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The open loop transfer function for a unit feedback system is G(s) = K/s(sT+1). By what factor the amplitude gain K should be reduced so that the peak overshoot becomes 25% from 75%?

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The open loop transfer function for a unit feedback system is G(s) = K/s(sT+1). By what factor the amplitude gain K should be reduced so that the peak overshoot becomes 25% from 75%?

(a) 75

(b) 25

(c) 20

(d) 10

I got this question in an internship interview.

Query is from Integral Square Error & its Minimization in section Error Analysis of Control Systems

1 Answer

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Correct choice is (c) 20

The explanation is: The peak overshoot is decreased by increasing the damping ratio. The damping ratio is increased by reducing the gain K by same proportion and for decreasing the peak overshoot from 75% to 25% the factor of amplitude becomes 19.6% which is approximately 20%.

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