Question $3.$

Suppose that the dynamics of a process are represented by the following transfer function and the process is to be controlled with a proportional control algorithm.

$G_p(s)=\frac{1}{20s+1}$

If the process and controller dynamics are the only significant dynamic elements in the feedback loop and a unit step change is applied to the setpoint, what is the minimum value of the controller gain that can be specified to ensure that the steady state control error corresponds to$,|e()|0\mathrm{.}2?$

$[20$ marks$]$