Second-Order Step Overshoot
Find fractional overshoot of a standard underdamped second-order step response.
Try this formula
Calculate overshoot as a fraction of the final response or choose another supported quantity.
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Try this formula
Calculate overshoot as a fraction of the final response or choose another supported quantity.
Use decimals or scientific notation, such as 1.2e3. Calculations update as you type.
Overshoot as a fraction of the final response
Enter the known values to see the result.
Use a stable, linear, underdamped second-order model with 0 < ζ < 1. Use a standard zero-free second-order step response from rest. M_p is a fraction; multiply by 100 to express percent overshoot.
Difficulty
Intermediate
Read time
5 min
Prerequisites
Basic algebra and introductory dynamic systems
Source
Donney Fan — MECH 466 — Automatic ControlReference equation: Second Order System — Overshoot. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Definition
Overshoot measures how far the first peak exceeds the final response relative to that final value. More damping reduces this excess for the standard second-order model.
Variables & Units
| Symbol | Meaning | Units |
|---|---|---|
| Overshoot as a fraction of the final response | ||
| Damping ratio |
Real-World Applications
Step-response estimates
Estimate overshoot from a damping ratio.
Damping selection
Compare overshoot against a response target.
Worked Example
Problem
A standard second-order system has ζ = 0.5. Find its fractional overshoot and interpret it as a percentage.
Given
Solution
Final Answer
Contents
Info
Tools
Source & review
Reference equation: Second Order System — Overshoot. FormuLab wrote new explanations, assumptions, applications, and numerical examples.
Assumptions
- • Use a stable, linear, underdamped second-order model with 0 < ζ < 1.
- • Use a standard zero-free second-order step response from rest.
- • M_p is a fraction; multiply by 100 to express percent overshoot.
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