Question

The simplified diagram of a DC motor is shown in Fig. 4. Assume that the rotor has inertia m J and viscous friction coefficient Bm. The torque developed by the motor is assumed to be related linearly to the field current by , m m f T  K i where the motor torque constant m f a K K K I  1 when the armature current a i is assumed constant (i.e. ) a a i  I . The toque due to load and disturbance is represented by TL and TD , respectively. Find: 1) A set of ordinary differential equations for the field-controlled DC motor; 2) Transfer function of the field-controlled DC motor, i.e., transfer function for f e (or E (s) f ) as input and angular  (or (s) ) as output; 3) Draw the block diagram of the field-controlled DC motor based on the model obtained in

The simplified diagram of a DC motor is shown in Fig. 4. Assume that the rotor has inertia Jm and viscous friction coefficient Bm. The torque developed by the motor is assumed to be related linearly to the field current by T -Ki,, where the motor torque constant K -K^KfI^ when the armature current i, is assumed constant (i.e. i^ -Ia). The toque due to load and disturbance is represented by T, and Tp , respectively. Find: 1) A set of ordinary differential equations for the field-controlled DC motor; 2) Transfer function of the field-controlled DC motor, i.e., transfer function for e, (or Ef (s) ) as input and angular θ (or θ(s)) as output; 3) Draw the block diagram of the field-controlled DC motor based on the model obtained in 1) La T. m2 R, Fig. 4: Diagram of a DC motor

Answer 1

dt 3 2