Step and Impulse Response of a Second-Order System
Step and Impulse Response of a Second-Order System
Consider a second-order process, where the transfer function is given by , where is the process time constant and is the damping coefficient.
H(s)=1+2γτs+1
2
τ
2
s
τ
γ
This Demonstration shows the response of this process when subject to a step input of amplitude (i.e., , where is the unit step function) or an impulse input of amplitude (i.e., , where is the Dirac delta function). The response is obtained by Laplace inversion using the Mathematica built-in function, InverseLaplaceTransform.
A
AU(t)
U(t)
A
Aδ(t)
δ(t)
When , one gets an underdamped response with oscillatory behavior. Critically damped and overdamped systems result when and , 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.
0<γ<1
γ=1
γ>1