High Performance Control of AC Drives with Matlab / Simulink Models

2.2 DC Motors

This section presents the modeling of separately excited and series DC motors, to provide educational benefits rather than for practical use. The mathematical models AC and DC machines can be found in [1–5].

2.2.1 Separately Excited DC Motor Control

An equivalent circuit of a separately excited DC motor is shown on Figure 2.1. The armature side of the motor is modeled using an ideal voltage source (back EMF) and an armature resistance. The excitation circuit is represented by a field resistor and an inductor. The two circuits are fed by separate voltage sources.

Figure 2.1 An equivalent circuit of a separately excited DC motor

The mathematical model of the separately excited DC motor can be represented as [1–5]

(2.1)

(2.2)

(2.3)

where u_a, u_f, i_a, and i_f are armature voltage, field voltage, armature current, and field current, respectively; R_a, R_f are armature and field resistances; L_a is armature inductance; J is machine inertia; ω_r is rotor angular speed; ψ_f is field flux; e is electromagnetic force induced in the armature; and t_l is the load torque.

The induced voltage ...