---
title: "Metrics for control objectives"
subject: "Embedded System"
chapter: 7
key: "semester_6/embedded_system:control-metrics-objectives"
source: https://www.bctengineer.com/q/semester_6/embedded_system/control-metrics-objectives
site: BCT Engineering
---

# Metrics for control objectives

Embedded System · Chapter 7: Control System

- Asked in: 2073 Bhadra, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/embedded_system/control-metrics-objectives
- Whole chapter: https://www.bctengineer.com/md/semester_6/embedded_system/chapter-7

## Question

Explain the metrics used to measure control objectives.

## Short answer

Metrics from step response: rise time (10-90% of final), peak time and overshoot percentage, settling time within a 2-5% band, steady-state error, stability/damping, disturbance rejection, and control effort. A good design has small rise time, minimal overshoot, short settling time, and near-zero steady-state error.

## Answer

Control objectives are measured with a set of performance metrics, mostly from the step response of the closed-loop system:

1. **Rise time (tr):** time for the output to go from 10 % to 90 % of the final value. Measures speed of response.
2. **Peak time (tp) and overshoot (Mp):** tp is the time taken to reach the first (maximum) peak; Mp is the maximum amount, usually in percent, by which the output exceeds the final value: Mp = (peak - final)/final × 100 %.
3. **Settling time (ts):** time after which the output stays within a band (usually 2 % or 5 %) of the final value.
4. **Steady-state error (ess):** final difference between set-point and output: ess = r - y(∞). Measures accuracy.
5. **Stability / damping:** the output must remain bounded and any oscillation must decay (damping ratio, gain and phase margins).
6. **Disturbance rejection:** size and duration of the output change caused by a disturbance.
7. **Control effort / robustness:** size of the actuator output and sensitivity to parameter change.

```text
 y
 |        _ Mp (overshoot)
 |   ____/ \___ ______ final value (+/-2% band)
 |  /          \/
 | /
 +--tr--------ts------- t
```

A good design has small tr, small overshoot, short ts and ess close to zero.

## Check yourself

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

1. How is rise time defined?
   A. Time to reach peak
   B. Time to settle within 2%
   C. Final error
   D. Time for output to go from 10% to 90% of final value
   Answer: D. Measures speed. (Key point: Rise time)

2. Mp is calculated as?
   A. (final - peak)/peak
   B. final/peak
   C. (peak - final)/final x 100%
   D. peak x final
   Answer: C. Percent exceeding final value. (Key point: Overshoot)

3. Settling time is when?
   A. Output first reaches final
   B. Output stays within 2% or 5% band of final value
   C. Output peaks
   D. Error is largest
   Answer: B. Band-based. (Key point: Settling time)

4. ess measures?
   A. Accuracy: r - y(infinity)
   B. Speed of response
   C. Overshoot
   D. Noise
   Answer: A. Final difference. (Key point: Steady-state error)

## Related in Embedded System

- [Control methods for interface communication](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Ainterfacing-control-methods) — Embedded System, chapter 5
- [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

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