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GATE 2021 EC – Question 23

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

The block diagram of a feedback control system is shown in the figure.

The transfer function $\frac{Y(s)}{X(s)}$ of the system is

Diagram for GATE 2021 EC question 23
  1. $\dfrac{G_1+G_2+G_1G_2H}{1+G_1H}$
  2. $\dfrac{G_1+G_2}{1+G_1H+G_2H}$
  3. $\dfrac{G_1+G_2}{1+G_1H}$
  4. $\dfrac{G_1+G_2+G_1G_2H}{1+G_1H+G_2H}$

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Correct answer: (C) $\dfrac{G_1+G_2}{1+G_1H}$

Explanation

The $G_2$ branch is in parallel with $G_1$, and both are driven by the error signal $E=X-H\,(G_1E)$ at the output of the first summing junction. So $Y=(G_1+G_2)E$ with $E=\frac{X}{1+G_1H}$, giving $\frac{Y}{X}=\frac{G_1+G_2}{1+G_1H}$.