Question

Given $G(s) = \frac{1}{(s+2)(s+6)(s+8)}$ and $D(s) = K$. The unit-step response has a settling time $T_s = 1.78$ sec. If the desired settling time is $T_s = 0.9$ sec, determine the desired pole locations without changing the damping ratio $\zeta = 0.456$.

Name: given gs frac1s2s6s8 and ds k the unit step response has a settling time ts 178 sec if the desired settling time is ts 09 sec determine the desired pole locations without changing the damp 59322
Uploaded: 2023-07-11T04:08:59-08:00
Duration: 1 min 10 s
Channel: Madhur L
Description: given gs frac1s2s6s8 and ds k the unit step response has a settling time ts 178 sec if the desired settling time is ts 09 sec determine the desired pole locations without changing the damp 59322

          Given $G(s) = \frac{1}{(s+2)(s+6)(s+8)}$ and $D(s) = K$. The unit-step response has a settling time $T_s = 1.78$ sec. If the desired settling time is $T_s = 0.9$ sec, determine the desired pole locations without changing the damping ratio $\zeta = 0.456$.

$given gs frac1s2s6s8 and ds k the unit step response has a settling time ts 178 sec if the desired settling time is ts 09 sec determine the desired pole locations without changing the damp 59322$

Added by Shannon T.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

07/11/2023

Step 1

We are given that the desired settling time is $T_s = 0.9$ sec and the damping ratio is $\zeta = 0.456$. We can find the desired natural frequency $\omega_n$ using the formula: $T_s = \frac{4}{\zeta \omega_n}$ $0.9 = \frac{4}{0.456 \omega_n}$ $\omega_n = Show more…

Show all steps

Thanks for your feedback!

Given $G(s) = \frac{1}{(s+2)(s+6)(s+8)}$ and $D(s) = K$. The unit-step response has a settling time $T_s = 1.78$ sec. If the desired settling time is $T_s = 0.9$ sec, determine the desired pole locations without changing the damping ratio $\zeta = 0.456$.