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GATE 2024 CH – Question 22

Instrumentation and Process Control · Cascade and feedforward control · 1 mark · Multiple choice

Consider the block diagram in the figure with control input $u$, disturbance $d$ and output $y$. For the feedforward controller, the ordered pair $(K, \alpha/\beta)$ is

the disturbance $d$ passes through $\frac{1}{(s+1)^2}$ to the output summer, and the control input $u$ passes through the process $\frac{2}{(0.5s+1)^2}$ to the same summer. The feedforward controller $K\left(\frac{\alpha s + 1}{\beta s + 1}\right)^2$ takes $d$ as its input and gives $u$.
  1. (0.5, 2)
  2. (−0.5, 0.5)
  3. (−2, 2)
  4. (2, 0.5)

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Correct answer: (B) (−0.5, 0.5)

Explanation

For perfect disturbance rejection the feedforward controller must cancel the disturbance: $G_f = -\frac{G_d}{G_p} = -\frac{1/(s+1)^2}{2/(0.5s+1)^2} = -0.5\left(\frac{0.5s + 1}{s + 1}\right)^2$. Comparing with $K\left(\frac{\alpha s + 1}{\beta s + 1}\right)^2$: $K = -0.5$, $\alpha = 0.5$ and $\beta = 1$, so $\frac{\alpha}{\beta} = 0.5$.