Question

A closed-loop control system with negative unity feedback has a plant with a transfer function $$ G(s)=\frac{8}{s\left(s^2+6 s+12\right)} . $$ (a) Determine the closed-loop transfer function $T(s)$. (b) Determine a second-order approximation for $T(s)$ using the method of Section 5.10. (c) Plot the response of $T(s)$ and the second-order approximation to a unit step input and compare the results.

   A closed-loop control system with negative unity feedback has a plant with a transfer function
$$
G(s)=\frac{8}{s\left(s^2+6 s+12\right)} .
$$
(a) Determine the closed-loop transfer function $T(s)$. (b) Determine a second-order approximation for $T(s)$ using the method of Section 5.10. (c) Plot the response of $T(s)$ and the second-order approximation to a unit step input and compare the results.

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Modern Control Systems

Modern Control Systems

Dorf 11th Edition

Chapter 5, Problem 18

Instant Answer

Step 1

To find the closed-loop transfer function T(s), we use the formula: $$ T(s) = \frac{G(s)}{1+G(s)} $$ where G(s) is the plant transfer function. Show more…

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A closed-loop control system with negative unity feedback has a plant with a transfer function $$ G(s)=\frac{8}{s\left(s^2+6 s+12\right)} . $$ (a) Determine the closed-loop transfer function $T(s)$. (b) Determine a second-order approximation for $T(s)$ using the method of Section 5.10. (c) Plot the response of $T(s)$ and the second-order approximation to a unit step input and compare the results.

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