---
title: "True/false: higher forward gain reduces disturbance"
subject: "Control Systems"
chapter: 1
key: "semester_3/control_systems:tf-disturbance-forward-gain"
source: https://www.bctengineer.com/q/semester_3/control_systems/tf-disturbance-forward-gain
site: BCT Engineering
---

# True/false: higher forward gain reduces disturbance

Control Systems · Chapter 1: Control System Background

- Asked in: 2068 Baisakh (old course), 1+3 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/control_systems/tf-disturbance-forward-gain
- Whole chapter: https://www.bctengineer.com/md/semester_3/control_systems/chapter-1

## Question

State whether the following statement is true or false and justify: Effect of disturbances can be reduced by increasing the gain of forward path TF.

## Short answer

True, if the gain is increased in the forward path before the disturbance entry. The disturbance output is C_D ≈ D/(G1H) for large loop gain, so raising G1 strongly reduces the effect. Increasing gain after the disturbance does not help.

## Answer

**True**, provided the gain is increased in the forward path **before** the point where the disturbance enters (and stability is kept).

Let the disturbance $D(s)$ enter between $G_1(s)$ and $G_2(s)$, with feedback $H(s)$. With $R = 0$:

$$
C_D(s) = \frac{G_2}{1+G_1G_2H}\,D(s) \approx \frac{D(s)}{G_1H} \quad (|G_1G_2H| \gg 1)
$$

Increasing the forward gain $G_1$ increases the denominator, so the output caused by the disturbance falls. Meanwhile the output due to the reference, $C_R = \dfrac{G_1G_2}{1+G_1G_2H}R \approx R/H$, is almost unchanged.

Example: raising $G_1G_2H$ from 9 to 99 cuts the disturbance effect from $1/10$ to $1/100$ of the open-loop value.

Note: increasing only $G_2$ (after the disturbance) does not help, since $C_D \to D/(G_1H)$; and very high gain may reduce damping or cause instability.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Disturbance effect can be reduced by increasing forward-path gain. The answer is
   A. False; forward gain never affects disturbances
   B. True, if the gain is increased before the point where the disturbance enters and stability is kept
   C. True for any block, including one after the disturbance point
   D. False; only reducing H helps
   Answer: B. Raising G1 enlarges (1+G1G2H) so the disturbance output D/(G1H) shrinks. (Key point: Verdict)

2. Increasing only G2 (after the disturbance entry) does not help because
   A. G2 makes the system unstable immediately
   B. G2 removes the feedback path
   C. C_D approaches D/(G1 H), which does not depend on G2
   D. C_D approaches D/G2, which grows
   Answer: C. For large loop gain C_D ~ D/(G1H), so only G1 and H matter. (Key point: Which gain matters)

3. When G1 is increased, the output due to the reference C_R is
   A. greatly increased
   B. reduced to zero
   C. doubled
   D. almost unchanged, approximately R/H
   Answer: D. C_R = G1G2R/(1+G1G2H) ~ R/H for large loop gain. (Key point: Reference output)

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