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GATE 2026 EC – Question 40

Control Systems · Compensators and PID Controller · 2 marks · Multiple choice

For the control system shown in the Figure, the transfer function of a plant, $G(s)=\frac{1}{(s+1)(s+2)}$ is connected in cascade with a compensator $C(s)=K(s+\alpha)$, where $K$ and $\alpha$ are positive real valued constants. Which of the following pairs $(K,\alpha)$ represent the correct values for the closed loop system to have poles at $(-3\pm j\sqrt5)$?

Diagram for GATE 2026 EC question 40
  1. 2, 3
  2. 3, 4
  3. 2, 4
  4. 3, 3

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Show answer and explanation

Correct answer: (B) 3, 4

Explanation

The characteristic equation is $s^2+(3+K)s+(2+K\alpha)=0$. The desired poles give $s^2+6s+14$. So $K=3$ and $2+3\alpha=14$, giving $\alpha=4$.