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GATE 2014 EC (EC1) – Question 58

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

The feedback system has $G(s)=1/((s+1)(s+2))$. Its step response must have 2% settling time below 2 seconds. Which compensator C(s) achieves this?

Diagram for GATE 2014 EC (EC1) question 58
  1. $3/(s+5)$
  2. $5(0.03/s+1)$
  3. $2(s+4)$
  4. $4(s+8)/(s+3)$

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Show answer and explanation

Correct answer: (C) $2(s+4)$

Explanation

With **C(s)=2(s+4),C**, the closed-loop denominator is(s+1)(s+2)+2(s+4)=s²+5s+10. Its poles are−2.5±j√15/2, so the standard2% settling estimate is4/(ζωn)=4/2.5=1.6s<2s. The actual step-error envelope is also below2% before2s. The other choices retain slower modes and do not satisfy the requested settling behaviour.