GATE 2016 EC (EC3) – Question 30

Control Systems · Transient and Steady-State Analysis of LTI Systems · 1 mark · Multiple choice

A unity-negative-feedback system has open-loop $G(s)=2/[s(s+1)]$, as shown. Its steady-state error to a unit step is

Diagram for GATE 2016 EC (EC3) question 30

0
0.5
1.0
$\infty$

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Correct answer: (A) 0

Explanation

For unity feedback, $E(s)=R(s)/(1+G(s))$. A unit step has R=1/s, so the final error is $\lim_{s\to0}1/(1+G(s))$.

The loop has an integrator, hence G(s) tends to infinity at DC and this limit is zero. The closed-loop polynomial $s^2+s+2$ is stable, validating the final value theorem. Therefore **0, A**.

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