Kostenloser Damping Ratio Rechner
Berechnen Sie damping ratio aus measured percent overshoot. Classify systems as underdamped, critically damped, or overdamped.
Dämpfungsgrad (zeta)
0.4559
Damping Ratio (zeta) vs Measured Percent Overshoot
Formel
## 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)| / sqrt(pi² + ln²(%OS/100))** - zeta < 1: underdamped (oscillatory) - zeta = 1: critically damped (fastest non-oscillatory) - zeta > 1: overdamped (sluggish, no oscillations)
Lösungsbeispiel
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
Häufig Gestellte Fragen
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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