How is overshoot quantified in a step response?

• A. Overshoot is the amount by which the response exceeds the final steady-state value, typically expressed as a percentage of the final value.
• B. The time to settle after a disturbance.
• C. The time to reach the maximum deviation from the final value.
• D. The difference between the initial value and the final value.

Answer: (A)

Overshoot in a step response is the amount the response exceeds its final steady-state value, typically expressed as a percentage of that final value. If the final value is F and the peak value reached during the transient is P, overshoot = ((P − F)/F) × 100%. For example, if the final value is 1.0 and the peak is 1.25, the overshoot is 25%. This metric specifically captures how far the response goes above its steady-state, not how long it takes to settle.

Settling time is a separate concept—it's the time it takes for the response to stay within a specified band around the final value, not the magnitude of the excess. Time to peak refers to when the maximum deviation occurs, which is related to when the overshoot happens but does not quantify how large the overshoot is. The difference between initial and final values is just the input step size, not the overshoot.

In some standard cases, the amount of overshoot is linked to damping: more damping reduces overshoot, and for a common second-order model, the percent overshoot can be described by a formula related to the damping ratio, illustrating why and how the system’s damping controls the peak excess.