GATE 2018 EC – Question 52
The figure below shows the Bode magnitude and phase plots of a stable transfer function $G(s)=\dfrac{n_0}{s^3+d_2s^2+d_1s+d_0}$.
Consider the negative unity feedback configuration with gain $k$ in the feedforward path. The closed loop is stable for $k<k_0$. The maximum value of $k_0$ is ________.
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Show answer and explanation
Correct answer: 0.09 to 0.11
Explanation
The phase crosses $-180^\circ$ at the frequency where the magnitude plot is at $20$ dB (the dashed vertical line), i.e. $|G|=10$. The closed loop is stable as long as $k|G|<1$ at that frequency, so $k<\frac1{10}$ and $k_0=0.1$.