Setting Time when Tolerance is 2 Percent Calculator

Calculate Setting Time when Tolerance is 2 Percent





Formula

The formula to calculate the Setting Time when Tolerance is 2 Percent is:

\[ t_s = \frac{4}{\zeta \cdot \omega_d} \]

Definition

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.

Example Calculation

Let's assume the following values:

Using the formula:

\[ t_s = \frac{4}{0.1 \cdot 22.88} = 1.74825174825175 \text{ seconds} \]

Conversion Chart

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