Settling Time Calculator

Calculate the settling time of a second-order system from natural frequency and damping ratio.

rad/s
%

Settling Time

0.7824 s

Settling Time (4/sigma approx)0.8000 s
Decay Rate (sigma)5.000 1/s

Settling Time vs Natural Frequency (omega_n)

Vedi formula →

Formula

## Second-Order Settling Time Settling time is the time required for the system response to remain within a specified percentage band (typically 2% or 5%) of the final value. ### Formula **ts ≈ -ln(criterion) / (zeta × omega_n)** For the common 2% criterion: ts ≈ 4 / (zeta × omega_n). For 5%: ts ≈ 3 / (zeta × omega_n). The decay rate sigma = zeta × omega_n determines how quickly oscillations die out.

Esempio Risolto

A second-order system with omega_n = 10 rad/s, zeta = 0.5, 2% criterion.

  1. 01sigma = 0.5 × 10 = 5 s⁻¹
  2. 02ts = -ln(0.02) / 5 = 3.912 / 5 = 0.782 s
  3. 03Approximate: 4 / 5 = 0.800 s