#### Question Details

A permanent-magnet dc motor is rated at 6 V with the following parameters:

ra = 7 Ã¢Â¦

kv = 0.0141 VÃ¢s/rad

Bm = 6.04Ãƒ10Ã¢6 NÃ¢mÃ¢s/rad

LAA = 120 mH

J = 1.06Ãƒ10Ã¢6 kgÃ¢m^2Â

K = 5Ãƒ10^Ã¢6 NÃ¢mÃ¢sÂ

1, Initially, the armature voltage is zero and TL = 0. Create a Simulink model based on class notes to determine the dynamic response of the machine to a sudden change in input voltage (from 0 to 6 V at t = 0.5 s) and then a sudden change in load torque (from 0 to TL = 3.53Ãƒ10^Ã¢3 NÃ¢m at t = 1 s). Plot the armature voltage, current and the speed. Confirm the results are correct by calculating the steady-state armature current and speed from the steady-state model.

2, Use the model created in question 1, replace the ideal dc voltage by a switching voltage waveform (you may use Pulse Generator). Repeat question 1, determine the dynamic response and plot the armature voltage, current and the speed by setting Pulse Generator with 1) Amplitude = 10, Period = 1/200 secs (Frequency = 200 Hz), and Pulse Width = 60%, and 2) Amplitude = 10, Period = 1/2000 secs (Frequency = 2000 Hz), and Pulse Width = 60%. Please observe and determine current ripple from simulation results. Which switching frequency (200 Hz or 2000 Hz) gives smaller ripple. (60 points)Â

3, Based on the model of question 1, design a closed speed control loop by applying load torque TL = KÃr. Determine the dynamic response to a sudden change in speed command from 0 to 200 rad/s at t = 0.5 s. You may use a PI controller and its output is controlled from 0 to 6 V to supply the machine.

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