SKEDSOFT

Critically damped system:

If the two poles of C(s)/R(s) are nearly equal, the system may be approximated by a critically damped one.

For a unit-step input, R(s) = 1/s and C(s) can be written

The inverse Laplace transform of the above equation may be found as

This result can be obtained by letting approach unity in equation given as

and by using the following limit: