Transient response

In and, a transient response is the response of a system to a change from an  or a. The transient response is not necessarily tied to abrupt events but to any event that affects the equilibrium of the system. The and  are transient responses to a specific input (an impulse and a step, respectively).

Damping
The response can be classified as one of three types of that describes the output in relation to the.


 * Underdamped
 * An response is one that oscillates within a decaying .  The more underdamped the system, the more oscillations and longer it takes to reach steady-state. Here  is always less than one.


 * Critically damped
 * A response is that response which reaches the steady-state value the fastest without being underdamped. It is related to  in the sense that it straddles the boundary of underdamped and  responses. Here, damping ratio is always equal to one. There should be no oscillation about the steady state value in the ideal case.


 * Overdamped
 * An overdamped response is the response that does not oscillate about the steady-state value but takes longer to reach steady-state than the critically damped case. Here damping ratio is greater than one.

Properties
Transient response can be quantified with the following properties.
 * Rise time
 * refers to the time required for a signal to change from a specified low value to a specified high value. Typically, these values are 10% and 90% of the step height.


 * Overshoot
 * is when a signal or function exceeds its target. It is often associated with.


 * Settling time
 * is the time elapsed from the application of an ideal instantaneous step input to the time at which the output has entered and remained within a specified.


 * Delay-time
 * The delay time is the time required for the response to reach half the final value the very first time.


 * Peak time
 * The peak time is the time required for the response to reach the first peak of the overshoot.


 * Steady-state error
 * 2003's Instrument Engineers' Handbook defines the steady-state error of a system as "the difference between the desired final output and the actual one" when the system reaches a, when its behavior may be expected to continue if the system is undisturbed.