GATE EC 2026 Set 1 — Question 40

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MCQ+2 / -0.67MediumOpen & Closed-Loop SystemsSystem ModellingControl SystemsCompensators & Controllers

Control Systems → Compensators & Controllers → Open & Closed-Loop Systems

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Question

For the control system shown in the Figure, the transfer function of a plant, G(s)=1(s+1)(s+2)G(s) = \frac{1}{(s+1)(s+2)} is connected in cascade with a compensator C(s)=K(s+α)C(s) = K(s + \alpha), where KK and α\alpha are positive real valued constants. Which of the following pairs (K,α)(K, \alpha) represent the correct values for the closed loop system to have poles at (3±j5)(-3 \pm j\sqrt{5})?
Control system block diagram showing a unity negative feedback loop with compensator C(s) and plant G(s) in cascade.
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