Calculator · Dynamics & Control
Percent Overshoot Calculator
Find the percent overshoot of the standard second-order unit-step response for a given damping ratio ζ.
Input
Percent overshoot does not depend on ωn; this value only populates the Lab.
Result
| Damping ratio ζ (input) | 0.5 |
|---|---|
| Damping regime | Underdamped (0 < ζ < 1) |
| Percent overshoot | 16.3 % |
| Peak time Tp | 0.3628 s |
The response overshoots by about 16.3% and rings down. Increasing ζ reduces overshoot.
Diagnostics
- · Info Settling times are exponential-envelope approximations (4/ζωn and 3/ζωn), not simulated crossing times.
Explore further
Technical reference
OS% = 100·exp(−πζ / √(1 − ζ²)), 0 < ζ < 1
Worked example: ζ = 0.5 gives 16.3% overshoot.
Assumptions and limitations
- · Canonical normalized second-order system with unit-step input and unity DC gain.
- · ζ = 0: no decaying envelope, so transient percent overshoot is not defined.
- · ζ ≥ 1: the standard response is monotonic and overshoot is zero.
- · Additional poles, zeros, delay or saturation change the real overshoot.