# Control Systems (Closed Loop; Amplifier Gain; Natural Frequency; Root Locus; Stable, Underdamped Response)

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Please consider the attached motor control system.

(i) Find the characteristic equation of the closed loop system, and find the amplifier gain K1 so that the natural frequency of the system is {see attachment}

(ii) Suppose that K2 = 1. Sketch the root locus of the closed loop system poles for {see attachment}

(iii) For what value of K1 will the closed loop system exhibit a stable, underdamped response with the damping ratio of 0.707?

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##### Solution Summary

The solution provides a step-by-step calculations for control-loops systems, such as finding amplifier gain and sketching the root locus of the closed loop system.

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Please see attached

Question C4.

If E is the error signal at the input of the amplifier gain K1, we get,

C = [30K1/(s+1)]*E

R - C -E*[6K1/(s+1)]*K2*s = E

E*[1 + ...

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