免费阻尼比计算器
计算振动系统的阻尼比。
阻尼比 (zeta)
0.4559
Damping Ratio (zeta) vs Measured Percent Overshoot
公式
## 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)
计算示例
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
常见问题
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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