GATE 2022 CH – Question 23

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

The appropriate feedforward compensator, $G_{ff}$, in the shown block diagram is

the disturbance $d$ passes through $\frac{2e^{-s}}{5s + 1}$ to the output summer and through the compensator $G_{ff}$ and a gain of −1 to a summer where it is added to the signal from the feedback controller to give $u$. The input $u$ passes through $\frac{3e^{-2s}}{8s + 1}$ to the output summer, which gives $y$.

$G_{ff} = \frac{2}{3}\frac{(8s + 1)}{(5s + 1)}$
$G_{ff} = -\frac{2}{3}\frac{(8s + 1)}{(5s + 1)}$
$G_{ff} = \frac{3}{2}\frac{(5s + 1)}{(8s + 1)}e^{-s}$
$G_{ff} = -\frac{3}{2}\frac{(5s + 1)}{(8s + 1)}e^{-s}$

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Correct answer: (A) $G_{ff} = \frac{2}{3}\frac{(8s + 1)}{(5s + 1)}$

Explanation

The compensator signal enters $u$ with a minus sign, so $y = G_pu + G_dd = -G_pG_{ff}d + G_dd$. For $y = 0$ we need $G_{ff} = \frac{G_d}{G_p} = \frac{2e^{-s}/(5s + 1)}{3e^{-2s}/(8s + 1)} = \frac{2}{3}\frac{(8s + 1)}{(5s + 1)}e^{s}$. The factor $e^{s}$ would be a prediction of the future, which cannot be built, so it is left out and the realisable compensator is $\frac{2}{3}\frac{(8s + 1)}{(5s + 1)}$.