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GATE 2019 EC – Question 42

Control Systems · Transfer Function, Block Diagram and Signal Flow Graph · 2 marks · Multiple choice

The block diagram of a system is illustrated in the figure shown, where $X(s)$ is the input and $Y(s)$ is the output. The transfer function $H(s)=\frac{Y(s)}{X(s)}$ is

Diagram for GATE 2019 EC question 42
  1. $H(s)=\dfrac{s^2+1}{s^3+s^2+s+1}$
  2. $H(s)=\dfrac{s^2+1}{s^3+2s^2+s+1}$
  3. $H(s)=\dfrac{s+1}{s^2+s+1}$
  4. $H(s)=\dfrac{s^2+1}{2s^2+1}$

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

Explanation

The parallel blocks $s$ and $\frac1s$ combine to $\frac{s^2+1}{s}$, which feeds the integrator $\frac1s$. Closing the loops around the blocks gives the numerator $s^2+1$ and the characteristic polynomial $s^3+2s^2+s+1$, which is option B.