Question

A unity feedback system has the loop transfer function $$ G_c(s) G(s)=\frac{K(s+1)}{s(s-3)} . $$ This system is open-loop unstable. (a) Determine the range of $K$ so that the closed-loop system is stable. (b) Sketch the root locus. (c) Determine the roots for $K=10$. (d) For $K=10$, predict the percent overshoot for a step input using Figure 5.13. (e) Determine the actual overshoot by plotting the response.

   A unity feedback system has the loop transfer function
$$
G_c(s) G(s)=\frac{K(s+1)}{s(s-3)} .
$$

This system is open-loop unstable. (a) Determine the range of $K$ so that the closed-loop system is stable. (b) Sketch the root locus. (c) Determine the roots for $K=10$. (d) For $K=10$, predict the percent overshoot for a step input using Figure 5.13. (e) Determine the actual overshoot by plotting the response.

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Modern Control Systems

Modern Control Systems

Dorf 11th Edition

Chapter 7, Problem 38

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Step 1

To determine the range of K for stability, we need to find the values of K for which the poles of the closed-loop system lie in the left half of the s-plane. This means that the real parts of the poles should be negative. The closed-loop transfer function is Show more…

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A unity feedback system has the loop transfer function $$ G_c(s) G(s)=\frac{K(s+1)}{s(s-3)} . $$ This system is open-loop unstable. (a) Determine the range of $K$ so that the closed-loop system is stable. (b) Sketch the root locus. (c) Determine the roots for $K=10$. (d) For $K=10$, predict the percent overshoot for a step input using Figure 5.13. (e) Determine the actual overshoot by plotting the response.

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