Do the mathematical solution as well as the MATLAB script that matches the following

exercise: Consider the control system shown in Fig:

when $G(s)=+\frac{2}{(s+3{)}^2}$ and select a PID controller such that the settling time $($with a $2\%$

criterion$)$ is less than $1\mathrm{.}5$ seconds for an ITAE step response.

Plot $y(t)$ for a step input $r(t)$ with and without a prefilter. Determine and plot $y(t)$ for a step

perturbation. Discuss the effectiveness of the system.

when $))$ and select a PID controller such that the settling time with a $2\%$ criterion$)$ is less than $1\mathrm{.}5$ seconds for an ITAE step response.

Plot $y(t)$ for a step input $r(t)$ with and without a prefilter. Determine and plot $y(t)$ for a step perturbation. Discuss the effectiveness of the system.