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GATE 2022 IN – Question 41

Control Systems · Time response and steady-state error · 2 marks · Multiple choice

A PID controller stably controls $P(s)=1/[(s+1)(s+2)]$. Its proportional gain is increased by factor 2, integral gain by factor 3, and derivative gain is unchanged. If the closed-loop system remains stable, the steady-state error for a ramp reference ______.

  1. Remains unchanged
  2. Decreases by a factor of 2
  3. Decreases by a factor of 3
  4. Decreases by a factor of 5

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Show answer and explanation

Correct answer: (C) Decreases by a factor of 3

Explanation

For type-one behavior from the integral controller, Kv=lim sC(s)P(s)=KI/2. Ramp error is 1/Kv=2/KI. Tripling KI divides error by three; KP and KD do not enter this limit.

Thus **C**.