Q$4$: Consider the plant with the transfer function given by

$G_P(s)=\frac{1}{s(s+2)(s+4)}$

$($a$)$ Design an analog PD controller such that the resulted closed loop system has dominant poles at

$s_{1,2}=-4+-j2$

$($b$)$ Discretize the controller obtained in $($a$)$ and write down the corresponding difference equation.

$($c$)$ Write down a programming code to implement the controller using digital computer or microcontroller.

$($d$)$ Sketch the block diagram of the closed loop digital control system showing AD and DA convertors