Setting Time when Tolerance is 5 Percent Calculator

Calculate Setting Time





Formula

The formula to calculate the Setting Time is:

\[ ts = \frac{3}{\zeta \cdot \omega_d} \]

Definition

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.

Example Calculation

Let's assume the following values:

Using the formula:

\[ ts = \frac{3}{0.1 \cdot 22.88} = 1.31118881118881 \text{ s} \]

Conversion Chart

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