---
title: "True/false: feedback makes response faster"
subject: "Control Systems"
chapter: 1
key: "semester_3/control_systems:tf-feedback-faster"
source: https://www.bctengineer.com/q/semester_3/control_systems/tf-feedback-faster
site: BCT Engineering
---

# True/false: feedback makes response faster

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-feedback-faster
- 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: Introduction of feedback on the system makes the system response faster.

## Short answer

True. Negative feedback reduces the time constant. For a first-order plant K/(τs+1) with unity feedback, closed-loop time constant becomes τ/(1+K), making response faster. Example: τ=1 s, K=9 reduces settling time from 4 s to 0.4 s.

## Answer

**True** (for negative feedback in a stable system). Feedback reduces the time constant and increases the bandwidth.

Take a first-order plant $G(s) = \dfrac{K}{\tau s + 1}$.

**Open loop:** for a unit step input

$$
c(t) = K\left(1 - e^{-t/\tau}\right), \qquad \text{time constant} = \tau
$$

**Closed loop (unity feedback):**

$$
\frac{C(s)}{R(s)} = \frac{G}{1+G} = \frac{K}{\tau s + 1 + K} = \frac{\dfrac{K}{1+K}}{\dfrac{\tau}{1+K}s + 1}
$$

$$
c(t) = \frac{K}{1+K}\left(1 - e^{-t(1+K)/\tau}\right), \qquad \tau_{cl} = \frac{\tau}{1+K}
$$

The time constant falls from $\tau$ to $\tau/(1+K)$, so the response is $(1+K)$ times faster, at the cost of reduced gain $K/(1+K)$.

Example: $\tau = 1$ s, $K = 9$. Open loop: $\tau = 1$ s, settling time $4\tau = 4$ s. Closed loop: $\tau_{cl} = 1/10 = 0.1$ s, settling time $= 0.4$ s, i.e. ten times faster.

## Check yourself

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

1. The statement 'feedback makes the response faster' is
   A. False, since feedback always slows the response
   B. True only for open-loop systems
   C. True, for negative feedback in a stable system, since the time constant falls
   D. False, since feedback only changes the steady-state value
   Answer: C. Negative feedback reduces the time constant and increases bandwidth. (Key point: Verdict)

2. For G = K/(tau s+1) with unity feedback, tau_cl equals
   A. tau(1+K)
   B. tau K/(1+K)
   C. tau - K
   D. tau/(1+K)
   Answer: D. Closed loop = [K/(1+K)] / [(tau/(1+K)) s + 1]. (Key point: Closed-loop time constant)

3. For tau = 1 s and K = 9, the closed-loop 2% settling time (4 tau_cl) is
   A. 0.4 s
   B. 4 s
   C. 0.9 s
   D. 0.04 s
   Answer: A. tau_cl = 1/10 = 0.1 s, so settling time is 4 x 0.1 = 0.4 s, ten times faster than 4 s. (Key point: Numerical example)

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