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:

- Damping Ratio (ζ) = 0.1
- Damped Natural Frequency (ωd) = 22.88 Hz

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 |