Sensorless Drive of Surfe Mounted Permnent-Mgnet Brushless DC Mhines with Dimetri Windings sed on Indutne Mesurements Fien Griel, Frederik De Belie, Psl Druyts, Xvier Neyt nd Philippe Ltire Royl Militry Ademy (RMA), venue de l Renissne, 1 Brussels, Belgium Ghent University (UGent), St-Pietersnieuwstrt 41, 9 Gent, Belgium Vrije Universiteit Brussel (VUB), Pleinln, 15 Elsene, Belgium Astrt Lst dedes, importnt progress hve een mde in sensorless ontrol methods sed on the trking of mgneti nisotropies linked to the rotor. These methods llow to estimte the rotor position t low speed down to stndstill. The mgneti nisotropy is generlly pprohed y sinusoidl shped funtion. However, the theory must e dpted in se of dditionl hrmoni ontent in the nisotropy funtion. This pper speifilly ddresses the prolem for the surfe-mounted permnent-mgnet rushless DC mhines with dimetri windings. They present peulir mgneti nisotropy tht suggests simple method to detet the inversion of the mgneti field s replement to the dedited sensors whih re often used. Index Terms AC motor drives, Brushless DC mhines, Sensorless ontrol I. INTRODUCTION In sensorless ontrol the dedited mgneti field sensors or position sensors, required in mny drives, re repled y estimtion methods using urrent nd voltge mesurements t the mhine terminls only. Avoiding dedited sensors redues ost nd improves the reliility y removing the risk of filure of these sensors [1]. Sensorless estimtion methods n e lssified in two min tegories: k-eletromotive fore (k-emf) sed methods []: s the k-emf is the voltge indued y the time vrition of the mgneti field produed y the rotor nd emred y the sttor iruits, this voltge n e used to estimte the rotor mgneti field nd hene the position of the rotor. At low speed however the k-emf dereses nd yields n inurte estimtion. indutne-sed methods [], [4]: mgneti nisotropies my e due to the vrition of the ir-gp length (rotor with slient poles), or to the different lol sturtion levels in the iron. The nisotropies indue vritions of the sttor indutne This work is finned y the Belgin government s prt of the Belgin Defense reserh progrm F79. It is performed in ollortion with UGent in the frmework of the Interuniversity Attrtion Poles progrm IUAP P/1. The UGent uthors lso wish to thnk the Reserh Foundtion-Flnders (FWO) for the finnil support in the frmework of projet numer G.5.. nd this n e used to estimted the position of the rotor. In priniple these methods n e used t ny speed. However, pronouned nisotropy is required to hieve urte estimtions. Most of the permnent-mgnet mhines stisfy this requirement. Mny ppers disuss very effiient sensorless solutions. However, most of them ssume tht the mgneti field density in the ir gp nd the mgneti nisotropy re distriuted s sinusoidl funtions. In permnent-mgnet synhronous mhines (PMSM) with trpezoidl-shped mgneti field, often referred to s rushless DC mhines (BLDCM) [5], these ssumptions re not met. As onsequene, speifi methods must e developed. In [], n initil rotor estimtion method is proposed for rushless DC motor sed on the phse indutne estimtion. It ompres the different phse indutnes with position look-up tle, ut no urte nlysis is performed. In [7], the use of look-up tle orretion is suggested to tke into ount nonidel nisotropy in relutne mhines. In [8], mesurements on PMSM with onentrted windings re presented. The results re similr to wht we hve mesured for BLDCM. However, the ltter two do not propose explntions of the oserved mesurements. This pper disusses the indutne vrition s funtion of the rotor position in BLDCM with surfemounted permnent-mgnets nd with dimetri windings. Low lod nd thus smll sttor urrents re ssumed. Theoretil nlysis will e ompred to experimentl mesurements performed on kw BLDCM. The indutne is estimted using injetion of voltge-dptive testpulse sequenes [9]. II. THE BLDCM MODEL This setion desries the BLDCM with dimetri windings. To highlight prtiulrities of this type of mhine, n idel single-pole simplified model will e onsidered. A. Cross-setion of BLDC As illustrted in Fig. 1(), the onsidered mhine hs pir of permnent-mgnets (PM) mounted on the rotor
Sttor PM ϑ PM Rotor () ϑ PM B PM () µ α() Fig. 1. Setion of the BLDCM showing the rotor struture with its PM (), PM mgneti field distriution (), Permeility funtion () Condutor slots ϕ ϕ Sttor ϕ ˆN ˆN N p() ˆN () () () () hll effet sensors () Fig.. Setion of the BLDCM showing the sttor struture with its phse ondutor slots (), Condutor distriutions (), Hll effet sensors () surfe. The xis of the PM forms n ngle with respet to the ngulr position =. Eh PM overs n ngle extent ϑ PM. The distriution of the mgneti field density B PM () produed y the PM nd rossing the ir-gp is onstnt under the PM. I.e., B PM () hs trpezoidl shpe entered round the ngle, s shown in Fig. 1(). The onsidered mhine hs three sttor phses where eh phse is leled y letter p {,, }. As illustrted in Fig. (), phse is mde of ˆN ondutor turns wound round the phse xis defined y ϕ =, ϕ = nd ϕ = 4. The winding of phse p is onentrted in pir of ondutor slots loted t ϕ p + nd ϕ p. Those slots ontin N p(ϕ p + ) = ˆN nd N p (ϕ p ) = ˆN ondutors respetively nd re illustrted y nd in Fig.. A ondutor is ounted positively when the urrent flows outside the figure for positive urrent in the phse. The ondutor distriutions N p () re shown in Fig. (), where nd re drwn to illustrte the slot lotions. The eletril urrent flowing in the sttor phse p is noted i p nd produes, lone, mgneti field density B p () ross the ir-gp. Smll sttor urrents re ssumed suh tht the totl mgneti field density rossing the irgp B totl n e pproh y liner ontriution of the different mgneti soures: B totl () = B PM () + B() where B() = 7 p=,, 11 B p () (1) where B p () << B PM (). The reltion etween i p nd B p () is developed herefter. B. The nisotropi model B µ dl = i enlosed in se of mhine with The mgneti nisotropy is due to the vrition of the lol sturtion level in the iron. Smll sttor urrents re ssumed nd therefore the sturtion is minly governed y the PM field. This sturtion n tke ple in the sttor nd rotor yokes or in the ondutor teeth [1]. Ref. [5] develops the reltion etween the phse urrents nd the mgneti indution in the ir-gp from the Ampere s lw C n infinite iron permeility, i.e. without sturtion effets. If we onsider finite nd vrile iron permeility, tht models the nisotropy, it is not possile to hve suh simple expression. Therefore we propose to use similr reltion in whih we hve introdued orretion ftor α() to tke into ount the vrile sturtion. It yields C( 1, ) B µ dl = δ B( 1) µ α( 1 ) δ B( ) µ α( ) where the losed pth C( 1, ) rosses the ir-gp t the ngles 1 nd, B is the mgneti indution, dl is the ontour element vetor, δ is the ir-gp thikness nd µ is the ir permeility. Assuming the design given y Fig. 1(), the reltion etween B p () nd i p is () B p () = H p () µ α() where { δ +ip ˆN if [ϕp H p () =,ϕ p + ] i p ˆN if [ϕp +,ϕ p ] () For dimetri windings, the mgneti flux emred y phse p is otined y totl,p = ˆN ϕp+ ϕ p B totl ()d (4) Using (1) in (4), the ontriution of the sttor urrents to the mgneti flux linked y phse p is ϕp+ p = ˆN B p () d (5) ϕ p p =,, This lst reltion llows to ompute the indutne mtrix L defined y Ψ = LI, where Ψ = [,, ] t, I = [i,i,i ] t. More detils re given in the ppendix setion VIII. As shown in Fig. 1(), we further ssume tht the permeility µ α() is pieewise liner funtion relted to B PM (). This hoie of α yields good greement with the mesurements s shown in setion V. C. The trditionl ontrol The most simple wy to drive three-phse BLDCM is to injet urrent i nd i in the two phses whose ondutors re in front of the PM, s shown in Fig. ()(I- III). The signs of i p N p () t the slot positions of the phse
(I) (II) (II) (III) i i rottion i i i () i p N p () i i i ˆN B PM () rottion field hng. detetion phse urrent ommuttion Fig.. For three onseutive PM orienttions (I-III): Setion of the BLDCM (), superposition of the PM mgneti field, the urrent distriutions nd the hll effet sensors () p re illustrted y nd. No urrent is injeted in the third phse. This is illustrted y. Assuming trpezoidl mgneti field density distriution, the torque will remin onstnt if the ommuttions our when is etween ϕ p + k + ϑpm nd ϕ p +k+ +ϑpm, where p is onseutive to p in {,,} nd k is n integer. This is illustrted in Fig. : t the positions (II), hll effet sensor detets n inversion of the field in the ir-gp nd initites ommuttion etween the phses nd, s shown in (II). This ontrol tehnique requires the detetion of the orienttion of the PM-rotor. For this, hll effet sensors re usully used in the ontrol loop. The gol of the sensorless BLDCM-ontrol is to estimte the PM-rotor position without ny dedited sensor, suh s hll effet sensors. A solution sed on the indutne vrition is proposed herefter. In this pper ontinuous vrition of the urrents i p is onsidered. III. THE INDUCTANCES This setion nlyzes the indutnes otined from the simple model desried in the previous setion. The spe vetor formlism, lso lled spe phsor, is used for the eletromgneti vriles. This is indited y using underlined letters. The spe vetors in referene-frme relted to the sttor result from the Clrke trnsformtion pplied to the phse vriles [11], [1]: x = C X, where X = [x,x,x ] t ontins the phse vriles nd () is the trnsformtion mtrix. This yields onvenient two-dimensionl vetors tht n e superimposed on the mhine setion. Assuming x + x + x =, we lso hve X = Cx, where I ( ) = CC. In ny αβ referene-frme rotted y n ngle ϕ αβ with respet to the sttor referene-frme, the oordintes of the spe vetor x αβ = [x α,x β ] t re given y: [ ] os ϕαβ sin ϕ x αβ = αβ x () sin ϕ αβ os ϕ αβ }{{} C x ϕ αβ where indites the rottion opertion. Without index, x is defined in the sttor referene-frme. A. Flux produed y the sttor urrents In referene-frme relted to the sttor, let s define the spe vetor of the sttor urrents i nd its orienttion ϕ i. The spe vetor of the flux indued y the ontriution of the sttor urrents is relted to i y = li, where l = C LC (7) is indutne mtrix. Note tht the spe vetor of emred fluxes, suh s, is mthemtil ojet tht does not define the entire mgneti field distriution sine this distriution is not sinusoidl funtion. B. Indutnes ssuming fixed rotor The permeility funtion µ α() is fixed if the PMrotor is fixed. As result, the indutne mtrix L omputed using (5) nd the indutne l omputed using (7) re onstnt. As L, nd therefore l, re symmetril, it is lwys possile to find referene-frme, noted xy, oriented suh tht l is digonl mtrix: ( ) lx xy = i l xy (8) y This reltion n lso e written xy = l C i xy + l i xy (9) where i xy = [i x, i y ] t nd where the indutne ftors re [7]: l C = l x + l y nd l = l x l y (1) Sine the spe vetor i xy is rotting in reverse diretion, using (), we hve : i xy = ( i ϕxy) = i ϕ xy (11) where ϕ xy is the ngle of the xy referene-frme with respet to the sttor referene-frme. Using () nd (11), (9) yields in the sttor referene-frme: = l C i + l i ϕxy (1) We define C s the prt of the flux tht rottes with i, nd s the prt tht rottes reversely with i: C = l C i = l i ϕxy (1)
5 7 () i ϕ i 11 5 7 y-diretion x-diretion ϕ xy 11 ϕ i,ii () () i II ϕ i,i i I /i II II l C /i I I ϕ i,ii II I () ϕ i,i () Fig. 4. Spe vetor of the flux () drwing n ellipse, shown y lue dshed line, when ϕ i ontinuously vrites. The lous of is represented for different typil orienttions i (), with = 5. 5 7 () i 11 7 5 () Fig. 5. Deomposition of the spe vetor of the mgneti flux () in two rotting vetors C nd, shown y lue dshed lines. The lous re represented for different typil orienttions i (), with = 5. Fig. 4 illustrtes the ellipti vrition of when i rottes. The x nd y diretions of the xy referene-frme re depited y turquoise dshed stright lines. Some typil orienttions of i re shown. They orresponds to the vlues tht tke the phse urrents in the trditionl ontrol, s explined in setion II-C. Fig. 5 illustrtes the deomposition of in the two rotting prts C nd. The xy-orienttion is relted to the PM-rotor position, ut is not neessrily oriented long the PM-xis in se of dditionl hrmoni ontent in the permeility funtion. The effet of the PM-orienttion on the xy-orienttion nd on the indutne ftors is nlyzed herefter. C. Effet of the PM rottion During the rottion of the PM-rotor, the different iruits links moving permeility µ α(). For seven different ngles etween / nd / nd ssuming onstnt spe vetor of the urrents orientted y ϕ i = /, Fig. (-e) shows the ontriution of the iruits, nd to the mgneti field distriution lulted using () nd ssuming the permeility funtion given y Fig. (). Fig. (f) shows the orresponding spe vetor of the flux C 11 Fig. 7. The spe vetors I nd II () respetively for two spe vetors i I nd i II oriented in qudrture (), nd grphil onstrution of l C = ( I /i I + II /i II )/, with =.. The lue dshed tringle in Fig. (f) illustrtes the lous of during the whole rottion. The explntion is given herefter. The flux p given y (5) is the sum of the surfe under the urves Fig. (-e) etween the two ondutor slot positions of the phse p, multiplied y ˆN. Between Fig. (I)-(II) nd etween (VI)-(V), there is no vrition of the different p while the PM re in front of the ondutors. The spe vetor is therefore onstnt. Between (II)-(VI) however, the mgneti field distriutions vry. It n e shown tht the spe vetor vries long stright line. More detils re given in the ppendix setion VIII. As desried in setion III-B, n e deomposed in C nd t ny PM-rotor ngle, s shown in Fig. (f). We n dedue tht C remins the onstnt t ny PMrotor ngle nd is t the enter of the tringle. Therefore l C remins lso onstnt t ny PM-rotor ngle. We see herefter how to nlyze the effet of the vrition of the PM-rotor ngle on. Note tht the tringle rottes reversely with i sine it orresponds to the lous of. D. The spe vetor indutne For onveniene, we define spe vetor indutne l y: l = /i (14) Note tht mny uthors suh s [1] define the spe vetor indutne dividing y i insted of i. The dvntge of our definition is tht l is independent of i. Using (1), (14) yields l = l 1 ϕxy (15) where 1 = [1,] t. Therefore, we hve l = l nd ngle(l ) = ϕ xy. E. Estimtion of the indutnes In prtie, is generlly estimted from signlinjetion-sed tehniques [9]. Our first ojetive is to estimte the prt in order to ompute (14). For this, it is importnt to ompute C from good estimtion of l C. This estimtion n e performed from two mesurements of in two different orienttions ϕ i, e.g. in qudrture
(I) (II) (III) (IV) (V) (VI) (VII) = 9 18 = 8 18 = 7 18 = 18 = 5 18 ϕ = PM = 4 18 18 ϕpm ϕpm () µ α() () B () () B () (d) B () (e) C (f) Fig.. For seven onseutive PM-rotor orienttions etween / nd / (I-VII) nd ssuming ϕ i = /: setion of the BLDCM (), permeility funtion (), ontriution of the phses, nd to the mgneti field density (-e) nd spe vetor of the fluxes linked to the ontriution of the phse urrents (d). The lue dshed tringle represents the lous of the spe vetor s funtion of. s illustrted in Fig. 7. These mesurements should e performed in short period of time ompred to the rottion speed of the mhine, in order to hve only smll vritions of. Then l is omputed from = l C i using (14). A. Simultion dt IV. SIMULATION RESULTS The simultion is sed on PM-rotor ngle extent of ϑ PM =.85. The ext mplitude of α() is not speified s it only influenes the size of the tringle, ut not the shpe. B. Results Fig. 8() illustrtes the lous of l, inditing some speifi positions. Fig. 9() nd Fig. 1() show respetively the indutne l nd the xy-orienttion ϕ xy s funtion of +. We hoose + s it orresponds to the mximum of the nisotropi permeility µ() illustrted in Fig. 1. We oserve tht the reltion etween ϕ xy nd is strongly nonliner. As result, it will e diffiult to urtely derive the orienttion of the PM-rotor from ϕ xy. It is however possile to use it to trk the trnsition from one PM-rotor pole to the other. Note tht ϕ xy is -periodil vlue. This introdues n well-known initil unertinty in the estimtion of tht must e initilly removed [14], [15]. The indutne l n lso e used to trk the trnsition from one PM-rotor pole to the other if its vritions re pronouned. A. Experimentl set-up V. EXPERIMENTAL RESULTS The experimentl BLDCM is kw in-wheel motor developed y Tehniré, Frne, for the propulsion of smll vehiles. Informtion out the design n e found in [1]. Its sttor indutne vries round l C =9µH nd the resistor is out.ω, inluding the 1.4 meters power les onneting the mhine to the voltge-soure. Its nominl eletril rottion frequeny is out 1Hz. With 14 pole-pirs, this orresponds to nominl mehnil rottion speed of out 5rpm. The mhine is fed with n IGBT voltge-soure inverter from SEMIKRON onneted to DC voltge retifier. Low DC-voltge of out 5V is used to limit the mplitude of the urrents ripples. The PWM genertor works t 1kHz. Using suh low DC voltge nd high swithing periods revels importnt nonlinerities in the inverter, suh s the voltge drop ross the semiondutors or the zero-lmp phenomenon.
= ϕ l ϕ xy + l - - 7 4 9 5 - () () 5 ϕ xy + - 7 4 9 5 - - () - - -1 1 (µh) Fig. 1. Simulted vlue () nd experimentl vlue () of ϕ xy s funtion of +. () Fig. 8. Simulted lous () nd experimentl lous () of l when vries. () (µh) 1 () l l 5 5 7 7 4 4 9 9 5 5 11 11 + + Fig. 9. Simulted vlue () nd experimentl vlue () of l s funtion of +. urrent response is extrted from the urrent sensor mesurements nd used to lulte the indutne. Note tht the test-pulses re mde dptive [9] nd tke into ount the dditionl resistive voltge drop in order to redue their impt on the urrent ontroller of the mhine driver [17]. C. Mesurements The mesurements re tken with the mhine unloded, to hve smll sttor urrents, nd rotting t n eletril frequeny of 1Hz, out 1% of the rted speed. In order to keep the rottion speed s onstnt s possile, n enoder feedk is used in the ontroller. Results, ssuming orret knowledge of l C, re shown in Fig. 8(), Fig. 9() nd Fig. 1(). One n see tht the experimentl results re in good greement with the results predited y our model. However the mesurements show rounded orners on the tringle whih might e relted to the ft tht the permeility funtion is not extly onstnt under the PM. These results re very stisftory for use in sensorless ontrol. Note tht suh tringulr lous hve lredy e oserved in previous experiments suh s [8]. Those nonlinerities re tken into ount s disussed in [17], [18]. B. Estimtion method To estimte the indutne, test-pulses re injeted every 8 swithing periods, i.e., every.8ms, in ddition to the norml operting voltge. The resulting high frequeny VI. SENSORLESS CONTROL Insted of using the dedited sensors to ontrol the phse ommuttion, it is suggested to use indutnesed sensorless ontrol method where the position of the phse ommuttions re estimted from the omputtion of (14). To stisfying the onditions for onstnt torque, the ommuttions should our etween two orners of the tringles shown y dimonds in Fig. 8, Fig. 9 nd Fig. 1.
VII. CONCLUSION In this pper, model for the vrition of the indutne s funtion of the PM-rotor position is disussed for surfe-mounted PM Brushless DC mhine with dimetri windings. The model n e used to detet the rotor position in sensorless wy y injeting high-frequeny test-pulses signls. The model is verified y ompring simultion results with experimentl dt. Further reserh will fous on the effet of lrger sttor urrents tht will typilly exist when the mhine is loded. VIII. APPENDIX Repling B p () y (), (5) yields ( p = ˆN µ δ (i p i q + i r ) +(i p i q i r ) ϕp ϕ p ϕp+ ϕ p α()d α()d ) ϕp+ +(i p + i q i r ) α()d ϕ p+ (1) where q is onseutive to p nd r is onseutive to q in {,,}. Let s define A p s the following integrl A p = ϕp+ ϕ p α()d (17) If we ssume tht α() is symmetril in, we hve A q = ϕp ϕ p Therefore, (1) yields α()d nd A r = p = ˆN µ δ (i p (A p + A q + A r ) +i q (A r A p A q ) ϕp+ ϕ p+ α()d (18) +i r (A q A p A r )) (19) From (19), we n extrt the mtrix of the phse indutnes L. Applying (7) on L yields: [ l = ˆN µ (4A ] + A + A ) (A A ) δ (A A ) (A + A ) () Note tht A, A, A re funtions of nd tht A + A + A is onstnt: A + A + A = 1 α()d = onst (1) Assume the funtion α() given in Fig. (). During the trnsition of one PM-pole to the other in front of the slots of the phse p, remrk tht A p remins onstnt. Therefore the expression () n e simplified using only one vrile A tht is omintion of A, A nd A. By onsequene, vries long stright line. REFERENCES [1] T.-H. Kim, H.-W. Lee, nd M. Ehsni, Stte of the rt nd future trends in position sensorless rushless d motor/genertor drives, in Industril Eletronis Soiety Conferene (IECON), pp. 1718 175, Nov. 5. [] J. Johnson, M. Ehsni, nd Y. Guzelgunler, Review of sensorless methods for rushless d, in IEEE Industry Applitions Conferene (IAS), vol. 1, 1999. [] M. Shroedl, Detetion of the rotor position of permnent mgnet synhronous mhine t stndstill, Pro. ICEM, Pis, Itly, pp. 195 197, 1988. [4] A. Consoli, G. Srell, nd A. Test, Sensorless ontrol of motors t zero speed, in Proeedings of the IEEE ISIE, vol. 1, pp. 7 79, 1999. [5] J. Chisson, Modeling nd high performne ontrol of eletri mhines. USA: IEEE Computer Soiety Press, 5. [] S. Shn, L. Qingfu, X. Wei, nd W. Xinghu, A novel strting method for the sensorless slient-pole rushless d motors, in Conferene on Eletril Mhines nd Systems (ICEMS), vol., pp. 895 897, Aug. 1. [7] P. Lndsmnn, R. Kennel, H. de Kok, nd M. Kmper, Fundmentl slieny sed enoderless ontrol for relutne synhronous mhines, in Interntionl Conferene on Eletril Mhines (ICEM), Sept. 1. [8] F. Demmelmyr, A. Eilenerger, nd M. Shroedl, Sensorless eletri trtion drive with 5 Nm outer rotor permnent mgnet synhronous mhine, in Interntionl Conferene on Eletril Mhines (ICEM), Sept. 1. [9] F. De Belie, P. Sergent, nd J. Melkeeek, A sensorless drive y pplying test pulses without ffeting the verge-urrent smples, IEEE Trnstions on Power Eletronis, vol. 5, no. 4, pp. 875 888, 1. [1] J. Moreir nd T. Lipo, Modeling of sturted mhines inluding ir gp flux hrmoni omponents, IEEE Trnstions on Industry Applitions, vol. 8, pp. 4 49, Mr/Apr 199. [11] R. H. Prk, Two-retion theory of synhronous mhines: Generlized method of nlysis - prt i, Amerin Institute of Eletril Engineers (AIEE), pp. 71 77, July 199. [1] P. Vs, Eletril Mhines nd Drives: A Spe-Vetor Theory Approh. United Sttes: Oxford University Press, 199. From inter-universitry lon. [1] F. D. Belie, J. Melkeeek, K. Geldhof, L. Vndevelde, nd R. Boel, A generl desription of high-frequeny position estimtors for interior permnent-mgnet synhronous motors, in Interntionl Conferene on Eletril Mhines (ICEM), Sept. 4. [14] J. Holtz, Initil rotor polrity detetion nd sensorless ontrol of pm synhronous mhines, IEEE Industry Applitions Conferene, 41st IAS Annul Meeting., vol. 4, pp. 4 47, Ot.. [15] O. Sglione, M. Mrkovi, nd Y. Perrird, Exploittion of new iron -h phenomenon for the stndstill position detetion of pm motors, in Interntionl Conferene on Eletril Mhines (ICEM), Sept. 1. [1] H. Mi, F. Dus, D. Chmgne, nd C. Espnet, Optiml design of surfe mounted permnent mgnet in-wheel motor for n urn hyrid vehile, in IEEE Vehile Power nd Propulsion Conferene (VPPC), pp. 481 485, 9. [17] F. Griel, F. D. Belie, P. Druyts, X. Neyt, J. Melkeeek, nd M. Aheroy, Compensting the influene of the sttor resistor nd inverter nonlinerities in signl-injetion sed sensorless strtegies, in IEEE Vehile Power nd Propulsion Conferene (VPPC 9), (Derorn, USA), pp. 8 9, Sept. 9. [18] F. Griel, F. D. Belie, P. Druyts, nd X. Neyt, Strtegy to detet nd prevent the urrent zero-rossing for inverter powered drives, in IEEE Interntionl Conferene on Eletril Mhines (ICEM 1), (Rome, Itly), Sept. 1.
Fien Griel reeived the Eletromehnil Engineering degree from the Université Lire de Bruxelles in 4. In 5, he worked in the ompny IRM group, in the R&D deprtment, on the design of eletroni rd for mesurement systems. Between 5 nd 7, he worked in projet development nd mngement for the uilding industry, in the ompny Axis-Engineering. Sine then, he hs een working s reserh engineer for the Royl Militry Ademy, Belgium, on power eletri mhines ontrol tehniques. He is urrently working towrd the Ph.D. degree. Frederik De Belie (M 5) ws orn in Belgium in 1979. He reeived the Mster degree in eletromehnil engineering from Ghent University, Ghent, Belgium, in, nd the Ph.D. degree in Mrh 1. His present reserh interests inlude modelling theory nd ontrol-system theory pplied to eletril drives nd, in prtiulr, sensorless ontrol of synhronous mhines. Psl Druyts reeived the M.S. degree in eletril engineering in 1991 nd the postgrdute degree in utomti ontrol in 199, oth from the Université Lire de Bruxelles, Brussels, Belgium. Sine 199, he is with the Signl nd Imge Centre of the Royl Militry Ademy in Brussels. His urrent reserh is on the modeling of EMI sensors nd ground penetrting rdrs within the frmework of mine lerne. Xvier Neyt reeived the engineering degree (summ um lude) from the Free University of Brussels (ULB) in 1994, post-grdute degree in signl proessing in 4 nd his PhD from the University of Liege in 8. In 1995 he reeived the Frerihs Awrd from the ULB nd the speil IBM grnt from the Belgin Ntionl Fund for Sientifi Reserh (NFWO). Up to 8, he hs een working s reserh engineer for the Royl Militry Ademy, Belgium. In 199-1997 he ws visiting sientist t the Frenh erospe enter (ONERA) nd in 1999 t the Germn erospe entre (DLR). In 1997-1999 he ws responsile for the design of the imge ompression module of the Europen MSG stellite nd in -5, responsile for the redesign of the ground proessing of the stterometer of the Europen ERS stellite following its gyrosope nomly. Sine 9, he is ssoite professor t the Royl Militry Ademy of Belgium. His reserh interests inlude signl proessing in generl nd pplied to rdr with emphsis on pssive rdrs, rry proessing, spe-time dptive proessing nd perture synthesis. Philippe Ltire reeived degree in eletromehnil engineering in 1975 nd degree in dotor in pplied sienes in 198 from the Vrije Universiteit Brussel (VUB, Brussels, Belgium). He is presently full professor t the VUB in the field of power eletronis, utomti ontrol nd eletri drives. The prime ftors of his reserh interest re in the field of eletri drives, power eletronis nd ontrol. The Deprtment FirW ETEC, heded y Prof. Philippe Ltire, developed reserh tivities in the fields of sustinle moility, omputtionl eletrohemistry, lighting, eletri mhines nd power eletronis pplitions.