What is percent overshoot?

Percent overshoot is how much the step response exceeds its final steady-state value, expressed as a percentage. For a second-order underdamped system, it depends only on the damping ratio zeta: %OS = exp(-pi*zeta / sqrt(1 - zeta^2)) * 100.

What damping ratio gives zero overshoot?

A damping ratio of 1.0 (critically damped) or above produces no overshoot. Values between 0 and 1 produce underdamped responses with overshoot; values above 1 produce overdamped responses.

What is natural frequency in a control system?

Natural frequency (omega_n, in rad/s) is the oscillation frequency of an undamped second-order system. It scales the speed of the response — higher natural frequency means faster rise and settling times.

How is settling time defined here?

Settling time uses the 2% criterion: the time for the step response to remain within 2% of the final value. The approximation is Ts ≈ 4 / (zeta * omega_n) for underdamped systems.

Can this calculator handle overdamped systems?

Yes. When the damping ratio is greater than or equal to 1, the system is critically damped or overdamped. Percent overshoot is 0%, and peak time is not applicable. Settling time and rise time are still estimated.

Overshoot Calculator

Name: Overshoot Calculator
Availability: InStock
Author: Nham Vu

Enter damping ratio and natural frequency to instantly compute percent overshoot, peak time, rise time, and settling time for a second-order control system.

System Parameters

Damping Ratio ζ (zeta)

0 < ζ < 1 = underdamped | ζ = 1 = critical | ζ > 1 = overdamped

Natural Frequency ω_n (rad/s)

Undamped natural frequency in radians per second

Unit Step Response

Click Calculate to plot the response.

Summary