西安石油大学电子工程学院：《自动控制理论 Modern Control System》精品课程教学资源（英文PPT课件）Time-Domain Analysis Of Control System

Unit-impulse response of the first-order syst 0.8 t=e/ 0.6 04 02 2 5 timet 2022-2-3 6

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Unit-step response of the first-order system may be found by assuming R(s)=1ys as Y R TS+1 zS+1八s)szs+1 y()=1-e (3-3-4 Unit-ramp response of the first-order system may be found by assuming R(s)=1/s2 as Y(S=RI Ts+1 τs+1八s2)s2szs+1 (3-3-5) ()=t-(1-e") (3-3-6) 2022-2-3 7

2022-2-3 7 Unit-step response of the first-order system may be found by assuming Rs  1 s as     1 1 1 1 1 1 1 Y s R s s s s s s                     Unit-ramp response of the first-order system may be found by assuming as   2 R s  1 s     2 2 2 1 1 1 1 1 1 1 Y s R s s s s s s s                         1  t y t t e         1 t y t e     (3-3-3) (3-3-4) (3-3-5) (3-3-6)

The error signal is then Q|c(0=-(0)y(02=(-c") (3-3-7) As t approaches the infinity, the error signal approaches t le 2022-2-3 8

2022-2-3 8 The error signal is then       1  t e t r t y t e        As approaches the infinity, the error signal approaches , i.e., t  e      (3-3-7)

3.4 Performance of a second-Order System Let's consider a unity feedback system shown below E(S K R(S) G)= s(s+ p) The output y(s can be found as 2022-2-3 9

2022-2-3 9 3.4 Performance of a Second-Order System Let's consider a unity feedback system shown below. The output can be found as Y s

G(S R K R +ps+ k R +250ns+ (3-3-8 where =√Kz=p/2K n OS 2 2022-2-3 10

2022-2-3 10             2 2 2 2 1 2 n n n G s Y s R s G s K R s s p s K R s s s             where n  K   p 2 K (3-3-8)