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GATE 2021 EE – Question 21

Control Systems · Mathematical modelling and representation of systems, Feedback principle, Transfer function, Block diagrams and Signal flow graphs · 1 mark · Multiple choice

For the closed-loop system shown, the transfer function $\dfrac{E(s)}{R(s)}$ is

Diagram for GATE 2021 EE question 21
  1. $\dfrac{G}{1+GH}$
  2. $\dfrac{GH}{1+GH}$
  3. $\dfrac{1}{1+GH}$
  4. $\dfrac{1}{1+G}$

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Correct answer: (C) $\dfrac{1}{1+GH}$

Explanation

With $E=R-HC$ and $C=GE$, we get $E=R-GHE$, so $E(1+GH)=R$ and $\frac{E}{R}=\frac{1}{1+GH}$.