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GATE 2014 EC (EC3) – Question 30

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

Find C(s)/R(s) for the block diagram shown.

Diagram for GATE 2014 EC (EC3) question 30
  1. $G_1G_2/(1+G_1G_2)$
  2. $G_1G_2+G_1+1$
  3. $G_1G_2+G_2+1$
  4. $G_1/(1+G_1G_2)$

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Correct answer: (C) $G_1G_2+G_2+1$

Explanation

The input bypass adds R at the first summing node, whose output is(G1+1)R. After G2 this becomes(G1G2+G2)R. The final bypass adds another R. Therefore **C/R=G1G2+G2+1,C**. All marked summing inputs are positive and there is no feedback loop.