2nd Order System Example 1

Problem

System transfer function:

Modify transfer function to increase response speed by 5 times. Plot responses to unit step input for system before and after modification.

Solution

Original system:

Underdamped (0 < ζ < 1) so,

then,

Modified system (5 times faster response than original):

Underdamped (0 < ζ < 1) so,

then,

Plot responses to unit step input for both systems:

Response as a function of time for both systems: