Q$3)$ Consider a PID controller with a transfer function of $K_c(1+\frac{1}{{}_{1}S}+{}_{D}S).$ The input error function

is in $mA.$

a$)$ With the information given below find out the response of the controller for a step error of $-10$

$mA.15pts$

$K_c=1\mathrm{.}5,{}_{\text{I}}=0\mathrm{.}5,{}_D=0\mathrm{.}2$

b$)$ Will derivative kick happen or not? Why? $(5$ pts$)$

c$)$ Is the controller direct$-$acting or reverse$-$acting? $(5$ pts$)$

Q$4)$ What kind of functional differences are between P vs PI$,$ and P vs PID controllers? $(15$ pts$)$