GATE 2023 IN – Question 48
A standard negative-feedback system has $G(s)=1/[(s-2)(s-3)]$ and PID controller $C(s)=K_P+K_I/s+K_Ds$. The root locus of $G(s)C(s)$ is shown. Given $C(j\omega)=2$ at $\omega=1$ rad/s, $K_D$ is ______ (one decimal place).
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Show answer and explanation
Correct answer: 0.9 to 1.1
Explanation
The plot shows a double controller zero at −1, so $C(s)=K_D(s+1)^2/s$ and $K_P=2K_D,K_I=K_D$. At $s=j$, the integral and derivative imaginary parts cancel, giving $C(j)=2K_D=2$.
Thus $K_D=\boxed{1.0}$.