---
title: "Why closed loop response is faster than open loop"
subject: "Control Systems"
chapter: 1
key: "semester_3/control_systems:cl-faster-than-ol"
source: https://www.bctengineer.com/q/semester_3/control_systems/cl-faster-than-ol
site: BCT Engineering
---

# Why closed loop response is faster than open loop

Control Systems · Chapter 1: Control System Background

- Asked in: 2080 Baisakh, 4 marks; 2078 Bhadra, 4 marks; 2079 Bhadra, 3 marks; 2078 Kartik, 3 marks (asked 4 times)
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/control_systems/cl-faster-than-ol
- 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: System response is faster in closed loop control system than in open loop control system.

## Short answer

True. Negative feedback reduces the system time constant, so the output reaches its final value sooner; for a first-order plant the time constant drops from tau to tau/(1+K).

## Answer

**True** (for a stable system with normal negative feedback). Negative feedback reduces the time constant of the system, so the output reaches its final value sooner.

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 closed-loop time constant is smaller by the factor $(1+K)$, so the response is $(1+K)$ times faster. The price is a lower gain, $K/(1+K)$ instead of $K$, which is made up by adding an amplifier in the forward path.

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.

For second-order systems the same idea holds: feedback raises the natural frequency $\omega_n$, so rise time and peak time fall (but too much gain can increase overshoot).

## Check yourself

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

1. For a first-order plant K/(tau s + 1) with unity negative feedback, what is the closed-loop time constant?
   A. tau/(1+K)
   B. tau(1+K)
   C. tau/K
   D. K tau/(1+K)
   Answer: A. G/(1+G) = K/(tau s + 1 + K), which divided by (1+K) gives a time constant tau/(1+K). (Key point: Time constant under feedback)

2. Why is the response of a closed-loop system faster than that of an open-loop system?
   A. Feedback increases the plant time constant
   B. Negative feedback reduces the time constant so the final value is reached sooner
   C. Feedback removes the plant dynamics entirely
   D. Feedback increases the steady-state gain
   Answer: B. Negative feedback shrinks the time constant by the factor (1+K), so the output settles sooner. (Key point: Why the statement is true)

3. With tau = 1 s and K = 9, the closed-loop settling time (4 time constants) is 0.4 s. What is the cost paid for this speed-up?
   A. Settling time rises to 4 s
   B. Time constant becomes negative
   C. Steady-state gain falls from K to K/(1+K)
   D. Steady-state gain rises to K(1+K)
   Answer: C. The closed-loop gain is K/(1+K) = 0.9 instead of 9; it is recovered by adding an amplifier. (Key point: Price of the faster response)

## Related in Control Systems

- [True/false: feedback makes response faster](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atf-feedback-faster) — Control Systems, chapter 1
- [True/false: air conditioner is closed loop](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atf-air-conditioning-closed) — Control Systems, chapter 1
- [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
- [Closed vs open loop step response analytically](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Acl-vs-ol-step-response) — Control Systems, chapter 1, asked 2×
- [Traffic light system of Kathmandu: open or closed loop](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atraffic-light-justify) — Control Systems, chapter 1
- [Control system block diagram and closed loop advantages](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Awhat-is-cs-bd-cl-advantages) — Control Systems, chapter 1

## Related in other subjects

- [Closed loop better than open loop (cruise)](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aclosed-loop-better-cruise-integral) — Embedded System, chapter 7
- [True/false: CT secondary kept open](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Atf-false-ct-secondary-open) — Electrical Machine, chapter 2
- [Open loop versus closed loop control](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aopen-vs-closed-loop) — Embedded System, chapter 7, asked 6×
- [Steps to design closed loop control system](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aclosed-loop-design-steps) — Embedded System, chapter 7