Task $2$:

$G_p(s)=\frac{400}{s(s+48\mathrm{.}5)}$

Consider a plant given above to be controlled by a PID controller. Using SIMULINK in MATLAB:

a$)$ Obtain the unit step response, $G_p(s).$

b$)$ Apply P controllers with $K_p=2,$ and $10.$ Investigate the unit step response in each case, compare the results and discuss.

c$)$ Apply PI controllers with $K_i=\frac{K_p}{10}$ following the $K_p$ in b$)$ with addition of $K_p=100.$ Investigate the unit step response in each case, compare the results and discuss.

d$)$ Let $K_p=100,K_i=10,$ and add a derivative term with $K_d=0\mathrm{.}1,0\mathrm{.}9,$ and $2.$ Investigate the unit step response in each case, compare the results and discuss.

Based on your results in parts b$),$ c$)$ and d$)$ conclude a suitable PID controller for this system and provide justification.