Problem $\backslash$#$2[10$ points$]$ A paper machine transfer function

G$($s$)=$ e$^(-2$ s$)/(3$s$+1)$

Where the input is stock flow onto the wire and the output is basis weight or thickness. Use Matlab$/$Simulink if needed to do the following:

$($a$)$ How much delay$-$time the system has?

$($b$)$ Find the value of P controller where the system becomes critically stable

$($c$)$ Find the PID$-$Controller parameter using Ziegler$-$Nichols tuning rules

$($d$)$ Simulate the response of the system to step input for PID

$[$Hint: Use Matlab feedback command, Simlulink or PID tuner app in Matlab. Solution is mostly by trial and error$]$