Consider a 3.08kW permanent magnet DC servo motor with the following parameters: Ra = 0.26Ω, La = 1.7mH, Rated Armature Current: 24.9A, Rated speed 3000rpm, rated armature voltage 139V and Inertia of the motor Ja = 0.00252kg.m2 . A load with the same inertia as the motor is connected to the motor. The load torque is linearly proportional to the speed TL = KL × ω where KL = 0.005. Do the following in Simulation (Matlab/Simulink):

1. Model the DC motor and the load in Simulink. 

2. Model a four-quadrant power electronic converter which drives this motor from dc bus of 300V . The switching frequency of the converter is Fs = 50kHz.

3. Give a step change in terminal voltage of magnitude 50V to the DC motor through the converter. Plot the speed ω and electromagnetic torque Tem response.

4. Design a current controller with bandwidth of 1KHz 

5. Design a speed controller with bandwidth one tenth of the current controller 

6. Model the complete system in Simulink. Add limiters such the current cannot exceed 24.9A and the terminal voltages are between 250V . 

7. For the following change in the speed reference 0 ≤ t ≤ 0.005s – ω∗ = 40,000t rpm, 

0.005 ≤ t ≤ 0.025s – ω∗ = 2000 rpm, plot the response of the speed ω and electromagnetic torque Tem response. 

8. Repeat (7) if the load torque remains constant at TL = 10Nm. 

9. Redesign the controller if the speed and current sensor gains are 0.25 and 0.15 respectively 

10. Repeat (8) for the redesigned controller.