Q$2.$ The open$-$loop transfer function of the plant for a specific application is

$Gp(s)=\frac{6}{s(2s+2)(3s+24)}$

Plot the root locus of the system using MATLAB.

Is it possible with proportional control to achieve settling time less than $2\mathrm{.}07$ sec for this

plant. Explain why based on the root locus plot.

Use PD control to improve the response, so that the dominant time constant is $0\mathrm{.}5$ sec or less and the damping ratio is $0\mathrm{.}707$ or greater.

Project Requirements:

i$.$ The deadline for this $20$ grades project is Sunday $12$ January $2025.$

ii$.$ You can work in a group $($max $3$ students$)$ or individually.

iii. You must submit a report with the results and simulation files $($MATLAB$/$Simulink$).$