Calculadora de Tiempo de Establecimiento Gratis
Determina el tiempo de establecimiento de un sistema de segundo orden. Ingresa amortiguamiento y frecuencia natural.
Settling Time
0.7824 s
Settling Time vs Natural Frequency (omega_n)
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.
Ejemplo Resuelto
A second-order system with omega_n = 10 rad/s, zeta = 0.5, 2% criterion.
- 01sigma = 0.5 × 10 = 5 s⁻¹
- 02ts = -ln(0.02) / 5 = 3.912 / 5 = 0.782 s
- 03Approximate: 4 / 5 = 0.800 s
Preguntas Frecuentes
What is the difference between 2% and 5% settling time?
The 2% settling time is when the response stays within ±2% of the final value. The 5% settling time is less strict and therefore shorter. The 2% criterion is more common in practice.
How does damping affect settling time?
Increasing damping ratio reduces oscillations but makes the system slower (higher tau). The settling time is minimized at zeta ≈ 0.7 for a given natural frequency. Very low or very high damping both increase settling time.
Does this formula work for overdamped systems?
The exponential envelope approximation works best for underdamped systems (zeta < 1). For overdamped systems (zeta > 1), the response has no oscillations and the settling time depends on the slower of two real poles.
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