$(20$ points$)$ Oscillation$-$based tuning is used to generate values of $Pu=3\mathrm{.}75$ and Kcu$=5$ for the process shown below:

$g_p(s)=\frac{1}{s^3+2s^2+3s+1}$

$*$Use this information to identify optimal tuning parameters for a PI controller for this process.