Question

The unit impulse of a system (which isn't necessarily 2nd order) is shown in the figure. In the figure, A denotes the shaded area. You must show that the percentovershoot of the output in response to a step input (%OS) is a linear function of the shaded area A. Show also that the %OS is dependent only on A and the transferfunction DC gain.

Answer 1

The response can be classified as one of three types of damping that describes the output in relation to the steady-state response.
An underdamped response is one that oscillates within a decaying envelope. The more underdamped the system, the more oscillations and longer it takes toreach steady-state. Here damping ratio 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 inthe sense that it straddles the boundary of underdamped and overdamped responses. Here, damping ratio is always equal to one. There should be nooscillation 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. Heredamping ratio is >1
[edit]Properties



Typical second order transient system properties
Rise time
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
Overshoot is when a signal or function exceeds its target. It is often associated with ringing.
Settling time
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 withina 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.[1]
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, when its behavior may be expected to continue if the system is undisturbed.[2]