Question 6.4.2: Model of a Field-Controlled dc Motor Develop a model of the ...

The voltage v_{f} is applied to the field circuit, whose inductance and resistance are L_{f} and R_{f} .
No back emf exists in the field circuit because it does not move within the field, and Kirchhoff’s voltage law applied to the field circuit gives
v_{f} = R_{f} i_{f} + L_{f} \frac{d i_{f}}{d t} (1)
For the inertia I,
I \frac{d ω}{d t} = T  −  cω  −  T_{L} = K_{T}  i_{f}  −  cω  −  T_{L}         (2)
where T_L is the load torque. These two equations form the motor model