---
title: "Short note: Characteristics of PI and PD control"
subject: "Control Systems"
chapter: 7
key: "semester_3/control_systems:short-pi-pd-characteristics"
source: https://www.bctengineer.com/q/semester_3/control_systems/short-pi-pd-characteristics
site: BCT Engineering
---

# Short note: Characteristics of PI and PD control

Control Systems · Chapter 7: Performance Specifications and Compensation Design

- Asked in: 2076 Chaitra, 3 marks
- Video: [P, PI, PD, and PID Controllers: A Comparative Analysis in Control System Engineering](https://www.youtube.com/watch?v=OYPXiC7QjUM) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/control_systems/short-pi-pd-characteristics
- Whole chapter: https://www.bctengineer.com/md/semester_3/control_systems/chapter-7

## Question

Write a short note on characteristics of PI and PD control actions.

## Short answer

PI control adds a pole at the origin, increasing system type; it eliminates steady-state error for step inputs but slows response and may cause overshoot, behaving like a lag compensator. PD control adds a zero providing phase lead; it increases damping, reduces rise time and overshoot, improves bandwidth, and acts like a lead compensator, but does not remove steady-state error and amplifies noise.

## Answer

#### PI control action
$G_c(s) = K_p + \dfrac{K_i}{s}$; output depends on the present error and the accumulated (integrated) error.
- Adds a pole at the origin, so the system type increases by one.
- Removes steady-state error to a step for a type-0 plant (no offset).
- Makes the response slower, with more overshoot; relative stability falls.
- Reduces bandwidth, so it filters noise. Behaves like a lag compensator.

#### PD control action
$G_c(s) = K_p + K_d s$; output depends on the present error and its rate of change.
- Adds a zero, giving phase lead; acts in anticipation of the error.
- Increases damping, so overshoot, rise time and settling time decrease.
- Improves stability and increases bandwidth.
- Does not change the system type, so steady-state error is not removed.
- Amplifies high-frequency noise. Behaves like a lead compensator.

## Check yourself

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

1. Which describes PI action?
   A. Increases bandwidth
   B. Pole at origin, raises type, slower response with more overshoot
   C. Leaves type unchanged
   D. Zero only, improves damping
   Answer: B. PI adds a pole at the origin, removing step error but slowing the response; it behaves like a lag compensator. (Key point: PI characteristic)

2. Which describes PD action?
   A. Adds a zero giving phase lead, more damping, shorter settling time
   B. Reduces bandwidth
   C. Removes steady-state error
   D. Adds a pole at the origin
   Answer: A. PD acts like a lead compensator, increasing damping and bandwidth without changing the type. (Key point: PD characteristic)

3. Which controller amplifies high-frequency noise?
   A. PI, due to its integral term
   B. PD, due to its derivative term
   C. Neither
   D. Both equally
   Answer: B. PD raises high-frequency gain; PI reduces bandwidth and filters noise. (Key point: Noise)

## Related in Control Systems

- [Short note: PD and PI controller](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Ashort-pd-pi) — Control Systems, chapter 7
- [P, I, D controllers and role of PI, PD](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Apid-pi-pd-role) — Control Systems, chapter 7
- [PD controller principle and working](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Apd-controller) — Control Systems, chapter 7, asked 2×
- [Range of PI gains Kp, KI for stability](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Api-kp-ki-range-stable) — Control Systems, chapter 4
- [PI controller and its effect on time response](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Api-controller-role) — Control Systems, chapter 7
- [Working of PI controller](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Api-controller-working) — Control Systems, chapter 7

## Related in other subjects

- [Control evaluation steps; PD and PI design](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Acontrol-evaluation-steps-pd-pi) — Embedded System, chapter 7
- [Closed loop diagram; P, PI, PD, PID](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aclosed-loop-block-diagram-pid-types) — Embedded System, chapter 7
- [Digital PD controller design for plant 1/s²](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Apd-design-double-integrator) — Digital Control System, chapter 4, asked 2×
- [Digital PI design for plant with 2 s dead time](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Api-design-dead-time-2s) — Digital Control System, chapter 4, asked 3×