A wound DC motor is connected in both a shunt and a series configuration. Assume generic resistance and inductance parameters Ra , Rf , La , Lf ; let the field magnetization constant be kf and the armature constant be ka . Assume ideal energy conversion, so that ka = kT . The motor has inertia Jm and damping coefficient bm, and it is rigidly connected to an inertial load with inertia J and damping coefficient b.
a. Sketch a system-level diagram of the two configurations that illustrates both the mechanical and electrical systems.
b. Write an expression for the torque-speed curve of the motor in each configuration.
c. Write the differential equations of the motor-load system in each configuration.
d. Determine whether the differential equations of each system are linear; if one (or both) is (are) nonlinear, could they be made linear with some simple assumption? Explain clearly under what conditions this would be the case.