LQR based Speed Control of BLDC Motors

Transcription

1 G Inrnaonal ournal o Elcrcal and Elcronc Engnrng (G-IEEE) volu 3 Iu 6 un 6 Q bad pd Conrol o BDC Moor Mha M., Awn.B.G udn, Aan proor Elcrcal & Elcronc Dp. Mar Balo collg o Engnrng, hruvananhapura, rala, Inda Abrac h objcv o h papr o copar proranc bwn wo yp o conrollr or BDC oor. BDC oor ar on o h oor yp rapdly ganng populary. h ajor probl n BDC drv ar ha o durbanc ar orgnad n h drv whch wll rduc h ably o h y. Convnonal conrollr ud o conrol h pd o h oor, bu h rpon o h y acd by ady a rror and gv a poor rann rpon. o w u a nar Quadrac gulaor conrollr o rgula h pd o h oor. In h papr Q bad conrollr dgnd and proranc copard wh radonal ID conrollr ung Malab and uln. y word- Q, ID, Malab, BDC oor I. INODUCION Bruhl dc oor ar ganng ground n h ndur pcally n h ara o applanc producon dcn, aronauc, conur and ndural auoaon c. h BDC oor ar ypcally prann agn ynchronou oor, hy ar wll drvn by dc volag and hy ar lcroncally couad oor. o o h advanag o BDC oor ar hr Hghr pd rang, Hghr cncy, Br pd vru orqu characrc, ong oprang l, Nol opraon c.[5]. h rucur o BDC oor lar o ha o a DC oor bu h an drnc nohng bu h abnc o bruh and couaor. In BDC oor couaon don lcroncally and durng h proc roaonal orqu producd by changng h pha currn a rgular nrval. h couaon proc can b don hr by nng h gnal gnrad by a nor aocad wh h nor or by analyzng h bac dvlopd acro h col. nor bad couaon ud n vral applcaon whr h varaon n arng orqu larg or whr a hgh nal orqu rqurd. nor-l conrol plnd n applcaon whr h varaon n orqu l and poon conrol no n ocu[8]. Convnonal ID conrollr algorh pl, abl, ay adjun and hghly rlabl. unng ID conrol parar vry dcul, poor robun; hror, ' dcul o achv h opal a undr ld condon n h acual producon. h ohr yp o conrol hod can b dvlopd uch a nar Quadrac gulaor (Q) opal conrol. h chnqu ud o nd h opal conrollr ha nz a gvn co uncon. h co uncon pararzd by wo arc, Q and, ha wgh h a vcor and h y npu rpcvly. h wghng arc rgula h pnal on h xcuron o a varabl and conrol gnal. On praccal hod o Q and o b dagonal arx. h valu o h ln n Q and rlad o conrbuon o h co uncon. o nd h conrol law, Algbrac cca Equaon (AE) r olvd, and an opal dbac gan arx, whch wll lad o opal rul valuang ro h dnd co uncon oband []. In h papr opal pd conrol o BDC oor wr don ung nar Quadrac gulaor (Q) chnqu. h rul o h hod copard wh radonal ID conrollr. Ung V, () () II. MODEING OF BDC MOO Elcroagnc orqu, (3) u Fg.A ypcal dc oor odl and V d d d d d d d V d IN: ag 7

2 G Inrnaonal ournal o Elcrcal and Elcronc Engnrng (G-IEEE) volu 3 Iu 6 un 6 (4). nd o zro d (5) d. >> 3. >> a laplac ranor,.f wll bco, (6) (4) G( ) v (7) A no load, (8) Fg. BDC oor chac dagra (9) () u qn.(9) n qn. (6) w g, V Mchancal conan 3 (5) Elcrcal conan, (6) hror ranr uncon o bldc oor, 3 () V (7) / G( ) () hror, (3). F By applyng o aupon, ( ) ABE.HE AAMEE OF BDC MOO Araur ranc (oh) Araur nducanc (H).46 Bac conan b.55 Mchancal nra (g/ ).93 Frcon cocn B (N./rad/c).8 IN: ag 8

3 G Inrnaonal ournal o Elcrcal and Elcronc Engnrng (G-IEEE) volu 3 Iu 6 un 6 o h ranr uncon o h BDC oor, () ( ) B B (8) 4.48 G( ) 6.44*.6 Whr h co uncon, = x() () Qx() + u() u()d III. INEA QUADIC EGUAO (Q) nar quadrac rgulaor or Q coonly ud chnqu o nd h a dbac gan or a clod loop y. I h opal rgulaor, by whch h opn-loop pol can b rlocad o g a abl y wh opal conrol and nu co or gvn wghng arc o h co uncon. ha by ung h opal rgulaor chnqu, ha rdo o choc lo or boh dcr- and connuou- y, bcau, n ordr o g a pov- dn cca quaon oluon, hr ar o ara whr h pol canno b agnd. h advanag o Q can gv br proranc o h y by conrollng h oor pd and poon. On h agnud o h conrol acon l ncludd n h u o a o p h nrgy xpndd by h conrol acon l ld. h Q algorh, a cor, ju an auoad way o ndng an appropra adbac conrollr. h dgn o a a dbac BDC oor conrol y bad on a uabl lcon o a dbac y rucur. h ably o BDC oor drv y a ajor concrn. I h a varabl ar nown, hn hy can b ulzd o dgn a dbac conrollr o ha h npu bco U=X. I ncary o aur and ulz h a varabl o h y n ordr o conrol h pd o h BDC oor. h dgn approach o a varabl dbac conrol gv ucn noraon abou h ably o h BDC drv y[]. A dcrpon o h lnar Quadrac gulaor y condrd n h wor how a, A (9) A B B h quaon calld h Algbrac ca Equaon (AE).For a yrc pov-dn arx. h rgulaor gan gvn by: Q h wo arc Q and ar lcd by h dgn ngnr by ral and rror hod. Gnrally pang, lcng a larg valu or Q rqur h valu o o b all. On h ohr hand, lcng a larg valu or, h conrol npu u u b allr o p valu o all. On hould lc valu o Q o b pov dn and o b pov dn. h an ha h calar quany alway pov or zro a ach. h Q & arx und by ral & rror hod. A. Malab crp l nu= [.88]; dn=[ ]; y=(nu,dn) [A,B,C,D]=(nu,dn) w = ; Q = w*c'*c; = [3]; = lqr(a,b,q,) % Our lqr nw y wll b, Alqr = A-B* Blqr = B; Clqr = C; Dlqr = D; [nulqr, dnlqr] = (Alqr,Blqr,Clqr,Dlqr); ylqr = (nulqr,dnlqr) = :.:; gur() p(y,) hold on p(ylqr,) grd on lgnd( 'or y','lqr y' ) hold o Fro h w g, =[ ] = IV IMUAION AND EU h Q conrollr uln odl how n h gur.3.h odl ha h p npu gnal. IN: ag 9

4 pd n rp pd n rp pd n rp G Inrnaonal ournal o Elcrcal and Elcronc Engnrng (G-IEEE) volu 3 Iu 6 un Fg.3 Q conrollr or BDC oor (c) 35 Fg.6 oupu wavor by ung ID conrollr (c) Fg 4 Oupu wavor o Q conrollr Fg.7 cobnd ulaon ung ID and Q h uln odl ung ID conrollr hown n h gur.5 Fro h ulaon w g h oupu wavor o boh Q and ID conrollr and ay o copar h oupu Fg.5 ID conrollr or BDC oor (c) Fg. 8 Cobnd oupu wavor ung ID and Q IN: ag

5 G Inrnaonal ournal o Elcrcal and Elcronc Engnrng (G-IEEE) volu 3 Iu 6 un 6 ABE. HE EFOMANCE CHAACEIIC MEHOD lng %ovrhoo ID conrollr Q conrollr c 53. c.55 V.CONCUION In h papr a a varabl dbac y wa dgnd or BDC drv o achv h drd y rpon. Fro h ulaon rul clar ha h Q conrollr ha horr lng and vry all ovrhoo han ha o h ID conrollr. o h coparon bwn h pd conrol o Bruhl DC oor by lnar quadrac rgulaor chnqu and radonal ID conrollr clarly how ha h lnar quadrac rgulaor chnqu gv br proranc han h ohr on. EFEENCE [] Nhl rpah, ahwar ngh Opzaon pd Conrol o DC paraly Excd Moor Ung unng Conrollr o nar Quadrac gulaor (Q) chnqu Inrnaonal ournal o Engnrng rnd and chnology (IE), Volu 9 Nubr - Mar 4. [] hnu C., ya Mary Franc, pd Conrol o BDC Moor ung a und Q Conrollr Inrnaonal ournal o cnc Engnrng and arch (IE) IN (Onln): , Volu 3 Iu 8, Augu 5 [3] uba M..Al-Mulla Huad ulaon o Opal pd Conrol or a DC Moor Ung nar Quadrac gulaor (Q) ournal o Engnrng, Nubr 3 Volu 8 arch. [4] Vnod ngh al, A..andy Modlng and roranc Analy o ID Conrolld BDC Moor and Drn ch o WM Conrolld BDC Moor Inrnaonal ournal o cnc and arch ublcaon, IN 5-353, Volu 3, Iu 4, Aprl 3. [5] Mcrochp chnology Incorporad 3, padaraja Ydaal, Bruhl DC oor undanal [6] Maloh urnalal,unl uar, Dvlopn O Mahacal Modl and pd Conrol o BDC Moor Inrnaonal journal o Elcrcal and Elcronc Engnr, IN-3-55(E), Volu 7, Iu, un 5 [7]. C. Balo and.. Mao, Dgn o I and ID Conrollr Wh rann roranc pccaon, IEEE ran. Educaon, pp , vol. 45, Iu No. 4,. [8] Harh Mohan, ya, Modlng and Conrol o DC Choppr Fd Bruhl DC Moor Inrnaonal arch ournal o Engnrng and chnology (IE), Volu: Iu: 3, un-5., IN: ag