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GATE 2023 EE – Question 12

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

For the block diagram shown in the figure, the transfer function $\dfrac{Y(s)}{R(s)}$ is

Diagram for GATE 2023 EE question 12
  1. $\dfrac{2s+3}{s+1}$
  2. $\dfrac{3s+2}{s-1}$
  3. $\dfrac{s+1}{3s+2}$
  4. $\dfrac{3s+2}{s+1}$

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Correct answer: (B) $\dfrac{3s+2}{s-1}$

Explanation

Let $u=2R+Y$ be the first summer output (the feedback branch has gain 1 and is added). Then $X=u/s$ and $Y=X+3R$. So $Y=\dfrac{2R+Y}{s}+3R$, giving $Y\left(1-\dfrac1s\right)=\left(\dfrac2s+3\right)R$, i.e. $\dfrac YR=\dfrac{3s+2}{s-1}$.