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Step and Impulse Response of a Second-Order System

damping coefficient

1.2

process time constant

0.25

input amplitude

1.8

step response

impulse response

Consider a second-order process, where the transfer function is given by

H(s)=1

+2γτs+1

, where

is the process time constant and

is the damping coefficient.

This Demonstration shows the response of this process when subject to a step input of amplitude

(i.e.,

AU(t)

, where

U(t)

is the unit step function) or an impulse input of amplitude

(i.e.,

Aδ(t)

, where

δ(t)

is the Dirac delta function). The response is obtained by Laplace inversion using the Mathematica built-in function, InverseLaplaceTransform.

When

0<γ<1

, one gets an underdamped response with oscillatory behavior. Critically damped and overdamped systems result when

γ=1

and

γ>1

, respectively. For these last two cases, the response does not exhibit oscillations. A critically damped response returns to steady state faster than an overdamped response when the system is subject to an impulse input.

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