Transient response with unit-step input y+250n)+07y=ou(t) Roots are S1,2=-0m c(t) R(S)= 1- S 1 c(t)=1-eo(1+0nt)(t≥0) 0 Without vibration,without overshoot. Rising monotone, 5=1 Critically damped
Roots are 1 Critically damped n s1,2 Without vibration, without overshoot, Rising monotone, c(t) 1 e (1 nt) (t0) t n s R s 1 ( ) Transient response with unit-step input 2 2 2 () nn n y y y ut
Transient response with unit-step input c() 2.0 1.8 1.6 =0 2 1.4 1.2 6 1.0 0.8 0.4 0.2 0 =1.5 =2.0 6 8 10 12a% 5>1 Overdamped (过阻尼) 5=1 Critically damped (临界阻尼) 0<<1 Underdamped (欠阻尼)
1 1 0 1 Overdamped (过阻尼) Critically damped (临界阻尼) Underdamped (欠阻尼) Transient response with unit-step input
--The impact of damping ratio b 2√mk Step Response 5 =0 5=1 1.6 0<5<1 5>1 0.4 0.2 5 10 15 20 30 35 Time (sec)
-- The impact of damping ratio Step Response Time (sec) Amplitude 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2 b mk 0 0 1 1 1