---
title: "How feedback rejects disturbance input"
subject: "Control Systems"
chapter: 1
key: "semester_3/control_systems:feedback-reject-disturbance"
source: https://www.bctengineer.com/q/semester_3/control_systems/feedback-reject-disturbance
site: BCT Engineering
---

# How feedback rejects disturbance input

Control Systems · Chapter 1: Control System Background

- Asked in: 2070 Chaitra, 3 marks
- Video: [Part 5 of 5 : Effect of Feedback on  Disturbance/Noise of Control System](https://www.youtube.com/watch?v=sN7kpigwxS8) — Learning Electronics
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/control_systems/feedback-reject-disturbance
- Whole chapter: https://www.bctengineer.com/md/semester_3/control_systems/chapter-1

## Question

Discuss how a feedback control system rejects the disturbance input.

## Short answer

Feedback senses the disturbance effect and produces a correcting action. The disturbance output is divided by (1+loop gain); when loop gain is large, the effect becomes very small (e.g., 99% rejection for gain 99). The system thus robustly cancels load changes.

## Answer

A feedback system senses the effect of the disturbance on the output and produces a correcting control action, so the disturbance is largely cancelled.

**Disturbance rejection.** Let the disturbance $D(s)$ enter between two forward blocks $G_1$ (controller) and $G_2$ (plant).

- Open loop: $C_D(s) = G_2(s)D(s)$.
- Closed loop (feedback $H$), with $R = 0$ (superposition):

$$
C_D(s) = \frac{G_2(s)}{1 + G_1(s)G_2(s)H(s)}\,D(s)
$$

The disturbance output is divided by $(1+G_1G_2H)$. If $|G_1G_2H| \gg 1$, $C_D \approx \dfrac{D}{G_1H}$, which is very small for large $G_1$.

**Example:** $G_1G_2H = 99$ means only 1% of the disturbance effect remains at the output, compared with 100% in open loop. In a motor speed system, a sudden load torque lowers the speed; the tachometer detects this, the error rises, and the amplifier increases armature voltage to restore the speed.

## Check yourself

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

1. With R = 0, the closed-loop output due to disturbance D (entering between G1 and G2) is
   A. G2 D
   B. G1 G2 D / (1 + G1 G2 H)
   C. D / (1 - G1 G2 H)
   D. G2 D / (1 + G1 G2 H)
   Answer: D. By superposition C_D = G2/(1+G1G2H) D, versus G2 D in open loop. (Key point: Disturbance effect)

2. If G1G2H = 99, how much of the open-loop disturbance effect remains at the output?
   A. 1%
   B. 99%
   C. 10%
   D. 0.1%
   Answer: A. The effect is divided by 1 + 99 = 100, leaving 1%. (Key point: Reduction factor)

3. In a motor speed loop a load torque lowers the speed. How does feedback correct it?
   A. The load torque is physically removed by the tachometer
   B. The tachometer detects the fall, error rises and the amplifier raises armature voltage
   C. The reference speed is lowered automatically
   D. Nothing; speed stays low until reset by an operator
   Answer: B. The sensed drop increases the error, which increases the control action and restores speed. (Key point: Mechanism)

## Related in Control Systems

- [Control system and why feedback makes response faster](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Awhat-is-cs-feedback-faster) — Control Systems, chapter 1
- [Derivative feedback for ramp input](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Aderivative-feedback-ramp) — Control Systems, chapter 7
- [K limiting disturbance effect to 2%](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Adisturbance-5k-s10-6-s2) — Control Systems, chapter 3
- [Tracking, disturbance rejection and pole sensitivity](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atrack-reject-sensitivity-160) — Control Systems, chapter 3
- [Feedback effect in DC motor speed control](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Afeedback-dc-motor-speed) — Control Systems, chapter 1
- [Feedback vs non-feedback control systems](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Afeedback-vs-nonfeedback) — Control Systems, chapter 1

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