# 1st Order System Example 3

## Problem

System transfer function:

Modify the transfer function such that the response reaches steady state
value after 8 seconds when unit step input is applied. Within 2% of steady state value
can be considered "reached."
Only the response speed should change and the form should not change to any input.
Plot the response before and after modification.

## Solution

Transfer function:

So

Response reaches less than 2% of steady state value at
around 4*τ* so we want *τ* to be 2 seconds. We want a slower response.
We time time-scale the response by 0.05/2 = 0.025. Modified transfer function is
then given by,

Response before and after modification as a function of time (unit step input so *A* = 1):

Plotting these equations: