Question

Permanent DC Machine Parameters

Ra = 3 Ohms Laa = 0.25 H v = 3.0e-02*( 1 – s*sin(qr) ) V s/rad s = 0.05 J = 2.0e-06 kg m2 Bm = 12.0e-06 N m s Rated Armature Voltage, Va, is 12 V Rated Load Torque is, TL, 28e-03 Nm

Provide All Matlab Code, i.e., m-file Without the Matlab code NO Credit Will be Given

1. For the Asymmetrical motor given above, do the following.
   1. (6 points) Derive the state space equations x' = Ax + Bu
      1. Note k_v is a function of q_r so the A matrix needs to show that.
   2. (10 points) Simulate the no load response with rated Armature Voltage applied.
      1. Analyze the motor’s transient and steady state response.
         1. Compare and contrast with the “idea” motor. Armature Current, Torque, Speed etc.
         2. Measure and quantify any differences.
         3. What affect does k_v = f(q_r) have on the motor’s performance? Life expectancy?
   3. (10 points) Simulate the motor where the rated load torque (28 mNm) is applied after 1 second (rated armature voltage is applied as in 1b).
      1. Analyze the motor’s transient and steady state response.
         1. Compare and contrast with the “idea” motor. Armature Current, Torque, Speed etc.
         2. Measure and quantify any differences.

Answer 1