Chapter 6, Problem 6.38P

Figure P6.38 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 $\omega$ to the voltage $v_f$ , and obtain the transfer function $\Omega \left(s\right)/V_f\left(s\right)$ .