Question

A closed-loop system with unity feedback has a loop transfer function $$ G_c(s) G(s)=\frac{K(s+20)}{s^2} . $$ (a) Determine the gain $K$ so that the phase margin is $45^{\circ}$. (b) For the gain $K$ selected in part (a), determine the gain margin. (c) Predict the bandwidth of the closed-loop system.

    A closed-loop system with unity feedback has a loop transfer function
$$
G_c(s) G(s)=\frac{K(s+20)}{s^2} .
$$
(a) Determine the gain $K$ so that the phase margin is $45^{\circ}$. (b) For the gain $K$ selected in part (a), determine the gain margin. (c) Predict the bandwidth of the closed-loop system.

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Modern Control Systems

Modern Control Systems

Dorf 11th Edition

Chapter 9, Problem 24

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Step 1

To find the gain $K$ so that the phase margin is $45^{\circ}$, we need to first find the gain crossover frequency. Show more…

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A closed-loop system with unity feedback has a loop transfer function $$ G_c(s) G(s)=\frac{K(s+20)}{s^2} . $$ (a) Determine the gain $K$ so that the phase margin is $45^{\circ}$. (b) For the gain $K$ selected in part (a), determine the gain margin. (c) Predict the bandwidth of the closed-loop system.

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