The formula to calculate the Setting Time is:
\[ ts = \frac{3}{\zeta \cdot \omega_d} \]
Setting Time is the time required for a response to become steady. Damping Ratio in control systems is defined as the ratio with which any signal gets decayed. Damped Natural Frequency is the particular frequency at which a resonant mechanical structure will continue oscillating if set in motion and left to its own devices.
Let's assume the following values:
Using the formula:
\[ ts = \frac{3}{0.1 \cdot 22.88} = 1.31118881118881 \text{ s} \]
| Damping Ratio (ζ) | Damped Natural Frequency (ωd) | Setting Time (ts) |
|---|---|---|
| 0.05 | 22.88 Hz | 2.622377622378 s |
| 0.06 | 22.88 Hz | 2.185314685315 s |
| 0.07 | 22.88 Hz | 1.873126873127 s |
| 0.08 | 22.88 Hz | 1.638986013986 s |
| 0.09 | 22.88 Hz | 1.456876456876 s |
| 0.1 | 22.88 Hz | 1.311188811189 s |
| 0.11 | 22.88 Hz | 1.191989828353 s |
| 0.12 | 22.88 Hz | 1.092657342657 s |
| 0.13 | 22.88 Hz | 1.008606777838 s |
| 0.14 | 22.88 Hz | 0.936563436563 s |
| 0.15 | 22.88 Hz | 0.874125874126 s |