Armature-Controlled dc motors

The dc motors have separately excited fields. They are either armature-controlled with fixed field or field-controlled with fixed armature current. For example, dc motors used in instruments employ a fixed permanent-magnet field, and the controlled signal is applied to the armature terminals.

Consider the armature-controlled dc motor shown in the following figure.

The armature current produces the torque which is applied to the inertia and friction; hence

 Assuming that all initial conditions are condition are zero/and taking the L.T. of    equations (1), (2) & (3), we obtain 

Kpsθ(s) = Eb(s)

(Las+Ra) Ia(s) +Eb(s) =Ea(s) (Js²+fs) 

θ (s) = T(s) = KIa(s)