A process is represented by the following empirical model, Gp $=5$e$^-$s$/(10$s$+1)(5$s$+1),$ Gv $=1\mathrm{.}5,$ Gm $=2.$

$($a$)$ Determine the PID controller parameters to control this process using IMC! Note: $($choose tc$=1).$

$($b$)$ Determine GM and PM for the answer to question $($a$).$