---
title: "Why closed loop rejects disturbances better"
subject: "Control Systems"
chapter: 1
key: "semester_3/control_systems:define-cs-disturbance-rejection"
source: https://www.bctengineer.com/q/semester_3/control_systems/define-cs-disturbance-rejection
site: BCT Engineering
---

# Why closed loop rejects disturbances better

Control Systems · Chapter 1: Control System Background

- Asked in: 2080 Bhadra, 2+4 marks
- Video: [ROBT 303 - Lecture 05.01 - Closed-loop control systems - Disturbance rejection (Slides 22-24)](https://www.youtube.com/watch?v=uVLwvXNEqk4) — Tohid Alizadeh NU
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/control_systems/define-cs-disturbance-rejection
- Whole chapter: https://www.bctengineer.com/md/semester_3/control_systems/chapter-1

## Question

Define control system. Why does closed loop system have better disturbance rejection capability than open loop? Illustrate your answer.

## Short answer

A control system regulates output to a desired value. Closed-loop systems measure output and use feedback to counteract disturbances, reducing their effect by a factor of 1+loop gain; e.g., a 100 rpm drop becomes 5 rpm with loop gain 19.

## Answer

#### Control system
A **control system** is an arrangement of components that regulates, commands or directs a system so that its output reaches and stays at a desired value, e.g. speed control of a motor or temperature control of a room.

#### Why closed loop rejects disturbances better
An open-loop system does not measure the output, so any disturbance passes straight to the output. A closed-loop system senses the change in output and generates a corrective control action.

```text
 R  +      +----+   +       +----+   C
 -->(Σ)--->| G1 |--->(Σ)--->| G2 |--+-->
     ^ -   +----+     ^ D   +----+  |
     |         +----+               |
     +---------| H  |<--------------+
               +----+
```

With $R = 0$ (superposition):

$$
\text{Open loop: } C_D = G_2D, \qquad \text{Closed loop: } C_D = \frac{G_2}{1+G_1G_2H}D
$$

The disturbance effect is reduced by the factor $(1+G_1G_2H)$. For large loop gain, $C_D \approx D/(G_1H)$.

#### Illustration
In a DC motor speed system, let a load torque cause a 100 rpm speed drop in open loop. With tachometer feedback and loop gain $G_1G_2H = 19$, the drop becomes $100/(1+19) = 5$ rpm. The tachometer sees the fall in speed, the error increases, and the amplifier raises the armature voltage, restoring the speed almost fully. With an integral controller the steady-state drop becomes zero.

## Check yourself

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

1. Why does an open-loop system reject disturbances poorly?
   A. It over-corrects every disturbance
   B. It has too many feedback loops
   C. It does not measure the output, so the disturbance passes straight to the output
   D. It divides the disturbance by 1+GH
   Answer: C. With no sensing, no corrective action can be generated. (Key point: Why open loop fails)

2. In closed loop the disturbance effect compared with open loop is
   A. multiplied by (1 + G1G2H)
   B. unchanged
   C. divided by G2
   D. divided by (1 + G1G2H)
   Answer: D. C_D = G2 D/(1+G1G2H) versus G2 D. (Key point: Reduction factor)

3. Open-loop speed drop is 100 rpm. With loop gain 19, the closed-loop drop is
   A. 5 rpm
   B. 19 rpm
   C. 100/19 = 5.3 rpm
   D. 50 rpm
   Answer: A. 100/(1+19) = 5 rpm. (Key point: Motor illustration)

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