Consider a system described by the following differential equation: 2y + y = Zu where Y and u are the output and input, respectively:
(a) Derive a transfer function of the system
(b) Check the stability of the system
Design a suitable controller for the system so that the closed-loop system is stable, and the output tracks step reference input.
Use MATLAB to simulate and plot the response of the closed-loop system to a unit-step reference input.
Does the output now track the reference unit-step input?
Show your full working, including all codes and plots from MATLAB.