Figure P6.36 is the circuit diagram of a speed-control system in which the dc motor voltage v a is supplied by a generator driven by an engine. This system has been used on locomotives whose diesel...

Figure P6.36 is the circuit diagram of a speed-control system in which the dc motor voltage v_a
is supplied by a generator driven by an engine. This system has been used on locomotives whose diesel engine operates most efficiently at one speed. The efficiency of the electric motor is not as sensitive to speed and thus can be used to drive the locomotive at various speeds. The motor voltage v_a
is varied by changing the generator input voltage v_f. The voltage v_a
is related to the generator field current i_f
by v_a
= K_f
i_f.

Derive the system model relating the output speed ω to the voltage v_f, and obtain the transfer function
(s)/V_f(s).