The formula to calculate the Setting Time when Tolerance is 2 Percent is:
\[ t_s = \frac{4}{\zeta \cdot \omega_d} \]
Setting Time is the time required for a response to become steady. Damping Ratio in control system is defined as the ratio with which any signal gets decayed. Damped Natural Frequency is a particular frequency at which if a resonant mechanical structure is set in motion and left to its own devices, it will continue oscillating at a particular frequency.
Let's assume the following values:
Using the formula:
\[ t_s = \frac{4}{0.1 \cdot 22.88} = 1.74825174825175 \text{ seconds} \]
| Damping Ratio (ζ) | Damped Natural Frequency (ωd) | Setting Time (ts) |
|---|---|---|
| 0.05 | 22.88 Hz | 3.496503496504 seconds |
| 0.06 | 22.88 Hz | 2.913752913753 seconds |
| 0.07 | 22.88 Hz | 2.497502497503 seconds |
| 0.08 | 22.88 Hz | 2.185314685315 seconds |
| 0.09 | 22.88 Hz | 1.942501942502 seconds |
| 0.1 | 22.88 Hz | 1.748251748252 seconds |
| 0.11 | 22.88 Hz | 1.589319771138 seconds |
| 0.12 | 22.88 Hz | 1.456876456876 seconds |
| 0.13 | 22.88 Hz | 1.344809037117 seconds |
| 0.14 | 22.88 Hz | 1.248751248751 seconds |
| 0.15 | 22.88 Hz | 1.165501165501 seconds |