In electrical engineering

Electrical engineering

Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...

 and mechanical engineering

Mechanical engineering

Mechanical engineering is a discipline of engineering that applies the principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems. It is the branch of engineering that involves the production and usage of heat and mechanical power for the...

, a transient response or natural response is the response of a system to a change from equilibrium. The transient response is not necessarily tied to "on/off" events but to any event that affects the equilibrium of the system. The impulse response

Impulse response

In signal processing, the impulse response, or impulse response function , of a dynamic system is its output when presented with a brief input signal, called an impulse. More generally, an impulse response refers to the reaction of any dynamic system in response to some external change...

 and step response

Step response

The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs change from...

 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 damping

Damping

In physics, damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory system, particularly the harmonic oscillator.In mechanics, friction is one such damping effect...

 that describes the output in relation to the steady-state response.

An underdamped response is one that oscillates within a decaying envelope

Envelope (mathematics)

In geometry, an envelope of a family of curves in the plane is a curve that is tangent to each member of the family at some point. Classically, a point on the envelope can be thought of as the intersection of two "adjacent" curves, meaning the limit of intersections of nearby curves...

. The more underdamped the system, the more oscillations and longer it takes to reach steady-state. Here damping ratio

Damping ratio

[[Image:Damped spring.gif|right|frame|Underdamped [[spring–mass system]] with ζ 1 , and is referred to as overdamped.*Underdamped:If s is a complex number, then the solution is a decaying exponential combined with an oscillatory portion that looks like \exp...

 is always <1.

A critically damped response is the response that reaches the steady-state value the fastest without being underdamped. It is related to critical points

Critical point (mathematics)

In calculus, a critical point of a function of a real variable is any value in the domain where either the function is not differentiable or its derivative is 0. The value of the function at a critical point is a critical value of the function...

 in the sense that it straddles the boundary of underdamped and overdamped responses. Here, damping ratio is always equal to one. There should be no oscillation about the steady state value in the ideal case.

An overdamped response is the response that does not oscillate about the steady-state value but takes longer to reach than the critically damped case.
Here damping ratio is >1

Properties

Rise time

Rise time

Rise time

In electronics, when describing a voltage or current step function, rise time refers to the time required for a signal to change from a specified low value to a specified high value...

 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

Overshoot

Overshoot (signal)

In signal processing, control theory, electronics, and mathematics, overshoot is when a signal or function exceeds its target. It arises especially in the step response of bandlimited systems such as low-pass filters...

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

Ringing (signal)

In electronics, signal processing, and video, ringing is unwanted oscillation of a signal, particularly in the step response...

.

Settling time

Settling time

Settling time

The settling time of an amplifier or other output device is the time elapsed from the application of an ideal instantaneous step input to the time at which the amplifier output has entered and remained within a specified error band, usually symmetrical about the final value.Settling time includes a...

 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 error band.

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.1

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 steady state

Steady state

A system in a steady state has numerous properties that are unchanging in time. This implies that for any property p of the system, the partial derivative with respect to time is zero:...

, when its behavior may be expected to continue if the system is undisturbed.