GATE 2023 EE – Question 13

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

In the Nyquist plot of the open-loop transfer function

$$G(s)H(s)=\frac{3s+5}{s-1}$$

corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in $s$-plane is mapped into a point at

Diagram for GATE 2023 EE question 13

$G(s)H(s)=\infty$
$G(s)H(s)=0$
$G(s)H(s)=3$
$G(s)H(s)=-5$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) $G(s)H(s)=3$

Explanation

On the large semicircle $|s|\to\infty$, $G(s)H(s)\to\dfrac{3s}{s}=3$, so the whole arc maps to the single point 3.