GATE 2016 EC – Question 56
The open-loop transfer function of a unity-feedback control system is given by
$$G(s) = \frac{K}{s(s + 2)}$$
For the peak overshoot of the closed-loop system to a unit step input to be 10%, the value of $K$ is ____________
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Show answer and explanation
Correct answer: 2.7 to 3
Explanation
The closed-loop characteristic equation is $s^2 + 2s + K = 0$, so $\omega_n^2 = K$ and $2\zeta\omega_n = 2$, giving $\zeta\omega_n = 1$. A 10% overshoot means $e^{-\pi\zeta/\sqrt{1 - \zeta^2}} = 0.1$, which gives $\zeta = 0.591$. Then $\omega_n = \frac{1}{\zeta} = 1.69$ and $K = \omega_n^2 = 2.86$.