Question

3 A closed loop transfer function is given as follows: \frac{C(s)}{R(s)} = \frac{96(s+3)}{(s+8)(s^2+8s+36)} For a unit step input, and assuming that complex poles dominate, find the following: a- C(s) and Css. b- Natural frequency, damping ratio and damped frequency c- Peak time and peak response. d- Settling time and percent overshoot e- Time response c(t). f- E(s) and ess.

          3 A closed loop transfer function is given as follows:
\frac{C(s)}{R(s)} = \frac{96(s+3)}{(s+8)(s^2+8s+36)}
For a unit step input, and assuming that complex poles dominate, find the following:
a- C(s) and Css.
b- Natural frequency, damping ratio and damped frequency
c- Peak time and peak response.
d- Settling time and percent overshoot
e- Time response c(t).
f- E(s) and ess.

3 A closed loop transfer function is given as follows:
(C(s))/(R(s)) = (96(s+3))/((s+8)(s^2+8s+36))
For a unit step input, and assuming that complex poles dominate, find the following:
a- C(s) and Css.
b- Natural frequency, damping ratio and damped frequency
c- Peak time and peak response.
d- Settling time and percent overshoot
e- Time response c(t).
f- E(s) and ess.

Added by Amber T.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Justin Swantek

Step 1

The transfer function T(s) represents the system's response to the input R(s). Since the input is a unit step, R(s) can be represented as 1/s. C(s) = 96(s+3) / T(s) R(s) C(s) = 96(s+3) / T(s) (1/s) Show more…

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Based on stability analysis, the transfer function of the system can be represented as C(s) = 96(s+3) / T(s) R(s) (9+8+8+). For a unit step input, and assuming that complex poles dominate, find the following: a- C(s) and Css. b- Natural frequency, damping ratio, and damped frequency. c- Peak time and peak response. d- Settling time and percent overshoot. e- Time response c(t) and ess.