First Peak Overshoot Calculator

Calculate First Peak Overshoot



Formula

The formula to calculate the First Peak Overshoot is:

\[ M_o = e^{-\left(\frac{\pi \cdot \zeta}{\sqrt{1 - \zeta^2}}\right)} \]

Definition

Peak Overshoot is the straight way difference between the magnitude of the highest peak of time response and the magnitude of its steady state. Damping Ratio in a control system is defined as the ratio with which any signal gets decayed.

Example Calculation

Let's assume the following value:

Using the formula:

\[ M_o = e^{-\left(\frac{\pi \cdot 0.1}{\sqrt{1 - 0.1^2}}\right)} = 0.729247614287671 \]

Conversion Chart

Damping Ratio (ζ) Peak Overshoot (Mo)
0.05 0.854467893006757
0.06 0.827922465180903
0.07 0.802155935246684
0.08 0.777139396601186
0.09 0.752845348176362
0.1 0.729247614287671
0.11 0.706321269855955
0.12 0.684042570596964
0.13 0.662388887807240
0.14 0.641338647406225
0.15 0.620871272922706