Calculadora de Tiempo de Establecimiento — Fórmula
## 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.
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.
Ejemplo Resuelto
A second-order system with omega_n = 10 rad/s, zeta = 0.5, 2% criterion.
- sigma = 0.5 × 10 = 5 s⁻¹
- ts = -ln(0.02) / 5 = 3.912 / 5 = 0.782 s
- Approximate: 4 / 5 = 0.800 s