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GATE 2020 BM – Question 44

Measurements and Control Systems · Control System Transfer Functions · 2 marks · Multiple choice

A non-unity-feedback system has $G(s)=12/(s+2)$ and $H(s)=2/(s+3)$. Find the magnitude of steady-state tracking error for a unit step.

  1. 0.50
  2. 0.45
  3. 0.25
  4. 0.20

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Correct answer: (D) 0.20

Explanation

At DC, G=6,H=2/3 and loop gain GH=4. The closed-loop output/input gain is G/(1+GH)=6/5=1.2. For unit input the tracking error is 1−1.2=−.2, with magnitude .20, D. The comparator error is also magnitude .2 here, although the two errors are conceptually different for non-unity feedback.

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