Calculateur de Marge de Phase
Calculez la marge de phase d'un système en boucle ouverte.
Coefficient d'amortissement (zeta)
0.4559
Damping Ratio (zeta) vs Measured Percent Overshoot
Formule
Damping Ratio from Overshoot
The damping ratio determines the character of a second-order system response. It can be extracted from a measured step response by noting the percent overshoot.
Formula
zeta = ln(%OS/100)
Exemple Résolu
A step response shows 20% overshoot.
- 01ln(0.20) = -1.6094
- 02zeta = 1.6094 / sqrt(9.8696 + 2.5902)
- 03zeta = 1.6094 / sqrt(12.4598) = 1.6094 / 3.5299
- 04zeta = 0.4559
Questions Fréquentes
What damping ratio is considered optimal?
For most control systems, zeta between 0.6 and 0.8 is considered good. This gives a fast response with acceptable overshoot (less than 10%). zeta = 0.707 gives the fastest response without resonance peak amplification.
Can I measure damping from the decay of oscillations?
Yes. The logarithmic decrement delta = ln(x_n / x_{n+1}) relates to damping as zeta = delta / sqrt(4*pi² + delta²). This method works well for lightly damped systems.
What if there is no overshoot?
If the step response has no overshoot, the system is critically damped (zeta = 1) or overdamped (zeta > 1). In this case, the overshoot method cannot be used directly.
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