Operation principle - Modelling

• Model of Brushed DC motor:

Where:
V: input voltage (V)
i: armature current (A)
θ: motor position (rad)
ω: motor velocity (rad/s)
R: armature resistance (Ω)
L: armature inductance (H)
E_b: back-EMF (electromotive force) voltage (V)
K_b: back-EMF constant (V.rad/s)
T_m: motor torque (N.m)
K_t: motor torque constant (N.m/A)
J: moment of inertia (kg.m2)
B: viscous friction (N.m.s/rad)
T_L: load torque (N.m)

From (1), (2), (3), (4), infer model of brushed DC motor: