Parameter Identification of a Brushless Resolver Using Charge Response of Stator Current

Transcription

1 Achiv of SID Paamt Intification of a Buhl Rolv Uing Chag Rpon of Stato Cunt D. Aa-Khaui*, F. Tootoonchian* an Z. Naii-Ghiai** Atact: Bcau of tmpatu inpnnc, high olution an noil output, uhl olv a wily u in high pciion contol ytm. In thi pap, at fit ynamic pfomanc chaactitic of uhl olv, coniing paamt intification a pnt. Thn a mathmatical mol a on - ai thoy i givn. Thi mol can u fo tuying th ynamic havio of th olv an tay tat mol i otain y uing ynamic mol. Th main ojct of thi pap i to pnt an appoach to intify lctical an mchanical paamt of a uhl olv a on DC chag citation an wight, pully an lt mtho, pctivly. Finally, th mol of olv a on th otain paamt i imulat. Epimntal ult appov th valiity of popo mtho. Kywo: Buhl Rolv, Dynamic Pfomanc, Elctical an Mchanical Paamt Intification, Stay Stat Bhavio. Intouction In High-pfomanc uhl moto ytm lik invt-ivn pmannt-magnt ynchonou moto (PMSM), aolut oto-poition with high accuacy an olution, i ncay fo alizing vcto contol. Among vaiou iting poition no [, ], tho which can povi aolut poition a olv an optical aolut nco. Both of thm povi lial an pci oto poition ignal. So compaing with optical aolut nco, olv a mo mchanically lial, an ay to intgat with moto ytm [3]. Taitional olv hav uh an lip-ing; ut in uhl olv, uh a plac y a otay tanfom [4]. Th implifi ynamic uation of olv hav n pnt in [5], in which th ffct of tato cunt an ccnticity hav n nglct an th tay tat havio of olv ha not n pnt too. Rf. [6] ci a magntic fil analyi mtho to tmin an optimal magntic ign which liminat hamonic, uing -D FEM (two-imnional finit lmnt mtho). But, it tim conuming poc. Alo autho mntion that thi mtho i not accuat an pactical nough [6]. Ianian Jounal of Elctical & Elctonic Engining, 007. * Davoo Aa-Kahui an Fai Tootoonchian a with th Dpatmnt of Elctical Engining, Ian Univity of Scinc an Tchnology, Than, Ian. kaui@iut.ac.i an tootoonchian@iut.ac.i ** Zaha Naii-Ghiai i with th Dpatmnt of Elctical Engining, Shaif Univity of Tchnology, Than, Ian. z_naii@.haif.u On th oth han, many pap hav pot on th accuacy of olv to igital convt [7-] an th a om pap that pnt paamt intification mtho fo otay tanfom []; ut paamt timation of uhl olv ha not n icu. Th pupo of thi pap i to pnt a mathmatical mol to pict th havio of th uhl olv an it uivalnt cicuit which i imila to inuction moto' tay tat uivalnt cicuit. Thfo th mtho u to intify inuction moto paamt, can u with uhl olv. In litatu th a many mtho fo tmination of inuction moto paamt [3-9]. Som of th mtho a a on gntic algoithm [3, 4] o nual ntwok [5, 6]. Oth wok a pfom to impov th accuacy [7, 8] an th a om wok to uc tim of tt [9]. Each of th mtho ha it avantag an iavantag. Thi pap pnt a DC-Pul mtho a on a impl configuation, which inca timat paamt accuacy an uc tim of tt. In thi mtho, uhl olv paamt a tmin y analyzing th tato cunt pon to th DC-Pul voltag, appli to th tato wining. An ponntial cuv i fitt to th tato cunt pon in DC chag conition. Cofficint an tim contant of th fitt cuv can tmin. Thn uhl olv paamt will calculat accoing to th lat uation. Of cou DC chag mtho i only u fo lctical paamt intification ut mchanical paamt (momnt of intia) mut mau uing oth mtho. 4 Ianian Jounal of Elctical & Elctonic Engining, Vol. 3, No. &, Jan. 007

2 Achiv of SID Finally imulation ult a compa with pimntal on an goo agmnt twn thm appov th paamt accuacy. Rolv Mol an Cunt Euation Th following aumption a coni in th analyi: a) Stato i aum to hav a inuoially itiut polypha wining. ) Roto ha a wining with inuoial upply. Figu how th mol of olv. Each tato wining flu conit of lakag flu an main flu, th latt flu link th oto. Th tato vaial a tanfom to th oto fnc fam which liminat th tim-vaying inuctanc in th voltag uation. Pak uation a otain y tting th p of th tato fam ual to th oto p. So, th voltag-cunt uation a a follow: p m V i p p V = m i V i p p 0 m () wh H i th intia contant p in con, T mch i Loa tou an T amp i factional tou. Fo tay tat conition th lctical angula vlocity of th oto i contant an ual to, whupon th lctical angula vlocity of th ynchonouly otating fnc fam. In thi mo of opation th oto wining o not pinc a chang of flu linkag [0]. Thu, with t ual to an th tim at of chang of all flu linkag nglct, th tay tat vion of () com: V V V = V = I = V = I = V = I I I m I (5) H th to atio i again inclu to accommoat analyi whn th opation funcy i oth than at. In th ynchonouly otating fnc fam an uing uppca ltt to not th contant tay tat vaial: ~ F = F jf (6) a wh: = = l l m m,, m m = 0 0 = m m () wh F i ach lctical vaial (voltag, cunt, flu ~ linkag), Fa i a phao which pnt a inuoial uantity; F an F a al uantiti pnting th contant tay tat vaial of th ynchonouly otating fnc fam. Hnc An p i /t, V, V a th - ai tato voltag, V i th citation ignal of th olv ( V = v co( f t ) ), i, i a th, ai tato cunt, i i th oto cunt, i th itanc of tato cicuit; l, m a, pctivly, th lakag an magntizing actanc of th tato wining;, a th itanc an actanc of oto cicuit, m, m a - ai mutual inuctanc twn oto an tato cicuit, i a angula funcy an i th oto angula funcy. Th lctomagntic tou vlop in th olv i givn y: T P ( i i ) m = (3) An th mchanical uation of olv in p unit can wittn a: V ~ = V jv (7) a Sutituting (5) into (7) yil: V ~ a = ~ I ( ) I I m (8) Fo ymmtical olv, = an =. So (8) can witing a: V ~ E ~ a a = ( j ) = mi ~ I a E ~ a (9) T m ( pu) T ( pu) T ( pu) mch amp = H t (4) wh = l m (0) Ianian Jounal of Elctical & Elctonic Engining, Vol. 3, No. &, Jan

3 Achiv of SID V θ L m σ = (5) L '.L V A 0 =. (6) Roto V f V T = AT A T (7) j l ' I j ' l a / I Stato Fig. Rolv mol. Coniing aov uation th tay tat uivalnt cicuit of olv i hown in Fig.. It i to notic that tato an oto pha num in th inuction moto can aum ual, ut olv i imila to a ynchonou gnato with ingl pha inuoi citation. Fo uing DC chag mtho fo paamt intification in olv, th oto poition mut at th angula poition that i ight a on pha an vtical vu oth pha wining, an th latt pha wining, houl hot. Fig. 3 how th olv uivalnt cicuit at thi poition which i imila to uivalnt cicuit of inuction moto. If th tato wining of th olv i cit y a DC tp voltag, th tato cunt tanf function a on th cicuit mol of Fig. 3, can otain a follow []: V ~ a m Fig. Stay tat uivalnt cicuit of th olv. I V ~ R L l L ' L m lf L ' l f R Fig. 3 Euivalnt cicuit of olv with hot oto. T T T T V = 0 V = (8) T σt T = (9) T V T I() =... () (T T ) ( σt T ) Applying inv Laplac tanfomation uation (), tato cunt in tim omain can wittn a: wh: T T (t) = A (A A ) () i 0 L' T, L' L L' ' t = = m l (3) L T =, L = L m L l (4) t Now, if cofficint A, A an tim contant T, T a known; lctical paamt of th olv can intifi. 3 Epimntal Tt Stup Figu 4 how th manufactu olv an pimntal tup of it. Th pimntal olv wa a pancak olv with th pcification, which pnt in Tal. Th DC voltag ouc of thi tup i chon to povi at cunt of olv. Whn witch S i clo, tato cunt (I ) will n y Hall-Effct cunt no an it output voltag i liv to th PC via an A/D cat o monito on igital ocillocop. Epimntal co ata of cunt cuv i hown in Fig. 5 an thi cuv i fitt y ponntial uation of () Ianian Jounal of Elctical & Elctonic Engining, Vol. 3, No. &, Jan. 007

4 Achiv of SID AD Digital Ocillocop V DC S Hall Effct Sno R L l Stato of Rolv L m L' l R' Roto of Rolv N N () (c) Fig. 4 Schmatic of tt olv, () chmatic of tt tup, (c) Epimntal tup of th tt olv fo DC chag tt. Tal Spification of tt olv. Input voltag (m) Maimum poition o (min) Maimum angula p (pm) Output voltag (m) Duty Cycl Pol num 7.07 v 0 min pm 3.53 v S Thfo cunt uation' cofficint an tim contant can otain. Finally uing uation (3-9), uhl olv paamt a calculat. Etimat paamt a pnt in Tal. Aft lctical paamt intification, mchanical paamt (momntum of intia) houl timat. Th momntum of intia i mot impotant mchanical paamt of olv. Many iffnt mtho a pnt fo calculation of th momntum of intia in []. Som of thm mau J aft iconncting oto fom olv, uch a Pnulum mtho an tnional viation. But th i oth mchanical mtho that can mau oto intia, without iconncting oto, Ianian Jounal of Elctical & Elctonic Engining, Vol. 3, No. &, Jan

5 Achiv of SID y uing wight, pully an lt. Th pully i ma of lightwight polym. Of cou, in thi mtho w ui a lightwight lt, om wight an two optical ky, which u fo accuat tim calculation, in oth n. Fig. 6 how th pimntal tup of olv. Th momntum of intia i calculat with an without DC coupl moto. In thi mtho, wight acclation i: a ( ) 4( ) = (0) (t t) wh a i lina acclation of wight, (t -t ) i th tim ui fo iplacmnt fom to. In (0), w uppo that acclation i contant at t -t an wight a havy nough that can ovcom to fiction. By ignoing of aing an uh fiction: J a g = ( ) ( ) W. Jp () Tal Etimat paamt a on ichag mtho. [Ω] 40 L l [H] L m [H] ' [Ω] 9 L' l [H] Fig. 5 Cunt pon to th DC tp voltag (Epimntal tt). Fig. 6 Schmatic of pully, wight an an f acclation Ianian Jounal of Elctical & Elctonic Engining, Vol. 3, No. &, Jan. 007

6 Achiv of SID Now y applying aing an uh fiction: wh ( J J ).a P = (W W.a / g) F () m = m l l ' l l (9) wh W i Wight of wight, g i gavitation acclation, i pully aiu, J p i pully momntum of intia an F i fiction foc. Sinc, fiction foc i contant up to nominal p [], y utacting two t of ata, th momntum of intia i calculat a: { w w (w a w a ) / g} J= (3) (a a ) That i calculat fo tt olv: J= [kg.m ] (4) 4 Mtho Valiation 4. Simulation Th tat uation on th otating 0 fnc fam a intouc. MATLAB/Simulink oftwa i u fo imulation pupo. Input, out put an tat vaial a: m = m l l (30) Now th output angula poition, tato an oto cunt can calculat a: t θ( t) =δ( t) =θ( t) θ( t) = ( ) tθ( 0) θ( 0) (3) 0 i i m = (3) l m = (33) l m = (34) i l StatVaial= [ InputVcto= [V, T OutputVcto= [ θ ], t mch, ] ] (5) Euation () how th voltag-cunt lation. Howv, it i mo convnint to u flu-linkag a th tat vaial [3]. Thfo, th cunt vu flu-linkag a calculat fom (5). Coniing flu-linkag a tat vaial, flulinkag uation a otain a follow: ( ) t = V m l = V l ( ) m V m = l ( ) t t (6) (7) (8) In ymmtical olv - ai impanc a ual. Thfo in th aov uation i ual to. It i conial that th popo mol i al to ci ccntic olv y tting unual amount of an ( ). Pfomanc piction of ccntic olv will tui in anoth pap. Figu 7 how th imulation lock iagam of olv. 4. Rult an Dicuion Figu 8 how th manufactu olv an pimntal tup of it. Th olv wa tt uing th 00 watt, 000.p.m. DC moto. It i to not, imulation an mau ult can compa in two catgoi: Loaing tt of olv, cau it i imila to a ynchonou gnato with inuoi citation. () Compaing of poition ata inc th olv i a poition no. Figu 9 how th tt an comput - voltag of olv with 4000 (Hz) citation an th nominal output cunt (0 ma). Ianian Jounal of Elctical & Elctonic Engining, Vol. 3, No. &, Jan

7 Achiv of SID Fig. 7 Block iagam of olv imulation. Manufactu Rolv DC Moto () Fig. 8 Schmatic of tt olv, () Epimntal tup of th tt olv. () 48 Ianian Jounal of Elctical & Elctonic Engining, Vol. 3, No. &, Jan. 007

8 Achiv of SID () (c) Fig. 9 Output voltag of olv vu tim with 4000 Hz citation an 0 ma output cunt imulat -ai voltag () imulat -ai voltag an (c) mau - ai voltag. It ha n hown that th amplitu of th mau voltag i lightly lag than imulat on an th maimum amplitu o i aout 5.89%. Thi o may com fom capacitiv ffct of wining in high funcy opation which i igno in ou imulation. So th imulation an pimnt ha n pat with th am cunt an low citation funcy uch a on tnth of nominal funcy (0. f n =400 Hz). Figu 0 how th ult of cnt conition. Maimum o ca to -.78%. Thi o uction confim th capacitiv ffct. In pactic, olv a loa y RDC (Rolv to Digital Convt). Th input impanc of RDC i vy high. So olv tato cunt a in th o of mico amp (Accoing to ADS80 ataht). Thfo th capacitiv ffct can nglct at pactic. Figu how tt ult in th nominal funcy (4 khz) an 60 µa output cunt (5 nominal cunt of RDC-ADS80). It can n goo agmnt twn calculat an pimntal ult (maimum o i aout.9%). (c) Fig. 0 Output voltag of olv vu tim with 400 Hz citation an 0 ma output cunt imulat -ai voltag () imulat -ai voltag an (c) mau - ai voltag. Tal 3 an Fig. how th compaion of th imulation an pimntal ult that valiat th olv mol an paamt timation mtho. It i oviou that olv i a poition no, o compaion of no output (poition) i impotant. Fo pactical tt w u fom a high pciion mchanical poition no (tycop ) that connct to VF5-HP0 CNC (Comput Numic Contol) Machin. Th olv output i otain fom actangnt of output voltag atio. Figu 3 how th poition output fom imulation, olv an high pciion mchanical poition no (tycop). Compaion of th ult how that th maimum poition o of olv i ±3 Acmin. Thfo th ult valiat th accuacy of popo paamt timation mtho. Sinc popo tup on t n any ta uipmnt an it ha impl tt configuation, thi mtho i not only accuat ut alo impl an fat. Th Tycop i a mchanical gao with high otay uction atio (:n, 500<n<3000). It can ivi otay poition into mall pat. Ianian Jounal of Elctical & Elctonic Engining, Vol. 3, No. &, Jan

9 Achiv of SID () () Fig. Compaion of calculat an mau ult of olv a lctical machiny output voltag (volt) () lativ o (%). Simulation Rolv Output High pciion poition no output (c) Fig. Output voltag of olv vu tim with 4000 Hz citation an 60 µa output cunt imulat -ai voltag () imulat -ai voltag an (c) mau - ai voltag. Tal 3 Compaiion of calculat an mau ul. Output cunt (ma) Funcy (Hz) Output voltag (imulat) Output voltag (mau) Eo (%) Fig. 3 Compaion of calculat angula poition with olv output an tycop output. 5 Concluion In thi pap a nw ynamic an tay tat analyi of uhl olv ha n pnt an a nw appoach a on DC tp voltag citation i pnt an appli to uhl olv tato wining. Stato cunt i mau an cunt cuv i awn. Uing uivalnt cicuit of olv at tay tat, th cunt uation i otain; th cuv i fitt to an ponntial cunt cuv, to tmin 50 Ianian Jounal of Elctical & Elctonic Engining, Vol. 3, No. &, Jan. 007

10 Achiv of SID cofficint an tim contant. By uing known uation, olv paamt a timat. Th pimntal tt fo a finit loa valiat otain ult. Avantag of thi mtho a: Simplicity of configuation Accuacy of th ult Ruction of th tim conuming. Futhmo, tay tat uivalnt cicuit of a uhl olv a pnt a fit tim. Rfnc [] Hanfo L. an N H. P., A Gnal Algoithm fo Sp an poition Etimation of AC Moto, IEEE Tan. Inutial Elctonic, Vol. 47(), pp , F [] Caicchi F., Capponi F. G., Ccimini F., an Solo L., Sinuoial uhl iv with lowcot lina Hall Effct Poition no, IEEE PESC 00, Vol., pp. 7-, 00. [3] Hanlma D. C, Thioau R. E. an Smith D. J., Vaial-luctanc Rolv Dign Guilin, IEEE IECON, Nw Yok, pp , 989. [4] Sun L. Z., Zou J. B. an Lu Y. P., Nw Vaial-luctanc olv fo Roto-poition ning, IEEE confnc, pp. 5-8, 004. [5] Jiuing W., inghan Li an Hong G., Th Analyi an Dign of High-p Buhl Rolv plu R/D Convt Shaft-angl Maumnt ytm, IEEE confnc, pp. 89-9, 000. [6] Maaki K., Kitazawa K., Mimua H., Nii M., Tuchimichi K., Wakiwaka H. an Yamaa H., Magntic fil analyi of a olv with a kw an ccntic oto, Elvi tan. Sno an Actuato, Vol. 8, pp , 000. [7] Maaki K., Kitazawa K., Mimua H., Tuchimichi K., Wakiwaka H., Yamaa H., Coniation on th angula o u to th haft ccnticity an th compnation ffct y hot-cicuit wining on a olv, J. Magn. Soc. Jpn., pp , 998. [8] Munay B. A., Li. W. D., A Digial Tacking R/D Convt with Hawa Eo Calculation Uing a TMS30C4, Fifth Euopan Confnc on Pow Elctonic an Application, pp , 3-6, Sp [9] Yim Ch., Ha I., KO M. S., A Rolv-to-Digital Convtion Mtho fo Fat Tacking, IEEE Tanaction on Inutial Elctonic, Vol. 39, Iu 5, pp , Oct 99. [0] Hanlman D. C., Tchniu fo Impoving Rolv-to-Digital Convion Accuacy, IEEE Tan. on Inutial Elctonic, Vol. 38, No. 6, pp , Dc. 99. [] Ay Company R&D Goup, Pancak Rolv Hanook, Ay.com, civ at 5 Dcm 006. [] Khaui D. A., Tootoonchian F., Dign, Paamt Intification an Simulation of Singl-Pha Rotay Tanfom, 5th Ianian Confnc on Elctical Engining, ICEE007, May 5-7, 007. [3] Wathfo H. H, Bic C. W., Etimation of Inuction Moto Paamt y a Gntic Algoithm, Pulp an Pap Inuty Tchnical Confnc 003 annual, pp. -8, 6-0 Jun 003. [4] Phumiphak T., Chat-Uthai C., Etimation of Inuction Moto Paamt Ba on Fil Tt Coupl with Gntic Algoithm, Poc. of Pow Sytm Tchnology 00, Intnational Confnc on Pow Con. 00, Vol., pp , 3-7 Oct. 00. [5] Matinz L. Z., Matinz A. Z., Intification of Inuction Machin Uing Atificial Nual Ntwok, Poc. of IEEE ISIE 97, Vol. 3, pp , 7- July 997. [6] Kaach N., Chtat B., Aaptiv Nonlina Contol of Inuction Moto Uing Nual Ntwok, Poc. of Phyic an Contol Intnational Confnc 003, Vol. l, pp , 0- Aug., 003. [7] Mack-Kaminka K., Wach P., Etimation of th Paamt of Mathmatical Mol of Suil Cag Inuction Moto, Poc. Of IEEE ISIE 96, Vol., pp , 7-0 Jun 996. [8] Noguchi T., Nakmahachalaint P., Watanakul N., Pci Tou Contol of Inuction Moto with On-Lin Paamt Intification in Coniation of Co Lo, Poc. of Pow Convion Confnc-Nagaoka 997, Vol., pp. 3-8, 3-6 Aug [9] Lani H., Naii Ghiai Z., Tootoonchian F., A Novl P.C. Ba Elctomoto Dynamomty, 3 Intnational Confnc on Tchnical an Phyical Polm in Pow Engining (TPE-006), Gazi Univity, Ankaa, TURKEY, May 9-3, pp. -6, 006. [0] Kau P. C., Analyi of Elctical Machiny, McGaw-Hill i in lctical ngining. Pow & ngy, Ianian Jounal of Elctical & Elctonic Engining, Vol. 3, No. &, Jan

11 Achiv of SID [] Ziay I., Vahi A., Intification of Singl- Pha Inuction Moto Paamt Uing Avag Chag Rpon of Stato Cunt, ICEE 004, Vol., pp.60-64, 004. [] I-Hai Lin P., Mal E. E., Dign of a Ral- Tim Roto Intia Etimation Sytm fo Moto with a Ponal Comput, IEEE Intumntation an Maumnt Tchnology Confnc, IEEE Catalog No. 9CH940-5, pp. 9-96, 99. [3] Ong C., Dynamic Simulation of Elctic Machiny Uing Matla/Simulink, Pntic Hall PTR. Upp Sal Riv, Nw Jy, 998. Davoo Aa-khaui wa on in 965. H ha civ B.Sc. in 990 fom Shaif Univity of Tchnology in Elctonic Eng. an M.Sc. an Ph.D. fom ENSEM INPEL, Nancy, Fanc in 994 an 998 pctivly. H alo wok at UTC in Compin, Fanc ( ). Sinc 000 h ha n a faculty mm of Ian Univity of Scinc an tchnology. Hi ach intt a Pow Elctonic an Moto Contol. machin an no. Fai Tootoonchian ha civ hi B.Sc. an M.Sc. g in Elctical Engining fom th Ian Univity of Scinc an Tchnology, Than, Ian in 000 & 007 pctivly. H ha on ov inutial pojct incluing on national pojct aout lctical machin ov th ya, an hol 5 patnt. Hi ach intt i ign of mall lctomagntic Zaha Naii-Ghiai ha civ h B.Sc. g in Elctical Engining fom th Ian Univity of Scinc an Tchnology, Than, Ian in 004. An h civ th Mat g in Elctical Pow Engining fom th Univity of Than in Ian in 006, gauating with Fit Cla Hono in oth of thm. Sh i cuntly icto of Elctical machiny La. in th Elctical Engining Dpatmnt of Shaif Univity of Tchnology, Than, Ian. H ach intt a ign an moling of lctical machin an iv. 5 Ianian Jounal of Elctical & Elctonic Engining, Vol. 3, No. &, Jan. 007