The formula to calculate the First Peak Overshoot is:
\[ M_o = e^{-\left(\frac{\pi \cdot \zeta}{\sqrt{1 - \zeta^2}}\right)} \]
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.
Let's assume the following value:
Using the formula:
\[ M_o = e^{-\left(\frac{\pi \cdot 0.1}{\sqrt{1 - 0.1^2}}\right)} = 0.729247614287671 \]
| 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 |