The GATE Grind

GATE 2022 IN – Question 15

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

A unity-gain negative-feedback control system has loop gain $L(s)=6/[s(s-5)]$. The closed-loop system is ______.

  1. Causal and stable
  2. Causal and unstable
  3. Noncausal and stable
  4. Noncausal and unstable

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Show answer and explanation

Correct answer: (B) Causal and unstable

Explanation

Closed-loop H=L/(1+L)=6/(s²−5s+6)=6/[(s−2)(s−3)]. The usual causal realization has two right-half-plane poles and is unstable.

Therefore **causal and unstable, B**.