CHAPTER 6 SPEED CONTROLLER DESIGN FOR AN INDIRECT VECTOR CONTROLLED INDUCTION MOTOR DRIVE

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1 40 CHAPER 6 SPEED CONROER DESIN FOR AN INDIREC VECOR CONROED INDUCION MOOR DRIVE 6. INRODUCION Nowdy, conqunc o th potnt pog n pow lctonc nd co coputng, th contol o AC lctc chn h n condbl dvlopnt nd th poblty o ndutl pplcton (Hzzb t l 005). h nducton oto, known o t obutn, ltvly low cot, lblty nd cncy, th objct o vl ch wok. Howv th contol o nducton oto dv pnt dcult bcu o t hgh non-lnty nd t coupld tuctu (Mnou t l 004). h tchnqu known vcto contol, t ntoducd by Blchk nd H, h ultd n lg chng n th ld o lctcl dv. h bcu, wth th typ o ppoch, th obut nducton oto cn b contolld o gvng btt ponc. h contol ttgy cn povd th ponc obtnd o ptly xctd DC oto (Bouhn nd Hzzb 006, Mzn t l 008). Nxt, Inducton oto th ot ud dv n ll th ndutl pd contol pplcton. In th gd dgn o pd contoll o jo pt o th oto contol yt. But n nducton oto hgh od, ultvbl, nonln, unctn yt whch to b vy dcult to contol. In pctc ny nonln poc ppoxtd by

2 4 ducd od odl only, pobly ln whch clly ltd to th undlyng poc chcttc. In th gd nw odl od ducton tchnqu ud to obtn th quvlnt ducd od odl o th nvt d ndct vcto contolld nducton oto dv. Syt odl ncy o tunng contoll cocnt n n ppopt nn (.g., pcnt ovhoot, ttlng t). PI contoll th ot coonly ud contol lgoth n ndutl dv. h n on t ltvly pl tuctu whch cn b ly undtood nd plntd n pctc nd tht ny ophtctd contol ttg uch odl pdctv contol, bd on t. In pt o t wdpd u th xt no gnlly ccptd dgn thod o th contoll (Wng nd Sho 000). h ln gulto dpnd only on two pt, nly th popotonl gn ( p ) nd th ntgl gn ( ). In th wok, th ntl vlu o contoll cocnt obtnd o ducd od odl o th yt wth th hlp o pol zo cncllton tchnqu. h obtnd contoll cocnt tund tll th dgn pccton t out. h tund contoll connctd wth th ognl yt nd th clod loop pon obvd o tblzton poc. Svl dgn tchnqu ud to obtn pct contoll chcttc ung tcl ntllgnt ch nd ptcl w tchnqu (Ngj t l 008). h dgnng nclud nw contol ch o bttnt o xtng contoll by tunng th. On uch popul xtng convntonl thod o tunng Zgl Nchol (Z-N).h thod ppld vn whn th tn uncton o th yt unknown, but t only n ppoxtd tunng thod whch do not gv optzd gn vlu. o ovco th dwbck o Z-N thod tcl ntllgnc tchnqu lk Fuzzy ogc (F), Nul Ntwok (NN), ntc Algoth (A) w ntoducd th oln o onln (Aun Dy t l 009). A ch gv povd pon und nol condton o vcto contolld nducton oto dv (hnn nd Bhdwj 99).

3 4 h A thod hv bn ployd uccully to olv coplx optzton pobl. h u o A thod n th dtnton o th dnt contoll pt pctcl du to th t convgnc nd onbl ccucy (W t l 00). h pt o th PI contoll dtnd by th nzton o n objctv uncton. h gol o th wok to how tht by th optzton o th pt o th PI contoll, nw cl o optzton cn b chvd. h cn b n by copng th ult o th Modl Od Rducton (MOR) tchnqu bd PI contoll ung gntc lgoth tund gn nd th convntonl Sytc Optu (SO) ppoxton thod bd PI contoll. 6. INDIREC VECOR CONROED INDUCION MOOR DRIVE MAHEMAICA MODE Vcto (Fld ontd) contol wdly ud n nduty o hgh ponc IM dv th ponc ptly xctd DC oto. H knowldg o ynchonou ngul vlocty otn ncy n ph tnoton to chv voubl dcouplng contol btwn oto toqu nd oto lux, th on ud o ptly xctd DC oto. h don by on o th two typ o vcto contol,.., dct o ndct vcto contol. Both th thod hv bn plntd n ndutl dv donttng ponc utbl o wd ng o tchnologcl pplcton. But IM contolld ponc tll ctd by unctnty uch chncl pt vton, xtnl dtubnc nd untuctud unctnty du to non dl ld ontton n tnnt tt. In th cton th ndct vcto contol nducton oto pt dvd o th dync quton o th nducton chn n th ynchonouly ottng nc. o ply th dvton, cunt ouc nvt ud. In tht c, th tto ph cunt v nput. Hnc th tto dync cn b nglctd. In tun th cn ld to ottng th tto quton o uth condton.

4 4 I th oto lux lnkg ud vbl thn th oto ccut quton o th nducton chn bco R p 0 (6.) q q l d R p 0 (6.) d d l q wh l (6.) h oto lux lnkg xpon cn b gvn q d (6.4) q d q (6.5) d wh R = oto tnc p ph = gntzng nductnc p ph = oto nductnc p ph d to tto d =`dct x oto cunt q = qudtu x oto cunt p = dntl opto d/dt. l = lp pd n d/c, = lctcl tto pd n d/c. = lctcl oto pd n d/c d = dct x oto lux lnkg nd q = qudtu x oto lux lnkg

5 44, lo known th oto luxlnkg pho ud to b on th dct x to duc th nub o vbl n th quton by on. Moov t copond wth th lty tht th oto lux lnkg ngl vbl. Hnc lgnng th d x wth oto lux pho yld d (6.6) q 0 (6.7) p 0 (6.8) q nw oto quton Subttutng quton (6.6) to (6.8) n (6.) nd (6.) cu th R 0 (6.9) q l R p 0 (6.0) d h oto cunt n t o th tto cunt dvd o Equton (6.4) nd (6.5) q q (6.) d d (6.) Subttutng o d nd q x oto cunt o Equton (6.) nd (6.) nto quton (6.9) nd (6.0), th ollowng obtnd. p (6.) l t tr. (6.4)

6 45 wh d (6.5) q (6.6) (6.7) R. t P (6.8) h q nd d x cunt lbld toqu cunt ( ) nd lux cunt ( ) poducng coponnt o th tto cunt pho pctvly. dnot th oto t contnt. h Equton (6.) bl th ld quton n ptly xctd dc chn who t contnt uully on th od o cond. kw th nducton oto oto t contnt lo on th od o cond to b notd. Slly by th ubttuton o th oto cunt o Equton (6.) nd (6.) nto th toqu xpon, th lctogntc toqu dvd P d q q d P d q t q t (6.9) wh th toqu contnt t dnd t P (6.0) h lctogntc toqu o th nducton oto popotonl to th poduct o th oto lux lnkg nd th tto q x cunt. h bl th gp toqu xpon o dc oto whch popotonl to th poduct o th ld lux lnkg nd th tu cunt. I th oto lux lnkg ntnd contnt thn th toqu ply popotonl to th toqu poducng coponnt o th tto cunt n th c o th

7 46 ptly xctd dc chn wth tu cunt contol wh th toqu popotonl to th tu cunt whn th ld cunt contnt. Sl to th dc chn tu t contnt th oto t contnt o th od o w llcond. h t contnt o th toqu cunt povd to b lo on th od n lt cton nd qul to th tto tnnt t contnt. h oto lux lnkg nd gp toqu quton gvn n Equton (6.4) nd (6.9) pctvly, coplt th tnoton o th nducton chn pt nto n quvlnt ptly xctd dc chn pt o contol pont o vw. h tto cunt pho whch th pho u o th d nd q x tto cunt n ny ; t gvn by q d (6.) nd th dq x to bc ph cunt ltonhp obtnd o q d co n co n co n b c (6.) whch copctly xpd nd qd bc (6.) qd q d t (6.4) t bc b c (6.5) co co co (6.6) n n n wh, b nd c th th ph tto cunt.

8 47 It known tht th lnt n th tx conuodl. h lctcl ld ngl n th c tht o th oto lux-lnkg pho nd obtnd th u o th oto nd lp ngl. l (6.7) nd th lp ngl obtnd by ntgtng th lp pd nd gvn l ldt (6.8) Futh th thtcl odl ud to dgn th pd contoll o n ndct vcto contolld nducton oto dv. 6. SPEED CONROER DESIN USIN CONVENIONA SYMMERIC OPIMUM MEHOD h dct vcto contol thod o nducton oto now dy pobl by dcouplng nonln contoll t pncpl nd plntton vy uch l. h lo pplcbl to ndct vcto contol whch h d pobl th ndpndnt contol o ld lux nd toqu o th nducton chn. oqu contol nd pd contol o nducton chn quntly plntd by ndut n lg nub o pplcton. Fo pd gulton o nducton oto whch nd nuou pplcton ncludd n th pd contol ccut thn th dgn o th pd contoll o potnc. Fo pd contol pplcton th pd gnl condd n th out loop o th popod contol yt. An nlytcl thod ung th tn uncton condd n th dgn o th pd contoll.

9 48 h vcto contoll od th nducton oto dv nto ln contol yt pctv o th gntud o th nput gnl whn th lux lnkg ntnd contnt nd hnc th bco l to ptly xctd dc oto dv n ll pct nd k th nly pl bd th dvlopnt o th block dg wll ynth o pd contoll. h cton ndct tp by tp th yttc dvlopnt o th tn uncton o th pd contolld ndct vcto contolld nducton oto dv. Sl dvton pobl o th dct vcto contoll by dvng block dg o th yt. Bd on th tn uncton th pd contoll dgnd by ung ytc optu thod. Sytc optu otn ud to ntn th unoty o th pd contoll dgn o ll c nd dc dv yt n th wok. 6.. Block Dg Dvlopnt h tn uncton o th vou ubyt uch th nducton chn, nvt, pd contoll nd tht o dbck tn uncton dvlopd tp by tp by howng th block dg o ndct vcto contolld chn. By block dg ducton tchnqu th ovll block dg o th nducton oto dv obtnd. h n ovlp btwn toqu cunt dbck loop nd nducd dbck loop. h ovlp dcoupld gn by block dg ducton tchnqu, kng th nn cunt loop totlly ndpndnt o th oto chncl tn uncton. h ppoch lnd tl to pl ynth o th cunt contoll. h pd contoll o th ndct vcto contolld nducton oto dv cd out by th ky upton o contnt oto lux lnkg. h upton ld to

10 49 contnt (6.9) p 0 (6.0) h tto voltg quton o th oto V ( R p) p (6.) q q d q d V ( R p) p (6.) d q d q d Fo th vcto contoll th ollowng ltonhp o th oto q nd d x lux lnkg d u o to ct th tto voltg quton q q (6.) d d (6.4) Subttuton o th oto cunt nto th tto voltg quton ult n V ) q ( R p q d (6.5) V ) d ( R p d d p (6.6) tto cunt contnt n tdy tt nd tht th d x tto cunt n th ynchonou. It dvtv lo zo gvng th ollowng. d (6.7) p 0 (6.8) d

11 50 h toqu coponnt o th tto cunt th q x cunt n th ynchonou whch gvn by q (6.9) Subttutng th quton (6.7), (6.8) nd (6.9) nto th q x voltg Equton (6.5) nd (6.6) gv q p R V ) ( (6.40) wh gvn by (6.4) Subttutng o gv th q x tto voltg n ynchonou nc q p R p R V ) ( (6.4) h cond tto quton do not qu th oluton o th whch wll yld tht th vbl und contol n th yt. h tto quncy pntd l R (6.4) h lctcl quton o th oto obtnd by ubttutng o o (6.4), l q p R V ) ( ) ( R p R ) ( ) (

12 5 p R R ) ( (6.44) o whch th toqu coponnt o th tto cunt dvd q q V p R R V ) ( (6.45) wh R R R (6.46) R (6.47) R (6.48) Fo th block whch convt th voltg nd pd dbck nto th toqu cunt, th lctogntc toqu wttn t (6.49) wh th toqu contnt dnd t P (6.50) h lod dync cn b pntd, gvn th lctogntc toqu nd lod toqu tht condd to b ctonl o th ptcul c l t B B dt t d J (6.5)

13 5 whch n t o th lctcl oto pd dvd by ultplyng both d by th p o pol. d t J dt B P t B l (6.5) nd hnc th tn uncton btwn th toqu nd th pd poducng cunt dvd ( ) ( ) (6.5) wh P B t t Bt B B l J (6.54) B t h nvt dlv th tto q x voltg wth cond nput tht th o btwn th toqu cunt nc nd th toqu cunt dbck. h cunt o pld though cunt contoll. h gn o th cunt contoll condd unty h but ny oth gn cn b ncopotd n th ubqunt dvlopnt. h nvt odld gn, n wth t lg o n. h gn obtnd o th dc lnk voltg to th nvt, V dc nd xu contol voltg, V c V n 65 V dc 0. (6.55) c h contnt 0.65 h ntoducd to ccount o th xu pk undntl voltg obtnbl o th nvt wth gvn dc lnk voltg. h toqu cunt o tctd wthn th xu contol

14 5 voltg, V c. h t lg n th nvt qul to th vg c wtchng cycl t..., hl th pod nd xpd n t o th PWM wtchng quncy n c (6.56) A uul Popotonl plu Intgl (PI) contoll ud to poc th pd o btwn th pd nc nd ltd pd dbck gnl. h tn uncton o th pd contoll gvn ( ) ( ) (6.57) wh nd th gn nd t contnt o th pd contoll pctvly. h dbck gnl cunt nd pd whch pocd though th t od lt. hy gvn n th ollowng. Vy lttl ltng coon n th cunt dbck gnl. h gnl gn dnotd by ( ) c H c (6.58) gvn by h pd dbck gnl pocd though t od lt ( ) H ( ) (6.59) ( ) wh H th gn nd th t contnt o th pd lt.

15 54 h pd lt ccpt th pd gnl nput nd poduc. h coplt th ncluon o ll th ubyt o th vcto contolld nducton oto dv wth contnt oto lux lnkg. By ncopotng Equton (6.44), (6.45), (6.47) nd o (6.55) to (6.59) wth th chncl pdnc o th lod, pd lt, pd contoll nd loop, th block dg hown n Fgu 6. dvd. Fgu 6. Block dg o th vcto contolld nducton oto wth contnt oto lux lnkg 6.. Block Dg Rducton h pd gnl pcko pont o th lctcl yt cn b ovd to th pont ultng n th dg hown n Fgu 6. () whch cn b uth pld n Fgu 6. (),wh th cunt clod loop tn uncton ( n ( ) (6.60) n b H c n ) wh th contnt gvn by (6.6) b

16 55 () (b) (c) (d) Fgu 6. Block dg Rducton o Fgu 6.

17 Cunt oop n Functon * h thd od cunt tn uncton, cn b * H ppoxtd to t od tn uncton ollow. n uully nglgbl copd to, nd nd n th vcnty o th coov quncy th ollowng ppoxton vld. c n (6.6) ( )( ) ( ) (6.6) n n wh n Subttuton o th nto () ult n n ( ) ( ) (6.64) ( )( ) H ( ) b c n whch wttn copctly wh n ( ) ( ). (6.65) ( )( ) b b, 4c (6.66). b H c n c b H c n

18 57 h tn uncton () ducd by ung th ct tht nd by condng th coov quncy th ollowng ppoxton vld. (6.67) (6.68) Subttutng Equton (6.67) nd (6.68) to Equton (6.65) gv n ( ). (6.69) ( ) ( ) wh nd th gn nd t contnt o th pld cunt loop tn uncton gvn by n (6.70) (6.7) h odl ducton o th cunt loop ncy to ynthz th pd contoll. h loop tn uncton o th pd gvn by th ubttuton o th pld tn uncton o th cunt loop hown n Fgu 6. () nd by cobnng ll th block to obtn th nl block dg hown n Fgu 6.5 (v) Spd Contoll Dgn h loop tn uncton o th pd loop gvn by H ( ) g (6.7) ( )

19 58 wh ppoxton + d nd th cunt loop t contnt nd pd lt t contnt cobnd nto ngl t contnt. (6.7) H g (6.74) h tn uncton o th pd to t cond dvd ( ) (6.75) ( ) H * g g nd by qutng th cocnt o th dnonto polynol to th cocnt o th ytc optu uncton nd cn b vlutd. h ytc optu uncton o dpng to o gvn by ( ) (6.76) ( ) H ( ) 8 6 * o whch th pd contoll contnt dvd 6 (6.77) 4 9 g (6.78)

20 59 h popotonl nd ntgl gn o th pd contoll pctvly obtnd p 4 9 g (6.79) (6.80) 7 g h ovhoot o th pd on th dv cn b uppd by cnclng th zo wth th ddton o pol (+ ) n th pth o th pd cond. h ollowng xpl condd to tt th vldty o th vou upton d n th dvton o th pd contoll dgn Expl gvn blow. h nducton oto wth th nvt nd lod pt I = 6A, c = 000 Hz, B t = 0.05, H = 0.05, = 0.00, V c = 0V, J = kg-,v dc = 85 V, H c = 0. V/A. Sytc optu bd pd contoll to b dgnd nd th vldty o th upton n dgn vd ollow. Soluton Atu tnc, R R R Atu contnt,. 885 R Atu nductnc, H

21 60 Atu t contnt, R 0.004c Mchncl t contnt, J B t 0.c P t Mchncl contnt, 6. 4 B t P oqu contnt, t.. I P t Inducd contnt, b.. I. 967 v B t d / c n c c c n V 0.65 v dc c 8.55 V V n c c 0.7c Appoxtd cunt loop R n c Spd contoll g H 04.0

22 c c 9 g Popotonl gn, p Intgl gn, obtnd. Wth th clcultd vlu, th ollowng tn uncton Exct cunt loop tn uncton, ( ) H n c ( ) n ( ) ( ) ( ) wh n ( ) n n ( ) ( ) ( ) ( ) ( ) ( ) b

23 6 h Spld cunt loop tn uncton ( ) nd xct pd loop tn uncton ( ) ( ) * ( ) ( ) ( ) ( ) wh ( ) ( ).. ( ) ( ) ( ) H Spld pd loop tn uncton gvn by It obtnd o pld cunt loop tn uncton nd ( ) ( ) ( ) ( ) wh ( ) (. ( ) ). ( ) All th tn uncton coputd nd th gn, ph plot nd tp pon gvn n Fgu 6. to 6.8. Evn though th to b gncnt dcpncy btwn th gn o th pld nd

24 6 th xct cunt loop tn uncton not tht th ph dntcl n th quncy ng o ntt. h dcpncy du to th ppoxton o th cunt loop o thd od to t od h hdly ctd th ccucy o th pd loop tn uncton, clly n o th gn nd ph plot. h jut th upton d n vou ppoxton. Fo tp pon plot o th xct nd pld cunt loop nd pd loop tn uncton th t don pccton ltd n bl 6. nd bl 6., pctvly Fquncy pon o xct nd pld cunt loop xct pld Fquncy (d/c) Fgu 6. Fquncy pon o xct nd pld cunt loop

25 64 45 Ph plot o xct nd pld cunt loop xct pld Fquncy (d/c) Fgu 6.4 Ph plot o xct nd pld cunt loop Stp Rpon o xct nd pld cunt loop.5.5 xct pld (c) Fgu 6.5 Stp pon o xct nd pld cunt loop

26 65 bl 6. Copon o t don pccton o cunt loop Sttgy o R t (t ) n Sttlng t % Pk Pk t n Contol c (t ) n c Ovhoot pltud c Exct Cunt loop Spld cunt loop Copon o pd loop quncy pon wth xct nd pld cunt lppo xct pld Fquncy (d/c) Fgu 6.6 Copon o pd loop quncy pon wth xct nd pld cunt loop

27 66 Copon o pd loop ph plot wth xct nd pld cunt lppo 0 xct pld Fquncy (d/c) Fgu 6.7 Copon o pd loop ph plot wth xct nd pld cunt loop 0 5 Copon o pd loop tp Rpon wth xct nd pld cunt loop xct pld (c) Fgu 6.8 Copon o pd loop tp pon wth xct nd pld cunt loop

28 67 bl 6. Copon o t don pccton o pd loop Sttgy o R t (t ) Sttlng t (t ) % Pk Pk t Contol n c n c Ovhoot pltud n c Exct pd loop Spld pd loop SPEED CONROER DESIN BY MODE ORDER REDUCION MEHOD WIH ENEIC AORIHM h dgn o pd contoll o nvt d Vcto contolld Inducton Moto (VCIM) dv qut dcult bcu t h pctclly coplxty n thtcl odl nd o hgh od. h dgn o contoll o hgh od yt nvolv coputtonlly dcult nd cubo tk. Hnc th nd o th dgn o hgh od yt though ducd od odl. H, odl od ducton tchnqu ud o ducng hgh od odl nto ducd od odl. h contoll dgnd on th b o ducd od odl hould ctvly contol th ognl hgh od yt. A contoll dgnd o th ducd cond od odl to t th dd ponc pccton. h contoll ttchd wth th ducd od odl nd clod loop pon obvd. h pt o th contoll tund ung gntc lgoth optzton tchnqu to obtn pon wth dd ponc pccton. h tund contoll ttchd wth th ognl hgh od yt nd th clod loop pon obvd o tblzton poc.

29 68 H, PI typ contoll ud to coct th oto pd. h popotonl t do th job o t ctng cocton whch wll poduc chng n th output quckly th o. h ntgl cton tk nt t to ct but h th cpblty to k th tdy tt pd o zo. A uth nnt u th t o chng o o pd to pply n ddtonl cocton to th output dv. h known Dvtv ppoch. It cn b ud to gv vy t pon to uddn chng n oto pd. In pl PID contoll t bco dcult to gnt dvtv t n th output tht h ny gncnt ct on oto pd. It cn b dployd to duc th pd pd ocllton cud by hgh popotonl gn. Howv, n ny contoll, t not ud. h dvtv cton cu th no (ndo o) n th n gnl to b pld nd lctd n th contoll output. Hnc th ot utbl contoll o pd contol PI typ contoll Cunt oop Ung th pt n cton 6..5, th cunt loop tn uncton o th xct yt ound o Fgu 6. () ( ) (6.8) h thd-od yt. o duc th od o th yt o nlytcl dgn o pd contoll, odl od ducton tchnqu v. Ung th odl od ducton tchnqu (Rh t l 0), th ducd (cond) od yt () obtnd whch utbl o u n th dgn o pd loop. Hnc, ( ) (6.8)

30 69 h tp pon, gn nd ph plot o th xct nd ducd cunt loop tn uncton hown n Fgu 6.9, 6.0 nd Stp Rpon o xct nd ducd cunt loop tn uncton xct ducd (c) Fgu 6.9 Stp pon o xct nd ducd cunt loop tn uncton 0 Fquncy pon o xct nd ducd cunt loop tn uncton xct ducd Fquncy (d/c) Fgu 6.0 Fquncy pon o xct nd ducd cunt loop tn uncton

31 70 45 Ph plot o xct nd ducd cunt loop tn uncton Fquncy (d/c) Fgu 6. Ph plot o xct nd ducd cunt loop tn uncton h tp pon cn b nlyzd wth th hlp o t don pccton uch t, ttlng t, ovhoot nd pk vlu whch gvn n bl 6..h ducd od cunt loop tn uncton ubttutd n th dgn o th pd contoll ollow. bl 6. Copon o tp pon o cunt loop tn Functon Sttgy o Contol Ognl hgh od yt Rducd od yt Sttlng R t % Pk Pk t t (t ) (t ) n c Ovhoot pltud n c n c

32 Spd Contoll h pd loop wth th pld cunt loop hown n Fgu 6.. h opn loop pd tn uncton wth th ducd cunt loop gvn by o ( ) ( ). ( ) (6.8) Fgu 6. h pd loop wth th ducd od cunt loop By ung th Pol-Zo cncllton tchnqu th ntl vlu o p nd obtnd o th ducd cond od cunt loop tn uncton : p = 64, =560. h ntl vlu o p nd obtnd though th ducd od odl n tund ung A bd on th nl ttlng t ct. h ultnt vlu o p nd obtnd, p = 8.798, = h contoll gn ud o th dgn o pd contoll o ducd yt nd xct yt.

33 7 Fo Fgu 6., th clod loop pd tn uncton wth th ducd od cunt loop obtnd ( ) ( ( ) ) * 5 4 ( ) (6.84) 4800 Fgu 6. h pd loop wth th ognl od cunt loop Fo Fgu 6., th clod loop pd tn uncton wth th ognl od cunt loop obtnd ( o) ( ) ( ) * ( ) (6.85) h tp pon o clod loop pd tn uncton wth th ducd nd ognl od cunt loop hown n Fgu 6.4. h tdy tt pon o th clod loop pd tn uncton wth ducd od cunt loop xctly tchng wth tht o th ognl cunt loop pd tn uncton. h cn b nlyzd wth th hlp o t don pccton uch t, ttlng t, tdy tt vlu nd pk vlu whch gvn n bl 6.4. h gntud plot nd ph plot o pd tn uncton wth ognl nd ducd cunt loop hown n Fgu 6.5 nd Fgu 6.6 pctvly.

34 7 0 Stp Rpon o pd loop tn uncton wth ognl nd ducd cunt loop ognl yt ducd yt (c) Fgu 6.4 Stp pon o pd loop tn uncton wth ognl nd ducd cunt loop tn uncton bl 6.4 Copon o tp pon o pd loop wth ognl nd ducd cunt loop Sttgy o Contol Spd loop tn uncton wth ognl cunt loop Spd loop tn uncton wth ducd cunt loop R t (t ) n c Sttlng t (t ) n c % Ovhoot Pk pltud Pk t n c

35 n plot o pd loop tn uncton wth ognl nd ducd cunt loop tn uncton Ognl hgh od yt Rducd cond od yt Fquncy (d/c) Fgu 6.5 n plot o pd loop tn uncton wth ognl nd ducd cunt loop tn uncton Ph plot o pd loop tn uncton wth ognl nd ducd cunt loop tn uncton 0 Ognl hgh od yt Rducd cond od yt Fquncy (d/c) Fgu 6.6 Ph plot o pd loop tn uncton wth ognl nd ducd cunt loop tn uncton

36 COMPARISION OF CONVENIONA MEHOD AND PROPOSED MODE ORDER REDUCION ECHNIQUE Fgu 6.7 how th copon o tp pon o pd loop tn uncton ung ognl cunt loop wth ytc optu pncpl nd odl od ducton tchnqu wth gntc lgoth tund contoll gn. h cn b nlyzd wth th hlp o t don pccton uch t, ttlng t, tdy tt vlu nd pk vlu whch gvn n bl 6.5. h tp pon o th pd loop tn uncton wth ognl cunt loop ung popod odl od ducton tchnqu wth gntc lgoth tund contoll gn thod gv btt t don pccton thn th convntonl ytc optu pncpl thod. h pk t ult tt tht ntc Algoth bd PI contoll 9 t l thn SO PI pd contoll. Wth condton ov th t th ntc Algoth PI contoll cnt gvng 0.45 t l t. 0 Copon o pd loop wth xct cunt loop tn uncton wth ytc optu thod nd MOR wth A convntonl ytc optu thod popod MOR wth A (c) Fgu 6.7 Copon o pd loop tn uncton ung ognl cunt loop wth ytc optu nd MOR-A thod

37 76 bl 6.5 Copon o tp pon o pd loop ung ognl cunt loop tn uncton Sttgy o R t Sttlng t % Pk Pk t Contol (t ) n c (t ) n c Ovhoot pltud n c Sytc optu pncpl MOR tchnqu wth A tund gn Fgu 6.8 how th copon o tp pon o pd loop tn uncton ung ducd od cunt loop wth ytc optu thod nd odl od ducton tchnqu wth gntc lgoth tund contoll gn. h cn b nlyzd wth th hlp o t don pccton uch t, ttlng t, tdy tt vlu nd pk vlu whch gvn n bl 6.6. It how tht pk pltud nd pcntg o ovhoot condbly ducd wth th copon o convntonl ytc optu thod. It obvd tht th convntonl thod h pk ovhoot 45% whl tht o th popod thod 0.%. h t o th convntonl thod ound c wh th popod thod h th t o

38 77 Copon o pd loop wth ducd cunt loop tn uncton wth ytc optu thod nd MOR wth A 0 Convntonl Sytc optu thod Popod MOR thod wth A (c) Fgu 6.8 Copon o pd loop tn uncton ung ducd cunt loop wth ytc optu nd MOR-A thod bl 6.6 Copon o tp pon o pd loop ung ducd cunt loop tn uncton Sttgy o R t Sttlng t % Pk Pk t Contol (t ) n c (t ) n c Ovhoot pltud n c Sytc optu thod MOR tchnqu wth A

39 SUMMARY In th chpt co ultplcton o polynol odl od ducton thod ud to duc th nvt d ndct vcto contolld nducton oto dv hgh od yt nto n quvlnt ducd cond od yt nd contoll dgnd to th ducd cond od odl. ntc lgoth optzton tunng tchnqu ud o obtnng optl cocnt o th ducd od odl. h tund contoll ttchd wth th ognl hgh od yt nd th clod loop pon obvd o tblzton poc. h tdy tt ponc o popod PI contoll wth th hlp o A h bn copd wth th convntonl (SO) PI contoll. It obvd tht th convntonl ytc optu thod h pk ovhoot 4.5% whl tht o th popod thod.7%. h t o th convntonl thod ound 0.08c, wh th popod thod h th ttlng t ound c. Pk pltud lo condbly ducd wth tht o convntonl thod. h tp pon o th pd loop tn uncton wth ducd od cunt loop ung popod odl od ducton tchnqu wth gntc lgoth tund contoll gn thod gv btt t don pccton thn th convntonl ytc optu thod.

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