(Solved): Design a PID controller for the system shown below: a. Formulate the required ideal derivative com ...

Design a PID controller for the system shown below: a. Formulate the required ideal derivative compensator, use a pole at \( -0.01 \) for the ideal integral compensator, and derive a new plant model. b. Determine resulting PID controller for the control system and find the values of \( \mathrm{K}_{1}, \mathrm{~K}_{2} \), and \( \mathrm{K}_{3} \). c. Plot the uncompensated system and compensated system in the time domain by using MATLAB. m-file