Task 1- PID control of a motor and an actuator [50 marks]In this task you will use MATLAB's Control System Toolbox only, Simulink is not allowed. Subtask 1Consider response of

angular speed to input voltage for a brushed DC motor withgiven parameters. Implement an open-loop transfer function of the plant. Tune P, Pl and PID controllers for the plant from Subtask 1. Compare responses oftuned controllers to a unit step input. If the closed-loop performance objective is toprovide the best tracking of the input signal, which PID design focus should be used?Subtask 2 Now consider different plant: a hydraulic brake actuator of the turbine. The transferfunction of the hydraulic brake in open loop is given as:Subtask 3 F_{(s)=} \frac{1}{(s+10)(s+2)} \text { Design a controller of the type } \frac{(s+a)}{(s+b)^{n}} \text { where } a

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7