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GATE 2022 IN – Question 37

Control Systems · Feedback and transfer functions · 2 marks · Multiple choice

The signal-flow graph is shown. The expression for $Y(s)/X(s)$ is ______.

Diagram for GATE 2022 IN question 37
  1. $\dfrac{2G_1(s)G_2(s)+2G_1(s)G_3(s)}{1+G_2(s)+G_3(s)}$
  2. $2+G_1(s)+G_3(s)+\dfrac{G_2(s)}{1+G_2(s)}$
  3. $G_1(s)+G_3(s)-\dfrac{G_2(s)}{2+G_2(s)}$
  4. $\dfrac{2G_1(s)G_2(s)+2G_1(s)G_3(s)-G_1(s)}{1+G_2(s)+G_3(s)}$

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Correct answer: (A) $\dfrac{2G_1(s)G_2(s)+2G_1(s)G_3(s)}{1+G_2(s)+G_3(s)}$

Explanation

The parallel forward branches combine as G2+G3, with negative unity feedback around them. Their closed-loop gain is (G2+G3)/(1+G2+G3). Multiply by input G1 and output 2 to obtain **2G1(G2+G3)/(1+G2+G3), A**.