Block diagram of a control system is shown in the figure.

The condition that must be satisfied to remove the effect of disturbance on the reponse of the system.

G_{2} H_{2} = 1

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G_{1} H_{1} = - 1

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G_{1} G_{2} G_{3} H_{1} = - 1

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G_{1} H_{2} = - 1

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Solution

The correct option is D $G_{1} H_{2} = - 1$
It is desirable to remove the effect of disturbance on response.

So $\frac{C (s)}{D (s)}$ ratio can be calculated as follows:
$C (s) = D (s) \frac{G_{3} (1 + G_{1} H_{2})}{1 + G_{1} G_{2} G_{3} H_{1} + G_{1} H_{2}}$

Response due to disturbance,

$C (s) = D (s) \frac{G_{3} (1 + G_{1} H_{2})}{1 + G_{1} G_{2} G_{3} H_{1} + G_{1} H_{2}}$

C(s) should be zero for $D (s) \neq 0$

$∴ G_{1} H_{2} = - 1$

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