---
title: "Controller recommended to reduce steady-state error"
subject: "Control Systems"
chapter: 7
key: "semester_3/control_systems:controller-reduce-sse"
source: https://www.bctengineer.com/q/semester_3/control_systems/controller-reduce-sse
site: BCT Engineering
---

# Controller recommended to reduce steady-state error

Control Systems · Chapter 7: Performance Specifications and Compensation Design

- Asked in: 2082 Baisakh, 4 marks
- Video: [Improving steady state error via cascade compensation (Lecture 30)](https://www.youtube.com/watch?v=dcp7Vr7UjKE) — Dr. Usman Nasim
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/control_systems/controller-reduce-sse
- Whole chapter: https://www.bctengineer.com/md/semester_3/control_systems/chapter-7

## Question

Which type of controller do you recommend to reduce the steady state error? Explain.

## Short answer

Use a PI controller (or lag compensator) because it adds a pole at the origin, increasing the system type by one. The integral term grows while any error remains, driving steady-state error to zero for step or ramp inputs.

## Answer

To reduce (or eliminate) steady-state error, an **integral-type controller**, usually a **PI controller** (or PID), is recommended. In frequency-domain design, the equivalent is a **lag compensator**.

#### Why integral action

The steady-state error of a unity feedback system depends on the system type and the error constants:

$$
e_{ss}(\text{step})=\frac{1}{1+K_{pos}},\qquad e_{ss}(\text{ramp})=\frac{1}{K_v}
$$

where $K_{pos}=\lim_{s\to0}G(s)$ is the position error constant and $K_v=\lim_{s\to0}sG(s)$ the velocity error constant.

A PI controller

$$
G_c(s)=K_p+\frac{K_i}{s}=\frac{K_p(s+K_i/K_p)}{s}
$$

adds a **pole at the origin**, so the system **type increases by one**:

| Plant type | Without PI | With PI |
|---|---|---|
| 0 | finite step error | zero step error |
| 1 | finite ramp error | zero ramp error |

Physically, the integral keeps growing while any error remains, so the controller output keeps changing until the error is exactly zero.

The zero at $-K_i/K_p$ is placed close to the origin so that the extra phase lag (and its effect on the transient response and stability) stays small.

#### Alternatives

- **Increasing proportional gain** reduces the error but cannot remove it, and makes the response oscillatory.
- **Lag compensator** $\frac{1+Ts}{1+\beta Ts}$ raises the low-frequency gain by $\beta$ ($K_v$ multiplied by β) without changing the transient much.

**Example:** $G(s)=\frac{10}{s+2}$ with unity-gain P control has $K_{pos}=5$ and step error $\frac{1}{1+5}=0.167$. With PI control the open loop has a pole at the origin and the step error becomes zero.

## Check yourself

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

1. Which controller is recommended to reduce steady-state error?
   A. PD controller
   B. Integral type, usually PI (or PID); equivalent to a lag compensator
   C. Derivative controller alone
   D. Lead compensator
   Answer: B. Integral action raises the system type and removes steady error; in the frequency domain this corresponds to a lag compensator. (Key point: Recommended controller)

2. Why does the PI controller reduce steady-state error?
   A. It adds a zero at the origin
   B. It adds a pole at the origin, raising the system type by one
   C. It increases bandwidth
   D. It reduces the damping ratio
   Answer: B. The extra pole at the origin raises the type, e.g. type 1 plants get zero ramp error. (Key point: Why it works)

3. Why is simply increasing proportional gain not recommended to eliminate the error?
   A. It removes error but destroys type
   B. It reduces but cannot remove the error, and makes the response oscillatory
   C. It increases the type by one
   D. It has no effect on error
   Answer: B. Higher Kp only lowers error (e.g. 1/(1+Kp)) and reduces damping. (Key point: Alternative)

## Related in Control Systems

- [True/false: proportional controller makes error zero](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Atf-proportional-sse-zero) — Control Systems, chapter 7
- [Velocity feedback increases ζ and steady-state error](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Avelocity-feedback-zeta-sse) — Control Systems, chapter 3
- [Controller to change transient properties](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Acontroller-transient) — Control Systems, chapter 7
- [Error constants of 108/[s²(s+4)(s²+3s+12)], r = 2+5t+8t²](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Asse-108-s2-input-2-2) — Control Systems, chapter 3, asked 4×
- [Error constants of 108/[s²(s+4)(s²+3s+12)], r = 2+5t+2t²](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Asse-108-s2-input-2-5t) — Control Systems, chapter 3, asked 4×
- [Error constants of 5/[s(s+2)(s²+2s+8)], r = 2+5t+2t²](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Asse-5-s-s2-s2-2s) — Control Systems, chapter 3, asked 4×

## Related in other subjects

- [Case study: recommended changes and convincing](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Acs-recommend-changes) — Instrumentation II, chapter 10, asked 2×
- [Compensation does not reduce load reactive demand](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Acompensation-does-not-reduce-load-q) — Power System Analysis I, chapter 6
- [Steady state vs transient stability; enhancement](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Asteady-transient-stability-enhancement) — Power System Analysis II, chapter 6, asked 2×
- [Force by vane on steady stream](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_mechanics_dynamics%3Asteady-stream-force-vane-deduce) — Applied Mechanics (Dynamics), chapter 3