STEADY STATE ERRORS IN UNITY FEEDBACK CONTROL SYSTEMS
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1 VU -lrning Courwr Control Enginring (ME55) SEADY SAE ERRORS I UIY FEEDBAC COROL SYSEMS Error in control yt y ttriutd to ny fctor. Chng in th rfrnc inut will cu unoidl rror during trnint riod, nd lo cu tdy tt rror. Any hyicl control yt inhrntly uffr fro tdy tt rror in ron to crtin ty of inut. Whthr gin yt will xhiit tdy tt rror for gin inut dnd on th ty of th on loo trnfr function of th yt. Clifiction of Control Syt Control yt y clifid ccording to thir ility to follow t inut, r inut, rolic inut tc. h gnitud of th tdy tt rror du to th indiidul inut r indicti of th goodn of th yt. Conidr th unity fdck control yt with th following on loo trnfr function G(): G It inol th tr in th dnointor, rrnting th ol of ultilicity t th origin which lo indict th nur of intgrtion in th on loo. A yt i clld y, y, y. If =,,, rctily. A th ty nur i incrd ccurcy i irod; howr, incring th ty nur ggrt th tility rol. Stdy Stt Error A unity fdck clod loo control yt i hown in Fig.. R() E() G() C() Figur Unity fdck control yt h clod loo trnfr function i C R G G Prof. S. C.Pilli, Princil, Sion: XIII, 5/9/6.L.E.S. Collg of Enginring nd chnology, Blgu-598.
2 VU -lrning Courwr Control Enginring (ME55) h trnfr function twn th rror ignl (t) nd inut ignl r(t) i E C, Which cn rrrngd E R R R G G h finl lu thor roid connint wy to find th tdy tt rror t t E R G hr ty of ttic rror contnt r ) Sttic oition rror contnt du to unit t inut. ) Sttic locity rror contnt du to unit r inut. 3) Sttic cclrtion rror contnt du to unit rolic inut which indict th figur of rit of control yt. Sttic Poition Error Contnt h tdy tt rror of th yt for unit t inut i G G h ttic oition rror contnt i dfind y G G hu, th tdy tt rror in tr of th ttic oition rror contnt i gin y For ty yt, For ty or highr yt nd nd Prof. S. C.Pilli, Princil, Sion: XIII, 5/9/6.L.E.S. Collg of Enginring nd chnology, Blgu-598.
3 VU -lrning Courwr Control Enginring (ME55) Prof. S. C.Pilli, Princil, Sion: XIII, 5/9/6.L.E.S. Collg of Enginring nd chnology, Blgu-598. Ron of fdck control yt to t inut inol tdy tt rror if thr i no intgrtion in th fd forwrd th. If zro tdy tt rror for t inut i dird, th ty of th yt ut on or highr. Sttic Vlocity Error Contnt h tdy tt rror of th yt with unit r inut i gin y G G h ttic locity rror contnt i dfind y G hu, th tdy tt rror in tr of th ttic locity rror contnt i gin y h tr locity rror i ud hr to xr th tdy tt rror for r inut. h locity rror i n rror in oition du to r inut. For ty yt, nd For ty yt nd
4 VU -lrning Courwr Control Enginring (ME55) Prof. S. C.Pilli, Princil, Sion: XIII, 5/9/6.L.E.S. Collg of Enginring nd chnology, Blgu-598. For ty or highr yt nd y yt i incl of following r inut in th tdy tt. y yt with unity fdck cn follow th r inut with finit rror. y nd highr ordr yt cn follow r inut with zro tdy tt rror. Sttic Acclrtion Error Contnt h tdy tt rror of th yt with unit rolic inut i gin y G G 3 h ttic cclrtion rror contnt i dfind y G hu, th tdy tt rror in tr of th ttic cclrtion rror contnt i gin y For ty yt, nd For ty yt nd For ty yt nd
5 VU -lrning Courwr Control Enginring (ME55) For ty 3 or highr yt 3 nd y nd ty yt r incl of following rolic in th tdy tt. y yt with unity fdck cn follow th rolic inut with finit rror. y 3 nd highr ordr yt cn follow rolic inut with zro tdy tt rror. l how th ury of rror contnt nd tdy tt rror for unit t, unit r nd unit rolic inut to unity fdck loo. l : Sury of tdy tt rror for unity fdck yt y of Error contnt Stdy tt rror yt Unit t inut Unit r inut Unit rolic inut /(+) / / 3 ot: ) h t, r, rolic rror contnt r ignificnt for th rror nlyi only whn th inut ignl i t, r nd rolic function rctily. ) Sinc th rror contnt r dfind with rct to forwrd th trnfr function G(), th thod i licl to unity fdck yt only. 3) Sinc rror nlyi rli on u of finl lu thor, it i iortnt firt to chck to if E() h ny ol on th j xi or in th right hlf of -ln. 4) Princil of uroition cn ud if cointion of th thr ic inut r rnt. 5) If th configurtion diffr, w cn ithr ilify to unity fdck yt or tlih rror ignl nd ly finl lu thor. Prof. S. C.Pilli, Princil, Sion: XIII, 5/9/6.L.E.S. Collg of Enginring nd chnology, Blgu-598.
6 VU -lrning Courwr Control Enginring (ME55) Exl: For ngti unity fdck yt dtrin th tdy tt rro du to unit t, unit r nd unit rolic inut of th following yt. i) G ii) G. 5 4 iii) G 4 Solution G() G() G() l how th rult of rror contnt nd tdy tt rror. l Rult of xl Prol Error contnt Stdy tt rror Unit t inut Unit r inut Unit rolic inut i 5 /5 ii / / iii / / Prof. S. C.Pilli, Princil, Sion: XIII, 5/9/6.L.E.S. Collg of Enginring nd chnology, Blgu-598.
7 VU -lrning Courwr Control Enginring (ME55) Prof. S. C.Pilli, Princil, Sion: XIII, 5/9/6.L.E.S. Collg of Enginring nd chnology, Blgu-598.
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