PERFORMANCE IMPROVEMENT OF THE INDUCTION MOTOR DRIVE BY USING ROBUST CONTROLLER

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1 PEFOMANCE MPOEMEN OF HE NDUCON MOO DE BY USNG OBUS CONOE S. SEAA, PG Schola,. GEEHA, ctu, N. DEAAAN, Aitant Pofo Abtact -: h tanint pon of th induction oto i obtaind by uing it d-q fnc odl. h tanint pon i ipovd by uing optial contol tchniqu bcau of th popty of bt poibl contol. By olving icatti quation, a contoll gain ati i dvlopd uch that th pfoanc ind i iniu. hi gain ati will giv fdback contol law. h contoll will giv contol ignal accoding to thi law. h output i fd back and th pon i analyzd. hu th tanint pon i ipovd. hi contoll i obut againt ditubanc nd t nduction oto, Q, Stability NOMENCAUE, Stato voltag and cunt pac vcto Stato flu pac vcto, oto cunt and flu pac vcto d, q Stato voltag in d-q otating f. fa d, q Stato cunt in d-q otating f. fa ψ d, ψ q oto flu in d-q otating f. fa d, q Stato cunt in d-q oto flu f. fa ω oto pd (ad/), Stato itanc and lf inductanc oto lf inductanc τ oto lctical i contant Magntic inductanc P Nub of pol pai otal oto intia contant (Kg ) F Daping cofficint (N) l oad toqu (N) Elctoagntic toqu (N) σ Cofficint of dipion Synchonou pd (ad/) h autho a with th Dpatnt of Elctical Engining, Govnnt Collg of chnology, Coibato, ndia. NODUCON nduction achin hav bn th ot widly ud achin in fid-pd application fo aon of cot, iz, liability and fficincy. Howv, bcau of th involvd odl high nonlinaiti, thy qui uch o copl thod of contol, o pniv and high atd pow convt than DC and pannt agnt achin. Nowaday, a a conqunc of apid advanc in pow lctonic tchnology, vcto contol tatgy bad lctical ac div hav gd a a powful tool fo high pfoanc contol of nduction achin. hi contol tatgy can povid th a pfoanc fo an invt divn nduction achin a i achivd fo a paatly citd DC achin. n thi thi th autho intoduc a nw contoll calld ina Quadatic gulato which i obut againt tnal ditubanc and povid cllnt pfoanc ipovnt with th ipovnt of tability agin. h yt i iulatd uing Matlab and it chaactitic and fatu a tudid in thi thi. d-q MODE OF HE NDUCON MOO A two pha d-q odl of an nduction achin otating at th ynchonou pd i intoducd which will hlp to cay out th dcoupld contol concpt to th induction achin. hi odl can b uaizd by th following quation d j () d j () h tato and oto flu a givn by th following lation: (3)

2 (4) n quation to 4, th voltag, cunt and flu pac vcto a function of th coponding th-pha vaiabl [3]. A an apl, th tato cunt pac vcto i linkd to th coponding th pha cunt by th following lation: c b a a a 3 / (5) Wh a = j /3. h poducd lctoagntic toqu i givn by p 3 (6) Figu. fnc fa and pac vcto pntation Uing th d-q coodinat yt, a illutatd in Figu, and paating th achin vaiabl tat vcto into thi al and iaginay pat, th wll-known nduction oto odl pd in t of th tat vaiabl i obtaind fo quation to 6, and i givn by: q d l q d d q q d q q d d q d q d q d q d q d q d P F p d (7) n (7), th cofficint of dipion σ i givn by: A hown in Figu, th d-ai i alignd with th oto flu pac vcto. Und thi condition w hav; ψ q = and ψ d = ψ. Conquntly, th induction oto odl tablihd in th oto flu fild coodinat i thn givn by th quation 9 to. q d l q d q d q d q d P F p d q p () d () q () n odinay u, only tato voltag, cunt and oto pd a availabl fo aunt. n thi ca, th d-q tato voltag and cunt a obtaind fo th coponding α β tationay fnc fa vaiabl though an appopiat tanfoation involving oto flu pac vcto angl θ, a hown in Figu. hi tanfoation i givn by: q d co in in co... (3) n quation 3, "" i a voltag, a cunt o a flu. A ntiond bfo, θ i th oto flu pac vcto angl. n dict vcto contol, th oto flu i availabl fo aunt o i tiatd fo aud tato voltag and cunt. h oto flu angl i thn givn by: a tan h oto flu aplitud i obtaind by olving quation, and it patial poition i givn by:

3 q h ndict vcto contol tatgy can now atifactoily b achivd inc both aplitud of oto flu vcto and it patial poition a known. A in DC achin, th toqu and th flu a contolld indpndntly: h lctoagntic toqu i contolld by q (toqu poducing cunt), and th flu i contolld by d (flu poducing cunt). Q QUADAC EGUAO A ina Quadatic gulato (Q) i ud to in th SFB K uch that th Pfoanc nd i iniizd. t co und Optial Contol. t i calld o bcau in vy contol tp th pfoanc ind i ducd to a iniu. Futho, it ha a copaabl high obutn againt paat chang. A yt can b pd in tat vaiabl fo a. (4) A Bu n With ( t), u( t). h initial condition i (). W au h that all th tat a auabl and k to find a tat-vaiabl fdback (SFB) contol. (5) u K hat giv diabl clod-loop popti. h clod loop yt uing thi contol bco. (6) ( A BK) Bu Ac Bu With Ac th clod-loop plant ati and u(t) th nw coand input. h output atic C and D a not ud in SFB dign. f th i only on input o that =, thn Ackann foula giv a SFB K that plac th pol of th clod-loop yt a did. Howv, it i vy inconvnint to pcify all th clod-loop pol, and a tchniqu i ndd that wok fo any nub of input. h optial contoll qui lat contol ngy fo contol th yt. Sinc any natually occuing yt a optial, it ak n to dign an-ad contoll to b optial a wll. o dign a AFB that i optial, a t pfoanc ind (P) i to b conidd. Q v v Subtituting th SFB contol into thi yild ( Q k k) (7) (8) h objctiv in optial dign i to lct th SFB K that iniiz th pfoanc ind. h pfoanc ind can b intptd a an ngy function, o that aking it all kp all th total ngy of th clodloop yt. f both th tat (t) and th contol input u (t) a wightd in, o that if i all, thn nith (t) no u (t) can b too lag. f i iniizd, thn it i ctainly finit, and inc it i an infinit intgal of (t), thi ipli that (t) go to zo a t go to infinity. hi in tun guaant that th clod-loop yt will b tabl. h two atic Q (an n n ati) and (an ati) a lctd by th dign ngin. Dpnding on how th dign paat a lctd, th clod-loop yt will hibit a diffnt pon. Gnally paking, lcting Q lag an that, to kp all, th tat (t) ut b all. On th oth hand lcting lag an that th contol input u (t) ut b all to kp all. hi an that lag valu of Q gnally ult in th pol of th clod-loop yt ati Ac = (A BK) bing futh lft in th -plan o that th tat dcay fat to zo. On th oth hand, th lag an that l contol ffot i ud, o that th pol a gnally low, ulting in lag valu of th tat (t). On hould lct Q to b poitiv i-dfinit and to b poitiv dfinit. hi an that th cala quantity Q i alway poitiv o zo at ach ti t fo all function (t), and th cala quantity u u i alway poitiv at ach ti t fo all valu of u (t). hi guaant that i wll-dfind. n t of ignvalu, th ignvalu of Q hould b non-ngativ, whil tho of hould b poitiv. f both atic a lctd diagonal, thi an that all th nti of ut b poitiv whil tho of Q hould b poitiv, with poibly o zo on it diagonal. Not that thn i invtibl. h u of ina Quadatic gulato (Q) i to in th SFB K uch that it iniiz th 3

4 Pfoanc nd. h wod gulato f to tack pobl, wh th objctiv i to ak th output follow a pcibd (uually nonzo) fnc coand. o find th optial fdback K it i pocdd a follow. Suppo th it a contant ati P uch that d( P) ( Q k k) hn, ubtituting into quation (7) yild, (9) d( P) () () P() Wh it i aud that th clod-loop yt i tabl o that (t) go to zo a ti t go to infinity. Equation () now ipli that i now indpndnt of K. t i a contant that dpnd only on th auiliay ati P and th initial condition. Diffntiating (7) and thn ubtituting fo th clodloop tat quation (4) it i n that (7) i quivalnt to ( A P PA Q k k) () c c inial valu of th P uing thi gain i givn by (), which only dpnd on th initial condition. hi an that th cot of uing th SFB (4) can b coputd fo th initial condition bfo th contol i v applid to th yt. h dign pocdu fo finding Q fdback K i: Slct dign paat atic Q and Solv th algbaic iccati quation fo P Find th SFB uing h ati Q and can b found out by tial and o thod o uing GA tchniqu. h a vy good nuical pocdu fo olving th AE. h MAAB outin that pfo thi i nad lq (A, B, Q, ).h Q dign pocdu i guaantd to poduc a fdback that tabiliz th yt a long a o baic popti hold. Q HEOEM: t th yt (A, B) b achabl. t b poitiv dfinit and Q b poitiv i-dfinit. hn th clod loop yt (A-BK) i ayptotically tabl. Not that thi hold gadl of th tability of th opn-loop yt. call that achability can b vifid by chcking that th achability ati ha full ank n. t ha bn aud that th tnal contol v(t) i qual to zo. Now not that th lat quation ha to hold fo vy (t). hfo, th t in backt ut b idntically qual to zo. hu, pocding it i n that. X=AX+BU C Y=CX A P PA Q k k k B P PBk () hi i a ati quadatic quation. Eactly a fo th cala ca, on ay coplt th qua. hough thi pocdu i a bit coplicatd fo atic, uppo if -K k B P (3). Figu. Syt Block Diaga hn, it ult in A P PA Q PB B P (4) hi ult i of t ipotanc in odn contol thoy. Equation (4) i known a th algbaic iccati quation (AE). t i a ati quadatic quation that can b olvd fo th auiliay ati P givn (A, B, Q, ). hn, th optial SFB gain i givn by (3). h SMUAON ESUS Siulation, uing Matlab-Siulink oftwa packag, hav bn caid out to vify th ffctivn of th popod contol thod. h ult a hown in figu 3. 4., & 5. Figu 3 how th unit tp pon bfo and aft applying contoll. Figu 4 how th cunt cuv id and iq of th oto div. Figu 5 how th location 4

5 of pol bfo and aft applying contoll. t alo how how th tability i nhancd by odifying th pol location. Figu 5. Pol location bfo and aft applying Q Figu 3. pon of yt bfo and aft applying Q t i alo obvd that tability i alo analyzd aft applying th contoll. h ult how that th agin of tability alo inca by incopoating th contoll. h tability tt a caid out uing h-infinity dfinition and yapunov tt fo poitiv dfinitn. CONCUSON h iulation of Q contolld induction oto div i uccfully iplntd in thi pap. h application of th contoll and it pon ipovnt contibuting to th tability nhancnt i tudid. hi pap can b futh tndd by copaing thi contoll pfoanc with th iting contolling thod lik P and o on. hi pap can b futh tndd to oth typ of div alo nhancing th pfoanc. EFEENCES Figu 4. pon cuv of id, iq and phid. Fata Gubuz, Eyup Akpina, Stability Analyi of a clod-loop contol fo a Pul Wih Modulatd DC Moto Div", ukih ounal of Elctical Engining, vol., No.3,.. Bial K. Bo," Modn Pow Elctonic & AC Div, Paon Education,. 3. Katuhiko Ogata, Modn Contol Engining, Pntic-Hall of ndia Pvt. td,. 4. Dign and Analyi of Contol Syt, Athu G.O. Mutabaa, CC P, ondon, ina Contol Syt Engining, Moi Dil, McGaw Hill intnational dition,

6 6. Modn Contol Dign with Matlab and Siulink, Ahih wai, ohn Wily and Son td.,. APPENDX nduction Moto Paat Un () = 44 (Stato lin voltag) P n (hp) = (Noinal output pow) (Ω) =.95 (Ω) =.75 (H) = 6.5 (H) = 6.4 (H) = 6 f (Hz) = 6 p = (kg. ) = 5 6