Control Systems - 1

Impulse Response Of Second-order Systems

Impulse response of second-order systems

 

Fig: 1 Second-order system.

 

For a unit-impulse input r(t), the corresponding Laplace transform is unity, or R(s) = 1. The unit-impulse response C(s) of the second-order system shown in Figure 1 is

 

 

The inverse Laplace transform of this equation yields the time solution for the response c(t) as follows:

 

 

            

Fig 2:

Note that without taking the inverse Laplace transform of C(s) we can also obtain the time response c(t) by differentiating the corresponding unit-step response since the unit-impulse function is the time derivative of the unit-step function. A family of unit impulse response curves given by Equations above with various values of is shown in Figure 2. The curves c(t)/ωn are plotted against the dimensionless variable ωnt, and thus they are functions only of .