The GATE Grind

GATE 2025 IN – Question 28

Control Systems · Stability and frequency response · 1 mark · Multiple choice

Consider the control-system block diagram in Figure (a). The loop transfer function $G(s)H(s)$ has no poles on the $j\omega$ axis. The counterclockwise contour of infinite radius in Figure (b) encloses two poles of $G(s)H(s)$. Which statement is correct for closed-loop stability?

Diagram for GATE 2025 IN question 28
  1. The locus of $G(s)H(s)$ should encircle the origin twice counterclockwise.
  2. The locus of $1+G(s)H(s)$ should encircle the origin twice clockwise.
  3. The locus of $G(s)H(s)$ should encircle $-1+j0$ twice counterclockwise.
  4. The locus of $1+G(s)H(s)$ should encircle $-1+j0$ twice clockwise.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) The locus of $1+G(s)H(s)$ should encircle the origin twice clockwise.

Explanation

For the stated counterclockwise contour, the mapped winding of 1+GH about zero is Z−P.

Stability requires Z=0 and the contour encloses P=2 open-loop poles, so winding is −2: twice clockwise.

Thus **B**; the contour orientation matters for the sign.