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GATE 2017 EE – Question 32

Control Systems · Stability analysis using Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci · 1 mark · Numerical answer

Consider the unity feedback control system shown. The value of $K$ that results in a phase margin of the system to be 30° is ________. (Give the answer up to two decimal places.)

A unity feedback loop with the forward path transfer function $\dfrac{Ke^{-s}}{s}$.

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Correct answer: 1.01 to 1.06

Explanation

The gain crossover frequency satisfies $\frac{K}{\omega} = 1$, so $\omega = K$. The phase of the loop is $-90° - \omega\ \text{rad} \times \frac{180°}{\pi}$. The phase margin is $180° - 90° - \frac{180°}{\pi}K = 30°$. So $K = \frac{60\pi}{180} = \frac{\pi}{3} = 1.047$.