Question

2. (20 points) A field controlled DC motor model is given below where eaſt) is an applied input voltage, ia(t) is the armature current, Ra and La are the armature resistance and inductance, respectively, e(t) is a back (or counter) emf (electro-motive force) le (t) = K w here K is a motor (torque) constant, t(t) is the torque generated by the motor, w(t) is the angular velocity, 0(t) is the angular position, J represents the rotor inertia and load inertia combined, and Bm is the motor viscous friction coefficient (damping coefficient); the torque generated by the motor is proportional to the armature current [t(t) = Kia(t)] where K is a motor (torque) constant. Find the differential equation relating the output position e(t) to the input voltage eat). Present your differential equation using D operator. Hint: You can refer to the section 1.8 of the textbook for solving this problem. ia(t) Raho W(1) Output MAM ea(t) eb(t) - 0(t) H D (t) boros Input Armature circuit Mechanical load