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GATE 2014 EC (EC2) – Question 31

Control Systems · Transfer Function, Block Diagram and Signal Flow Graph · 1 mark · Multiple choice

For the system shown, find Y(s)/X₂(s) when X₁(s) = 0.

Diagram for GATE 2014 EC (EC2) question 31
  1. $(s+1)/s^2$
  2. $1/(s+1)$
  3. $(s+2)/(s(s+1))$
  4. $(s+1)/(s(s+2))$

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Show answer and explanation

Correct answer: (D) $(s+1)/(s(s+2))$

Explanation

With X1=0, the first summing-node output is−Y. The second is−sY/(s+1)+X2, followed by1/s. Hence sY=−sY/(s+1)+X2, giving Y/X2=(s+1)/[s(s+2)], **D**. X2 enters after the first block, so its path differs from X1’s.