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GATE 2023 EC – Question 41

Control Systems · Transient and Steady-State Analysis of LTI Systems · 2 marks · Multiple choice

A closed loop system is shown in the figure where $k>0$ and $\alpha>0$. The steady state error due to a ramp input ($R(s)=\alpha/s^2$) is given by

Diagram for GATE 2023 EC question 41
  1. $\dfrac{2\alpha}{k}$
  2. $\dfrac\alpha k$
  3. $\dfrac\alpha{2k}$
  4. $\dfrac\alpha{4k}$

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Show answer and explanation

Correct answer: (A) $\dfrac{2\alpha}{k}$

Explanation

The open loop transfer function $\dfrac{k}{s(s+2)}$ is type 1 with velocity error constant $K_v=\lim_{s\to0}sG(s)=k/2$. For a ramp of slope $\alpha$, $e_{ss}=\alpha/K_v=2\alpha/k$.