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GATE 2019 EE – Question 24

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

The open loop transfer function of a unity feedback system is given by

$$G(s)=\frac{\pi e^{-0.25s}}{s}.$$

In $G(s)$ plane, the Nyquist plot of $G(s)$ passes through the negative real axis at the point

  1. $(-0.5,j0)$
  2. $(-0.75,j0)$
  3. $(-1.25,j0)$
  4. $(-1.5,j0)$

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Show answer and explanation

Correct answer: (A) $(-0.5,j0)$

Explanation

The phase of $G(j\omega)$ is $-\frac\pi2-0.25\omega$, which equals $-\pi$ at $\omega=2\pi$. The magnitude there is $\frac{\pi}{2\pi}=0.5$, so the plot crosses the negative real axis at $-0.5$.