Question $2($MATLAB etc$)$: $($Cohen$-$Coon$)$

a$)$ The step response of a open loop system depicted in Figure $2$ is given in Figure $3.$ Design $,$ P$,$ PI and PD controllers for

system given in Figure $2-3.$ Illustrate the closed$-$loop system behaviour for each designed controller using matlab.

Fig. $2$ Closed$-$loop control system

Fig. $3$ Step response of controller

b$)$Plot the response of the closed$-$loop system, control signal etc via Matlab, and comment on results. Explain the reason of

more overshoot. Plot control signal. Show all result via matlab.

$($c$)$Disturbance Rejection: Apply a step type input disturbance and illustrate whether the designed controller rejects the

disturbance for PD designed in previous step. Find the disturbance rejection time. Depict the control signal.

Measurement noise: Add a measurement noise with or $n(t)=0\mathrm{.}2$rand$(t))$ value. Illustrate the system output, control

signal etc.