Chapter4 Time Domain Analysis of Control System
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1 Chpr4 im Domi Alyi of Corol Sym Rouh biliy cririo Sdy rror ri rpo of h fir-ordr ym ri rpo of h cod-ordr ym im domi prformc pcificio h rliohip bw h prformc pcificio d ym prmr ri rpo of highr-ordr ym Dfiiio of chrcriic quio C R b b m L b b G L m m m h chrcriic quio of h ym i dfid L Auomic Corol Sym
2 Auomic Corol Sym rfr fucio:, p σ ± ± pol of h clod loop q r m i i p z R C ] ][ [ G σ σ z i : zro of h clod loop 4 q r C p α β i i co q r i p q r p D C B C ϕ p z C q r m i i ] ][ [ σ σ Sp rpo:
3 Auomic Corol Sym 5 Coidr h h chrcriic quio of LI ym F L Whr ll h coffici r rl umbr. I ordr h hr b o roo of h bov quio wih poiiv rl pr, i i cry bu o uffici h. All h coffici of h polyomil hv h m ig.. No of h coffici vih. 4. Rouh biliy cririo F E F F E C ED C A C C A C E C AD BC A A D A A C A B A B A h Rouh bulio F L for 6
4 Rou-Hurwiz cririo h roo of h polyomil r ll i h lf hlf of h -pl if ll h lm of h fir colum of h Rouh Arry r of h m ig. If hr r chg of ig i h lm of h fir colum, h umbr of ig chg idic h umbr of roo wih poiiv rl pr. h cry d uffici codiio for h biliy of ym 7 Exmpl: Soluio: h chrcriic quio of ym i 4 5 Drmi h biliy of h ym uig Rouh cririo.. Chc h cry codiio. Rouh rry i h ym h wo roo locd i h righ hlf of h -pl. 8 Auomic Corol Sym 4
5 Spcil c h fir lm i y o row of h Rouh Arry i zro bu h ohr lm r o. W c rplc h zro lm i h Rouh bulio by rbirry mll poiiv umbr ε d h procd wih h Rouh. 9 Exmpl: h chrcriic quio of ym i Drmi h biliy of h ym uig Rouh cririo. Soluio: Rouh rry i 5 4 ε 5ε ε 5ε ε 5ε 5 5 hr r wo ig chg i h fir colum of h bulio, h ym h wo roo locd i h righ hlf of h -pl. Auomic Corol Sym 5
6 Spcil c h lm i o row of h Rouh Arry r ll zro. Exmpl: h chrcriic quio of h ym i: 6 6 h Rouh rry i : h uxiliry quio i: A h ig of h lm i h fir colum do o chg, h ym i bl. Auomic Corol Sym 6
7 Exmpl: R C Drmi h vlu of d o m h clod loop b bl. Soluio: h chrcriic quio: Rouh rry: >, >, > > > h codiio for h biliy i: < < 4 Auomic Corol Sym 7
8 6 4 < Sbl < < 5 Exmpl: h chrcriic quio of h ym i 8 Drmi h biliy of h ym. Alyz how my roo li bw h imgiry xi d h li. Soluio: Rouh rry: h ym i bl. L h chrcriic quio bcom: Im 5 R 6 Auomic Corol Sym 8
9 5 Rouh rry for h bov quio: 5.8 hr i o roo o h righ id of h li -. Im R Sdy rror c r 8 Auomic Corol Sym 9
10 R E C G B H R E G H E R G H 9 h yp of h corol ym G z z L z r r m i ν q p p L pq ν m v z p i ν, yp ym ν, yp ym ν, yp ym Auomic Corol Sym
11 Auomic Corol Sym. poiio rror co For p ipu u R r / H G R H G R H G R E R R GH GH P GH b. vlociy rror co For rmp ipu: R r / H G R H G R H G R E v G H v R
12 Auomic Corol Sym c. Acclrio rror co for cclrio ipu r R / H G R H G R H G R E H G R 4 Sdy rror
13 Exmpl: Soluio: Drmi h dy rror, wh h ipu i u, d. R C 5 p G H 5 v G H 5 G H 5 5 p P v v 6 Auomic Corol Sym
14 4. h ri rpo of h fir-ordr ym 4.. h mh modl C R R C h p rpo r u, R/ C GR c 8 Auomic Corol Sym 4
15 c lop % 95% 98.% 99.% 6.% Impul rpo: R C C R g c c c / 4 Auomic Corol Sym 5
16 Rmp rpo : R C C G R / c / c / c r r c [ c r ] [ / ] Auomic Corol Sym 6
17 4. h ri rpo of h cod-ordr ym 4.. h mhmicl modl R C R C Φ C R l ς Φ 4 Auomic Corol Sym 7
18 h chrcriic quio : h roo of h chrcriic quio r, udrdmpd < <, - -, σ ± d If ipu i ui p u: C d d 6 Auomic Corol Sym 8
19 c co d i d co d i d - - i d θ - θ rcco 7 c 4 8 Auomic Corol Sym 9
20 Auomic Corol Sym 9, - -, c c c r c. Criiclly dmpd rpo u 4 >, ± ] [ ] [ c c Ovr dmpd c L ] [ ] [ c r c c
21 4. udmpd c, - -, ± c c - co c 4 4. im domi prformc pcificio. Ri im r. h p im p 4 Auomic Corol Sym
22 . Prcg ovrhoo σ p σ c P - c c P % 4. Sdy- rror c r % r 4 5. Slig im 44 Auomic Corol Sym
23 4.4 h rliohip bw h prformc pcificio d ym prmr < <. Ri im-ym prmr c Accordig o dfiiio: i θ c r d c r r i d r θ d r θ π r π θ d π θ 45. P im -ym prmr P P π π d π d π c.9. σ p r ±.5 or±. r p 46 Auomic Corol Sym
24 . Prcg ovrhoo -ym prmr c co d i d P π d π π π P d ξ ξ c p p co i d p d p π P coπ i π c 47 π π c P coπ i π σ P c P c c P % % c σ P π 48 Auomic Corol Sym 4
25 σ p π % 8 Φ σ p 6 σ p Prcg ovrhoo σ p i oly rld o h lig im - -ym prmr c c c ±.or.5 5 Auomic Corol Sym 5
26 c l - 5 < <.9 pproximly: 4 for. for.5 5 Auomic Corol Sym 6
27 Exmpl: R C h dird pcificio r: σ %, P P Wh hould h vlu of d b? Drmi h vlu of d r. Soluio: h rfr fucio of h clod loop i C R, 5 π..456 P π d π.5rd / C R 54 Auomic Corol Sym 7
28 r π -θ r.65 - θ g - -. rd for 5% ri rpo of highr-ordr ym. Sp rpo of highr ordr ym C q p r m [ σ z i i ][ σ ] C p q r α β 56 Auomic Corol Sym 8
29 q r p co i C B C q r p i φ i D r c r c c r 57. h domi pol of highr-ordr ym q r p co i C B C q r p i φ i D 58 Auomic Corol Sym 9
30 domi clod loop pol 主导极点 [ ] σ R[ polof clod loop] < R[ domi pol] 5 hr i o zro of h clod loop r h domi pol 59 Auomic Corol Sym
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