GATE 2021 EE – Question 56
Consider a closed-loop system as shown. $G_p(s)=\dfrac{14.4}{s(1+0.1s)}$ is the plant transfer function and $G_c(s)=1$ is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is ________ rad/s. (Round off to 2 decimal places.)
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Correct answer: 10.80 to 11.00
Explanation
The closed-loop transfer function is $\frac{14.4}{0.1s^2+s+14.4}=\frac{144}{s^2+10s+144}$, so $\omega_n=12$ rad/s and $\zeta=\frac{10}{24}=0.4167$. The damped frequency is $\omega_d=12\sqrt{1-0.4167^2}=10.91$ rad/s.