Robustness Evaluation of SMO in Sensorless Control of BLDC Motor under DTC Scheme
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1 Robutn Ealuation of SMO in Snol Contol of BDC Moto und DTC Schm Giija P.., Studnt Mmb, IEEE, and Pinc A., Mmb, IEEE Abtact-- Dict Toqu Contol (DTC i a mthod to contol th toqu in aiabl fquncy di. Thi pap dcib nol DTC of buhl dc (BDC moto di opating in contant toqu gion und two pha conduction mod to gt intantanou toqu contol. Sliding Mod Ob (SMO which i low niti to paamt aiation i popod to timat th pha-to-pha tapzoidal back-emf fo th nol opation. Thi timatd back-emf i ud to dduc th oto poition and th angula locity of th oto. And intantanou lctomagntic toqu can b calculatd by th poduct of back-emf and cunt. Th pap focu th obutn aluation of th Sliding Mod Ob to th aiation of moto paamt and th ffctin i alo intigatd with ignum and atuation function fo DTC chm. Indx Tm-- Buhl dc moto (BDCM; Dict toqu contol (DTC; non-inuoidal back-emf; Sliding mod ob(smo; two-pha conduction I. INTRODUCTION A BDC moto i an inid-out DC commutato moto with th mchanical commutato placd by an lctonic witching cont. Th dmand of BDC moto in domtic a wll a indutial application uptun du to thi high fficincy, high toqu and pow dnity, low cot, impl tuctu, btt contollability and lag toqu to intia atio compad to buhl AC moto. Th mot popula way to contol a BDC moto i ia oltag ouc cunt-contolld int. Th int mut upply a ctangula cunt wafom who magnitud i popotional to th moto haft toqu. Th back-emf wafom of a BDC moto i tapzoidal hap du to th concntatd winding. In thi pap BDC with 120º conduction mod i popod, that man only two-pha conduct at any intant of tim. BDC moto fd by two-pha conduction ha high pow/wight and toqu/cunt atio [1]. Idally a BDC moto upplid with ctangula 120º lc. Pha cunt poduc a tapzoidal back-emf wafom who amplitud Giija P.., M. Tch Schola i with th Dpatmnt of Elctical Engining, Raji Gandhi Intitut of Tchnology, ottayam, ala, India (-mail:giijaanka37@gmail.com. Pinc A., Aociat Pofo i with th Dpatmnt of Elctical Engining, Raji Gandhi Intitut of Tchnology, ottayam, ala, India (-mail: pinc@it.ac.in /14/$ IEEE i contant o 120º lc. will ult a ippl f toqu. How, in a pactical BDC di toqu pulation ai du to th diation of back-emf wafom fom th idal. In DTC chm, th toqu command obtaind fom twoll hyti contoll by compaing th timatd lctomagntic toqu with thi fnc alu which i obtaind fom pd o. Fo th contol, oltag cto i lctd fom a look-up tabl which dpnd on oto flux cto poition and th toqu o to duc witching fquncy and toqu ippl in commutation gion [1]. Hall-ffct no a uually ud a poition no to know th poition of commutation point. Nomally th no a mountd on th tato with 120º apat. Th no inca th cot, iz and wight of th moto and duc th liability of th total ytm. To ocom th poblm, intad of uing poition no, th nol mthod ha bn dlopd to timat th poition and locity of th oto fom th timat of pha-to-pha back- EMF uing liding mod ob. Th popod ob i ay to dign and ha obutn againt dign paamt [2]-[7]. Sliding mod ob i a non-lina high gain ob ha th ability to bing co-odinat of th timato o dynamic to zo in finit tim. In thi pap, obutn of liding mod ob fo th pd and poition timation i tudid by aying th tato inductanc and itanc. Th pap i oganizd a follow. In ct. II, th mathmatical modl of BDC moto i dcibd. In ct. III, th dict toqu contol of BDC moto i xplaind. In ct. IV, dign pocdu of liding mod ob i dicud. Sct. V dal with th timation of lctical oto pd and poition. In ct. VI, th obutn of SMO i aluatd. Th imulation ult and it analyi a gin in ct. VII. II. MATHEMATICA MODE OF BDC MOTOR Th pha ta connctd BDC moto can b dcibd by th following quation, ab bc ca d R ia ib ia ib a b d R ib ic ib ic b c (1 d R ic ia ic ia c a Th quation of motion can b xpd a:
2 dm T T Bm J (2 Wh, i and dnot th pha-to-pha oltag, pha cunt and back-mf pctily in th th pha a, b and c. R and dnot th lin-to-lin itanc and inductanc of tato winding. T i th lctomagntic gnatd toqu, T i th load toqu, B i th fiction cofficint, J i th pola momnt of intia and m i th angula locity of oto [3],[4]. V 3 ( V 4 ( IV III V β V 2 ( V 1 ( II 30º I 0 VI V 6 ( III. DIRECT TORQUE CONTRO OF BDC MOTOR Tanfoming th tat quation of BDC moto in -β tationay fnc fam can b wittn a: R i Wh,, i, i di di Ri (3,, a th tato oltag, tato cunt and back-mf pctily in th -β tationay fnc fam. Elctomagntic toqu fo DTC can b xpd a: 3p d T i 4 d d i d Wh and a th -β axi oto flux cto componnt, p i th no. of pol and i th oto lctical angl. Th diffntial fom of oto flux componnt pct to can b did fom th atio of th back-emf to th lctical angula locity. i.., Wh d d d d d d d 1 d d 1 d d Thn th lctomagntic toqu can b wittn a, T 3p i 4 i Roto angula locity fo th lctomagntic toqu calculation can b obtaind fom th timat of liding mod ob. Fo th dict toqu contol, a witching pattn of int i lctd accoding to th output of hyti contoll and th flux cto poition. (5 (4 (6 Fig. 1 Two-pha oltag pac cto and cto Fig. 1 how th ix oltag cto and th cto. Th pop oltag cto, V i fo DTC chm i lctd fom th witching tabl a hown in Tabl. I. τ dnot th output of hyti contoll and th cto i dnotd a θ. If th fnc toqu gat than th actual toqu, within th hyti band limit, th output of th hyti contoll i dfind a τ=1 othwi τ= -1, out of th ix oltag cto, th pop oltag cto fo int i lctd bad on th witching tabl. Uing oto flux ob, th oto flux cto componnt fo (5 can b calculatd, i Ri i Ri (7 To contol lctomagntic toqu in DTC chm, th oto flux cto poition can b obtaind a, 1 tan (8 TABE I SWITCHING TABE FOR DTC OF BDC DRIVE τ θ I II III IV V VI 1 V 2 V 3 V 4 V 5 V 6 V 1-1 V 5 V 6 V 1 V 2 V 3 V 4 IV. SIDING MODE OBSERVER Sliding mod ob i ud fo th pha-to-pha back- EMF timation accuatly. By aanging (3 and nglcting th zo qunc componnt, th tat quation fo SMO can b wittn a, di di R R V 5 ( i i (9
3 In od to tup a back-emf ob th pha-to-pha back-emf componnt can b conidd a ditubanc with th following aociatd modl, d d 0 and 0 Sliding mod ob i popod a: di R i di R i d 31gn( i d 42gn( i î î gn( i 11 gn( i 22 (10 Wh,,, a th timation of -β ax tato cunt and back-emf pctily. Th liding ufac S i dfind a th o btwn th actual and timatd cunt (, it i pntd a Wh, i i i S S S T, (11 S i i 0 S S i i 0 Whn th timation o tajctoi ach th liding ufac i.., S=0, th obd cunt will cong to actual. To find th ob gain, conid th poiti dfinit yapuno function a: V 2 2 i 1 i i (12 2 Sliding mod occu whnv S S0. Onc th liding mod achid, th ytm will main on that liding mod [5]-[7]. Diati of dv R 2 i 11 i T V with pct to tim conclud i i i i 22 i 2 0 (13 In od to nu th congnc of th ob, th gain hould atify th following condition, (a 11 1 and max (b 0 and H S1 = 11 = 22 and S2 = 31 = 42 max Th ignum function i dfind a: 1; S 0 ign ( S 0; S ; S 0 To dca chatting ffct, th ignum function in (14 i placd with atuation function. Satuation function i dfind a: S ; S at S ign( S; S ( (15 Wh i th liding ufac band. In od to duc th pu intgato influnc in th back- EMF timation, a PI contoll i ud in thi ob [2]. V. ROTOR POSITION AND SPEED ESTIMATION Th dtction of th ix oto poition (θ fo th pop commutation of a BDC moto can b aily dtmind fom th timatd back-emf in th -β tationay fnc fam [5]-[7]. Th timatd oto poition a follow, 1 tan (16 Th back-emf ignal contain th oto pd infomation. In od to timat th intantanou oto angula locity, th following mathmatical lation i conidd. E E max( pha to pha (17 2 Wh, max( pha to pha i th amplitud of pha-to-pha back-emf and i th back-emf contant [4]. VI. ROBUSTNESS EVAUATION WITH PARAMETER VARIATION ow niti to paamt aiation i th wll-known fatu of liding mod ob. Thi fatu of SMO i aluatd by aying th moto paamt uch a inductanc and itanc. Vaiation in R only, Th fit t of imulation w caid out by kping th alu of inductanc at =0.6H fo atd pd and changing th alu of itanc, R. Th oiginal alu of moto itanc i 70 ohm. Th accuat back-emf timation i poibl fo a ang of alu of R, ohm by uing SMO with ignum function and a ang fom 64 to 95 ohm with atuation function a contol law. Vaiation in only, Th cond t of imulation w caid out by kping th alu of itanc at R=70 ohm fo
4 ω * atd pd and changing th alu of inductanc,. Th oiginal alu of moto inductanc i 0.6H. Fo a ang of alu of, H, th popod ob with ignum and atuation function timat th back-emf accuatly. Combind aiation in R and, Th combind ffct of moto paamt i aluatd by changing thi alu imultanouly. By changing moto inductanc fo a ang H, th accuat timation of back-emf can b poibl in th ang of alu of R, ohm by uing SMO with ignum function and th ang of R, ohm with atuation function. By changing moto itanc fo a ang ohm, th popod ob with ignum and atuation function can accuatly timat th back-emf fo a ang of alu of inductanc in btwn H and H pctily. + - PI T * - T Toqu Etimation ω τ Voltag Vcto Tabl S Scto Slction Fig 2.block diagam of dict toqu contol of BDC di VII. SIMUATION RESUT Th oall block diagam of liding mod ob bad nol dict toqu contol of BDC di hown in fig. 2 wa imulatd by MATAB/Simulink. Moto paamt ud fo th imulation a litd in Tabl. II and th liding mod ob co-fficint a gin in Tabl. III In od to chck th ffctin of popod ob againt paamt aiation, ctain numb of imulation w don. Fom th analyi of abo imulation, it i found that th popod ob can timat th back-emf θ Roto Flux Ob Sliding Mod Ob Spd Etimatio i i β S 1 S 2 S 3 S 4 S 5 S 6 V V β β abc β + dc-link - Int BDC Moto accuatly fo th wid ang of aiation in moto paamt. And th liding mod ob i l niti to paamt unctainti. TABE II PARAMETERS OF BDC MOTOR DC-link oltag(v 300 No. of pol 16 in-to-in inductanc(h 0.6 in-to-in itanc(ohm 70 Back-EMF contant(v/(ad/c 3.36 Pola momnt of intia(g.m Fictional co-fficint(n.m.c Ratd pd(pm 350 TABE III SIDING MODE OBSERVER PARAMETERS S1 900 S2-260 P 30 I 1 Sliding ufac band, 0.05 Th actual and timatd -β tationay fnc fam pha-to-pha back-emf, Eab uing ignum and atuation function a hown in Fig.3 and Fig.4 pctily. Tanfoming th timatd and in to abc-fam by modifid in Clak tanfomation [8], th pha-topha back-emf ab and ca i obtaind. Whn liding mod ob with ignum function i implmntd to timat th back-emf of BDC moto th ultd gaph ha chatting du to th highly dicontinuou natu of th ignum function. In od to duc th chatting, intad of ignum function, atuation i gin. Thn it i obd that th chatting i ducd to gat xtnt. Fig.5 and Fig.6 how th actual and timatd oto poition uing SMO with ignum and atuation function pctily. In fig.5 th timatd oto poition how th ffct of chatting poblm. Whn th atuation function ud a a contol ignal in SMO, th ffct of chatting conidably ducd which i hown in Fig.6. Th abo gaph how a pha dlay fom th actual oto poition bcau of th intoduction of low pa filt ud in th oto poition timato. Th timatd oto poition o i not mo than 3 dg. Fig.7 and Fig.8 how th actual and timatd oto pd. Whn th fnc pd of 350pm wa gin, th timatd pd tack th actual pd which i hown in Fig.7. Fig.8 how th pd pon of SMO with atuation function a contol ignal; th timatd pd ach it fnc alu y quickly. Th timatd lctomagntic toqu fo DTC chm with ignum and atuation function a hown in Fig.9 and Fig.10
5 pctily. By compaing th ult it i obd that commutation toqu ippl i ducd to gat xtnt by th application of atuation function a th contol ignal. Th oto flux cto poition which i th output of oto flux ob and th ix cto fo DTC opation i hown in Fig.11and Fig.12 pctily. Fig.7 actual and timatd oto pd uing ignum function Fig.3 actual and timatd back-emf uing ignum function Fig. 8 actual and timatd oto pd uing atuation function Fig.4 actual and timatd back-emf uing atuation function actual timatd Fig.9 timatd toqu uing ignum function Fig.5 actual and timatd oto poition uing ignum function Fig.10 timatd toqu uing atuation function Fig.6 actual and timatd oto poition uing atuation function Fig.11 oto flux cto poition
6 Fig.12 cto lction [5] Hyun and Jangmyung, Dign of itati liding mod ob fo nol PMSM contol, IEEE Tan. on Contol Syt. Tchnol., ol. 21,no. 4, pp , Jul [6] Wub Eom, Imyong ang and Jangmyung, Enhancmnt of th pd pon of PMSM nol contol uing an impod adapti liding mod ob, IEEE/IECON, 34 th Annu. Conf., pp , [7] Chn Wi, Chn Yankun, i Hongfng and Song Zhanfng, Snol contol of pmannt magnt ynchonou moto bad on liding mod ob, IEEE 7 th Int. Pow Elcton. and Motion Contol Conf., Jun [8] Salih Bai Oztuk and Hamid A. Toliyat, Dict toqu and indict flux contol of buhl dc moto, IEEE/ASME Tan. on Mchatonic, ol. 16, no. 2, Ap Fom th analyi of th ult, it i hown that th timatd output a accuat. How th i a poblm of chatting ffct in th timatd wafom. By nglcting that ffct of chatting, liding mod ob i a y good nol mthod fo th timation of pha-to-pha back- EMF, oto poition and angula locity. VIII. CONCUSIONS In thi pap, an ob bad nol dict toqu contol of buhl DC moto i dlopd. Uing lctomagntic toqu o and oto flux cto poition pop oltag cto fo int witching wa lctd fom look-up tabl to duc th toqu o within a pdfind hyti band limit. Th pfomanc of SMO with ignum and atuation function fo th lctomagntic toqu timation, oto pd and poition timation and timation of back-emf a ifid und DTC chm. Th obutn of popod ob againt paamt unctainti i alidatd by diffnt alu of moto paamt uch a linto-lin inductanc and itanc. Th imulation ult how th obutn i high in SMO with ignum function than th atuation function. How, SMO with atuation function ha btt pd pon, ducd toqu ippl and th l ffct of chatting in th timation of oto poition and back-emf. It i a y good option fo th timation of back- EMF, oto poition, and oto pd pctily. In liding mod contol, th i a poblm with chatting ffct du to th pnc of witching impfction, witching tim dlay and dicontinuity in contol. An analyi can b pfomd by placing th dicontinuou contol function uch a ignum and atuation function with a continuou igmoid function and compa th ffct of chatting. REFERENCES [1] Salih Bai Oztuk and Hamid A. Toliyat, Dict toqu contol of buhl dc moto with non-inuoidal back-emf, IEEE Int. Elctic machin and Di Conf., ol. 1, pp , [2] G. R. Aab Makadh, S. I. Mouai, S. Abazai and A. aga, Poition nol dict toqu contol of BDC moto, IEEE Int. Conf. on Ind. Tchnol [3] A. Dnadayalan and G. Saaana Ilango, Modifid liding mod ob fo poition and pd timation in buhl dc moto, IEEE Annu. India Conf. (INDICON, pp. 1-4, [4] H.Fakham, M.Djmai and.buawon, Dign and pactical implmntation of a back-mf liding mod ob fo a buhl dc moto, IET Jounal on Elctic Pow Appl. Vol. 2, No. 6, pp , 2008.
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