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Performance Characteristics for Step Response of an Underdamped Process

steady-state gain

time constant τ

damping coefficient ζ

0.2

step magnitude M

response

performance

Consider an underdamped second-order process with a transfer function (the ratio of output to input of a system), given by

G(s)=

+2ζτs+1

, where

is the steady-state gain,

is the time constant, and

is the damping coefficient (with

0<ζ<1

). The process is subjected to a step input

U(t)=

. This Demonstration shows plots of the response

y(t)=

-1

ℒ

(G(s)U(s))

and finds its performance characteristics: overshoot

a/b

, decay ratio

c/a

, time to rise

, time to first peak

, and period of oscillations

. You can vary the values of

, and

. Here, the values of

are restricted to the interval

[0.05,0.3]

in order to clearly identify

, and

in the plot of the output function

y(t)

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