Stat Flux Vect It is essential t study the machine defining equatins in de t extacting f DTC methd. The stat flux linkage vect can be expessed as t ϕ s = (v s R is ) + ϕ s (1) S whee ϕ s = stat flux vect cmpnent, v s = stat vltage vect cmpnent, is = stat cuent vect cmpnent, R s = stat esistance and ϕ s = initial value f the stat flux vect. Except at the lw vltage levels, the vltage dp thugh the stat esistance is dispensable, s fm Eq. (1): dϕ s vs dt () If the time inteval is small enugh, then () can be witten as Δϕ s = v s Δt (3) This shws that, in de t cntl f the vaiatin f the stat flux, the vltage space vects can be utilized. The applied vltage vect pduces a stat flux vaiatin which is in the same diectin as the vltage vect. Magnitude f the vaiatin is pptinal t the vltage vect magnitude and Δt. As a esult, ne f the tw basic pinciples f DTC in SRM is that "The stat flux linkage vect f the mt is kept at cnstant amplitude by using Eq. (3)". Selectin f the stat flux ptimal level f vaius speeds f the mt has been pesented in [13]. In the SRM the vltages ae highly nn-sinusidal, s the individual flux linkage f each phase shuld be fistly fund by using Eq. (1). The magnitude f phase flux linkage is vaiable with time, but its diectin is alng the elated phase stat ple axis. Thus thee ae five statinay pulsating phase flux vects in -phase 1/8 SRM. T deive the unique stat flux vect, the phases flux vects ae tansfmed nt a statinay thgnal tw axis α β efeence fame as shwn in Fig. 1. It is suppsed that the phase a axis and α axis ae in the same diectin, s ϕ α = ϕ1 + ϕ cs 7 - ϕ 3 cs 3 - ϕ cs 3 + ϕ cs 7 ϕ β = ϕ sin 7 + ϕ 3 sin 3 ϕ sin 3 ϕ sin 7 Fig. 1. Tansfmatin f phases fluxes n tw axis thgnal statinay efeence fame Ianian Junal f Electical & Electnic Engineeing, Vl., N. 3, Sep. 9 ()

3 The magnitude ϕ s and angle δ f btained flux vect ae Dwnladed fm ijeee.iust.ac.i at 18:19 IRST n Fiday Septembe 8th 18 ϕ s = ϕ α + ϕβ, δ = actan( ϕβ ) ϕα (). Mt Tque Equatin Extactin f mt utput tque equatin has been illustated in [11] that has defined the mt utput tque as a functin f system enegy instead f cenegy as T =i ϕ(θ,i) w f θ θ () The SRM is usually peated at heavy magnetic satuatin in de t achieve a lage ati f tque t mass. It was shwn in [1] that cntibutin f the secnd tem in Eq. () is dispensable due t satuatin, s ϕ(θ,i) T i θ (7) On the the hand elatin f the stat cuent and flux in the s (Laplace) dmain can be deived as i= e dϕ ω dθ sl (8) whee ω = dθ dt and l = ϕ i. It can be seen that the stat cuent has a fist de delay elative t ϕ θ, thus it can be suppsed that the stat cuent is nealy cnstant duing ϕ θ vaiatins. This means that the mt tque cntl can be based nly n ϕ θ vaiatin. Cnsequently the secnd basic pinciple f DTC in SRM is that "The mt tque is cntlled by psitive and negative vaiatin f ϕ θ in the wds, by acceleating and deceleating f the stat flux vect". The phases f the SRM ae exited independently, thus ttal tque f mt is the sum f the five phases tques. As a esult the individual tque f each phase Tj (t,i j, θ j ) shuld fistly be btained by using lk-up tables. Afte extacting each phase tque, ttal tque f the mt is expessed as n Tm = Ti i =1 (9) whee n is the numbe f phases..3 Pwe Cnvete Cnfiguatin The cicuit mst cmmnly used f switched eluctance dives is the asymmetic half bidge cicuit Fig.. With this cnfiguatin thee is a sepaate half bidge f each phase, s the vltages and cuents supplied t each phase ae cmpletely independent f all the phases. It is necessay t cntl f cuent in ne phase and fce demagnetizing t sme the phases f the mt at the same time. This is essential f eductin f the tque ipple. Phase cuent in asymmetical half bidge cnvete is cntlled by selecting fm thee pssible states: i) Bth switches in a phase leg ae n, and phase is enegized fm pwe supply (magnetizing stage). ii) Bth switches in a phase leg ae ff. Phase cuent cmmutates t the dides and decays apidly (demagnetizing stage). iii) Only ne f the switches is ff. The vltage acss winding is nea ze and phase cuent decays slwly (fee wheeling). Phase vltage state S j can be defined as 1 S j = -1 bth switches in a phase leg ae n bth switches in a phase leg ae ff ne switch is n and anthe is ff. (1) S accding t Fig. when phase vltage state is 1, 1 the psitive vltage f dc link, a ze vltage the negative vltage f dc link is applied t phase winding espectively. It shuld be nticed that thee ae legs in the pwe cnvete f 1/8 SRM.. Vltage Space Vects When the psitive vltage f invete dc link is applied t the phase winding, a vltage space vect can be defined in the elated phase ple axis diectin (e.g. vect Phase 1(+) in Fig. 3). By applying negative vltage same vect is definable but in the evese diectin (e.g. vect Phase 1(-)). Nw with ppe aangement f the phases vltage states, the vltage space vects v i (i = 1,,...,1) suitable f mt tque and flux cntl can be deived as shwn in Fig. 3. As seen, nly 1 vects ae selected fm 3 pssible vects. Each vect lies in the cente f decuple sects with π/1 adians width. Anthe vect v is definable when a ze vltage is applied t all five phases, in the wds; v is achieved when each leg f the pwe cnvete is in the ze vltage state. This vect is utilized when it is nt equied t apply simultaneus changes in the tque and the flux.. Switching Table As mentined abve, basic pinciples f DTC methd in SRM ae: 1) The stat flux linkage vect f the mt is kept at cnstant amplitude by using Eq. (3). ) The mt tque is cntlled by psitive and negative vaiatin f ϕ θ in the wds, by acceleating and deceleating f the stat flux vect. The stat flux and the mt ttal tque levels ae cntlled within tw sepaate hysteesis bands, s when the instantaneus tque and flux css the elated band limits, they need t incease decease in de t Feyzi & Ebahimi: Diect Tque Cntl f -phase 1/8 Switched Reluctance Mts 7

4 Dwnladed fm ijeee.iust.ac.i at 18:19 IRST n Fiday Septembe 8th 18 emain inside the bands. T emve these equiements, the vltage space vects and tw mentined basic pinciples f DTC methd in SRM ae utilized. Table 1 shws the switching table and equied vltage space vect selectin in each situatin, whee T = Requied vaiatin in tque, ϕ = Requied vaiatin in flux, N = Stat flux sect, NL = Negative Lage, NS = Negative Small, ZE = Ze, PS = Psitive Small and PL = Psitive Lage. As an example when T = NL and ϕˆ = NS, it means that mt tque needs t lage eductin and stat flux needs t small eductin, s vect v N will be able t espnd t the system equiement. v is a vect that has n influence n the stat flux, and it causes the mt tque t educe vey gently. The vects in ciclets ae nt cmpletely able t cmply with the simultaneus equests f tque and flux, but they ae the best available vects. As an example f N=1, T = NS and ϕˆ = NL vect v 8 can nt satisfy the system equiements that ae small eductin in tque and lage eductin in flux. Mt tque ipple minimizatin is ne f the main aims f DTC methd in SRM, s espnding t tque equests by selecting f the suitable vltage space vect is pi t thes. Namely a vltage space vect shuld be selected that causes t small eductin (NS) in mt tque. Available vects ae v 8, v 9, v1, but nly v 8 can educe (N) the flux, and v 9, v1 cause t flux incement (P) that is against the system equest. As a esult, espnding t the tque equest is pi t the flux equest but the singe f the flux vaiatin (N P) shuld be cnsideed. Table 1. Switching table Fig. 3. Vltage space vects f -phase 1/8 SRM 3 The Phases Tanspsitin Phenmenn The t instantaneus psitin calculatin f each phase θ j ( j = a, b, c, d, e) and cnvesin it t the t nmalized psitin θ nm _ j suitable t be applied t the tque and flux lk-up tables is nt a new tpic, but in de t illustate the phases tanspsitin phenmenn in a -phase 1/8 SRM it is necessay t discuss abut it. The t nmalized psitin f each phase θ nm _ j is always a numbe inside the ange f θ nm _ j π N whee, N is the t ples numbe. Thus the nnlinea electmagnetic tque chaacteistic Tj (t,i j, θ j ) can be used easily. T btain the phase instantaneus tque, sepaate lk-up tables shuld be utilized f each phase, s it is needed thee simila lk-up table f / mt and five simila nes f 1/8 mt. The ze pint f the t psitin encde can be defined as the t ze axis. Assume that the t psitin is equal t ze when the t ze axis and the phase a axis ae in the same diectin. Nw the t psitin with espect t the phases can be btained by using Fig., whee 1 k = 3 Fig.. Thee pssible states in a phase leg f SRM asymmetic pwe cnvete 8 (11) f phase f phase f phase f phase f phase a b c d e (1) Fig.. Extacting f t psitin Ianian Junal f Electical & Electnic Engineeing, Vl., N. 3, Sep. 9

5 Dwnladed fm ijeee.iust.ac.i at 18:19 IRST n Fiday Septembe 8th 18 The t psitins ae shwn in Fig. f all phases. These ae nt adequate t apply t the lk-up tables, and have t be efmed ppely. Duing t tatin within ples eplacement with each the (e.g. up t π/n), the psitive tque is pduced duing fist half ( up t π/n), and the negative tque is pduced duing secnd half (π/n up t π/n). Theefe the t cicumfeence can be divided t 1 sepaate sectins as shwn in Fig. whee symbls + and - efe t psitive and negative tque geneatin espectively while the t ze axis passes thugh the elative sectin. Thus the t psitin axis θ f the -phase SRM utput tque chaacteistic is scaled within ze and 3 8* =., whee 8 is the t ples numbe. With desciptin abve, while the t ze axis lies in the dd numbeed sectins f Fig. -(a), the t nmalized psitin is: θ nm _ j = θ j (M j 1)*. θ nm _ c is applied t lk-up table f phase b, θ nm _ d is applied t lk-up table f phase e and θ nm _ e is applied t lk-up table f phase c. θ (deg) θa θb θc θd θe θ (deg) Fig.. Rt psitin θ j f all five phases (13) As an example, f phase a equivalent angle f θ a = 11 psitined in sect M a = is, s angle θ a = 11 is eplaced with angle θ a =. When the t ze axis lies within the even numbeed sectins f Fig. -(a), the t nmalized psitin is: θ nm _ j =. [θ j (M j 1)*. ] (1) As an example, equivalent angle f θ a = 1 psitined in sect M a = is 7., s angle θ a = 1 is eplaced with angle θ a = 7. (Fig. -(a)). Examples abve ae f phase a. Fig. -(a) changes t Fig. -(b) f phase b, s angle θ a = 11 in the abve example is equal t θ b = 38 psitined in sect Cnsequently accding t Eq. (1), Mb =. (a) phase a θ nm _ b = 7. Similaly, t nmalized angles can be btained f the phases. Appling Eqs. (13) and (1) t Fig. esults Fig. 7 which shws the elatin f the t psitin and the t nmalized psitin f ne phase. If Fig. 7 is pltted f all five phases, the t nmalized psitin f all phases will be deived as shwn in Fig. 8. As shwn in Fig. each phase gaph fllws its pevius phase gaph. Namely phase b cmes afte a, c afte b, d afte c, e afte d and a afte e, but in Fig. 8 phases sequence is diffeent in cmpaisn with Fig.. It means that the cntlle senses phase c instead f b, e instead f c, b instead f d and d instead f e. As a esult, while applying θ nm _ j and i j t the b b b lk-up table in de t btain each phase instantaneus tque, phases de shuld be cnsideed as fllwing: θ nm _ a is applied t lk-up table f phase a, θ nm _ b is applied t lk-up table f phase d, (b) phase b Fig.. Rt psitin sects Feyzi & Ebahimi: Diect Tque Cntl f -phase 1/8 Switched Reluctance Mts 9

6 θ (deg) θj θj θ (deg) θ nm _ d θ nm _ b θ nm _ e θ (deg ) θ nm _ c Fig. 7. Rt psitin θ j and t nmalized psitin θ nm _ j (Numbes ae f phase a) θ nm _ a θ (deg ) the lk-up table f phase d des nt mean that tw diffeent phases paametes ae used t deive Tj (t,i j, θ j ). In fact this appach is cntinuatin f deiving θ nm _ j fm the encde utput t psitin θ by using Fig. and Eqs. (13) and (1). Time(Sec) Fig. 9. Mt tque unde steady state cnditins Tque (Nm) Simulatin Results T cnfim the validity f the ppsed methd, a mdel f the system was cnstucted in Matlab/ Simulink. Obtained esults wee cmpaed with the esults f DTC methd in the 3-phase / SRM. In bth mts, bth static tque T(t,i, θ) and flux ϕ ( t, i, θ) chaacteistics ae suppsed t be same. In all belw figues uppe nes ae f the -phase mt. Fig. 9 shws the mts ttal tque unde steady state cnditin. Mt tque and stat flux efeence levels ae adjusted t Nm and.3 Wb espectively. As seen, in bth cases the mt instantaneus tque fllws the efeence value within the cetain band limits. Tque ipple in the -phase mt is abut % f the ne in the 3-phase mt that is the mst nticeable advantage f the -phase mt. Tque(Nm) These changes ae nt equied f 3-phase / SRM, because phase tanspsitin is nt ccued in the / SRM. Phase tanspsitin phenmenn has such a cnsideable significance that it is nt pssible t apply DTC t the 1/8 SRM withut taking it int accunt. It shuld be nticed applying θ nm _ b and i d t Tque (Nm) Fig. 8. Rt nmalized psitin θ nm _ j f all five phases Tque (Nm) Dwnladed fm ijeee.iust.ac.i at 18:19 IRST n Fiday Septembe 8th 18 θ nm _ j Fig. 1. Mt tque espnse t step change f tque cmmand (stat flux level is cnstant) Ianian Junal f Electical & Electnic Engineeing, Vl., N. 3, Sep. 9

7 Cnclusin In this pape the main cncepts f DTC methd in -phase 1/8 SRM wee ppsed then the phase tanspsitin phenmenn that ccus as a pblem in 1/8 SRM and its slutin wee intduced. Cmpaable simulatin esults between tw 3-phase and -phase mts wee pesented. Fm these esults, it can be seen that cmpaed with 3-phase mt, the phase ne has the advantages such as less tque ipple, faste flux tansient espnse, less phase tque peak value, cnsequently less phase cuent peak value. In the fllwing study DTC methd by using fuzzy lgic cntlle will be applied t the -phase 1/8 SRM, and its pefmance will be cmpaed with the -phase mt pefmance studied in pesent pape. Tque (Nm) Tque (Nm) Fig. 11. Mt tque espnse t step change f tque cmmand (clsed view f Fig. 1) Tque (Nm) Fig. 1. Stat flux espnse t step change f flux cmmand (tque level is cnstant) Tque (Nm) Dwnladed fm ijeee.iust.ac.i at 18:19 IRST n Fiday Septembe 8th 18 Mt tque espnse t the step change f the tque cmmand with a cnstant stat flux level is shwn in Figs. 1 and 11. The -phase mt tque is able t fllw the cmmand value as fast as the 3phase ne. Simila test is dne t check the stat flux step espnse with a cnstant level f the mt tque cmmand. Fig. 1 shws that in bth cases, stat flux fllws the cmmand value pecisely, but the -phase mt espnse is faste than the 3-phase ne. Statup test esults ae shwn in Figs. 13, 1 and 1. This test is dne in de t examine the lw speed pefmance f the cntl system. In bth mts cmmand tque and flux ae set n Nm and. Wb espectively. As shwn in Fig. 13, in the utput tque a lage unwanted disttin ccus in tansient peid f t = up t 3 ms that is smalle in -phase mt. Stat flux and its tajecty in statup peid ae shwn in Figs. 1 and 1 espectively. Afte a sht tansient peid, cmmand fluxes ae fllwed pecisely in bth cases but thee is me linea incement in the -phase case. Me ple numbes in the -phase mt causes me flux tajecty tatin in tansient peid, because the electical cycle is shte in the -phase mt. In anthe test, simultaneus lage changes ae applied t the tque and flux cmmands at lw speed in de t examine the system pefmance unde difficult cnditin. The mt tque and flux cmmands expeience a % and 1% change espectively at t =.3 sec when the mt speed is nly ad/sec in 3-phase mt and 1 ad/sec in phase mt. As seen in Figs. 1, 17 and 18 the phase mt is able t fllw the tque and flux cmmands as well as the 3-phase ne. Anthe pint t ntice is that the stat flux level in the -phase mt is highe than the ne in the 3-phase mt. In de t have an equal satuatin level in tw mts, the phase flux magnitude shuld be equal in bth cases. This causes highe stat flux level in -phase mt, s selecting the highe stat flux level in -phase mt helps t have an equal satuatin level. It shuld be nticed that the highe stat flux level impses me tque ipple while the lwe level educes the ttal tque density. T cnfim the validity f this test in all levels f the tque and flux, linea changes in tque and flux cmmands ae applied. Figs. 19 and shw that the -phase mt instantaneus tque and flux can tace the elative cmmands like 3-phase ne successfully x 1 Fig. 13. Mt tque at statup Feyzi & Ebahimi: Diect Tque Cntl f -phase 1/8 Switched Reluctance Mts 11

8 Fig. 17. Flux espnse t simultaneus step change f tque and flux cmmand at lw speed cnditin Fig. 1. Stat flux at statup.3.. Flux Vect Tajecty (Wb) Flux Vect Tajecty (WB) Tque (Nm) Fig. 1. Stat flux tajecty at statup Tque (Nm) Dwnladed fm ijeee.iust.ac.i at 18:19 IRST n Fiday Septembe 8th Fig. 18. Stat flux tajecty at simultaneus step change f tque and flux cmmand unde lw speed cnditin Fig. 1. Tque espnse t simultaneus step change f tque and flux cmmand at lw speed cnditin 1 Ianian Junal f Electical & Electnic Engineeing, Vl., N. 3, Sep. 9

9 [] 7 Tque (Nm) [3] 3 [] Tque (Nm) [] 3 [] [7] Fig. 19. Linea change in tque cmmand [8]... [9] [1] Dwnladed fm ijeee.iust.ac.i at 18:19 IRST n Fiday Septembe 8th 18 [11].3.3 [1] [13] Fig.. Linea change in flux cmmand Refeences [1] Xu L. and Ruckstadte E., "Diect mdeling f switched eluctance machine by cupled fieldcicuit methd", IEEE Tans. Enegy Cnv., Vl. 1, pp. -, Sep [1] Nagel N. J. and Lenz R. D., "Mdeling f a satuated switched eluctance mt using an peating pint analysis and the unsatuated equatin", IEEE Tans. Ind. Applicat., Vl. 3, pp. 71-7, May/June. Tayl D. G., "Adaptive cntl design f a class f dubly-salient mts", in Pc. 3th IEEE Cnf. Dec. Cnt., Vl. 3, pp , Nagel N. J. and Lenz R. D., "Cmplex tating vect methd f smth tque cntl f a satuated switched eluctance mt", in Pc. 3th Annu. Meeting IEEE Ind. Applicat. Vl., pp , Matsui N.,Aka N. and Wakin T., "High pecisin tque cntl f eluctance mt," IEEE Tans. Ind. Aplicat., Vl. 7, pp. 9-97, Sep./Oct Ma B. Y., Liu T. H. and Feng W. S., "Mdeling and tque pulsatin eductin f a switched eluctance mt dive system", in Pc. IEEE IECON. nd Int. Electn. Cnt. Instum., Vl. 1, pp. 7-77, 199. Ilic'-Spng M., Main R., Peesada S. M. and Tayl D. G., "feedback lineaizing cntl f switched eluctance mts", IEEE Tans. Autmat. Cnt., Vl. AC-3, pp , May Wallace R. S. and Tayl D. G., "A balanced cmmutat f switched eluctance mt t educe tque ipple", IEEE Tans. Pwe Electn., Vl. 7, pp. 17-, July 199. Stankvic A. M., Tadm G., Cic Z. J. and Agiman I., "On tque ipple eductin in cuent-fed switched eluctance mts," IEEE Tans. Ind. Electn., Vl., pp , Feb Jinupun P. and Luk P. C. K., "Diect tque cntl f sensless switched eluctance mt dives", in Pc. 7th Int. Cnf. Pwe Electn. Vaiable speed dives, pp , Chek A. D. and Fukuda Y., "A new tque and flux cntl methd f switched eluctance mt dives", IEEE Tans. Pwe Elect. Vl. 17, pp. 3-7,. Chan S. and Bltn HR., Develpment f subkw single phase switched eluctance dives, Cnf. Rec. f ICEM, Vl., pp. 7-31, 199. Gu H. J., "Cnsideatin f diect tque cntl f switched eluctance mts",s IEEE ISIE, pp. 31-3, July. Byn J. V. and Lacy J. G., "Chaacteistics f satuable steppe and eluctance mts," in Pc. Cnf. Small Elect. Mach., pp. 93-9, 197. Feyzi & Ebahimi: Diect Tque Cntl f -phase 1/8 Switched Reluctance Mts 13

10 Dwnladed fm ijeee.iust.ac.i at 18:19 IRST n Fiday Septembe 8th 18 Mhammad Reza Feyzi eceived his BSc and MSc in 197 fm univesity f Tabiz in Ian with hn degee. He wked in the same univesity duing 197 t He stated his PhD wk in the Univesity f Adelaide, Austalia in Sn afte his gaduatin, he ejined t the Univesity f Tabiz. Cuently, he is an assciate pfess in the same univesity. His eseach inteests ae finite element analysis, design and simulatin f electical machines and tansfmes. Yusef Ebahimi eceived the B.S. degee in cntl engineeing fm Sahand Univesity f Technlgy, Tabiz, Ian, in 1, and the M.S. degee in electical engineeing fm Tabiz Univesity, Tabiz, Ian, in 8. Since he has been with the Natinal Ianian Gas Cmpany (NIGC). His maj eseach inteest is design and simulatin f electical mts dive. 1 Ianian Junal f Electical & Electnic Engineeing, Vl., N. 3, Sep. 9