Q$3.$ The following process model has been developed from

plant data,

$Gp(s)=\frac{2}{5s}$

It is intended to control the process using a proportional control

law with a controller gain, $k_c=0\mathrm{.}5.$

a$)$ Derive the closed loop transfer function describing the

change in process output gibe a change in the set$-$point. It may

be assumed that the dynamics of all other elements in the

feedback loop are negligible compared to that of the process.

b$)$ Use the final value theorem to determine the value of the

process output $($as time tends to infinity$)$ when the system is

subjected to a step change in the set$-$point of magnitude, $2.$