Calculator · Dynamics & Control
Settling Time Calculator
Estimate the approximate 2% and 5% settling times of a canonical second-order step response from ζ and ωn.
Input
Result
| Damping regime | Underdamped (0 < ζ < 1) |
|---|---|
| Approx. 2% settling time | 0.8 s |
| Approx. 5% settling time | 0.6 s |
Within ±2% of the final value after roughly 0.8 s. The estimate scales with 1/(ζωn), so raising either parameter settles the response faster.
Diagnostics
- · Info Settling times are exponential-envelope approximations (4/ζωn and 3/ζωn), not simulated crossing times.
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Technical reference
Ts,2% ≈ 4 / (ζωn) · Ts,5% ≈ 3 / (ζωn), 0 < ζ < 1
Worked example: ζ = 0.5 and ωn = 10 rad/s give approximately 0.8 s (2%) and 0.6 s (5%).
Assumptions and limitations
- · Values are exponential-envelope approximations, not simulated threshold-crossing times.
- · Valid for the underdamped regime 0 < ζ < 1 only.
- · ζ = 0 never settles; ζ ≥ 1 is reported as not applicable rather than estimated.
- · Canonical second-order model: extra poles, zeros, delay or saturation change the real settling time.