DC Motors

Properties

The DC motor model represents both the static and dynamic behaviors of two types on industrial motors: shunt and separately excited.

Main features

• Two common types of industrial motors.
• Types of connections of either rotoric and statoric circuits.
• Parallel connection (shunt) or two distinct circuits.

DC Motor Introduction

The following equations govern the voltages of the motor as a function of the currents:

where:

• Vf voltage at the terminals of the stator winding
• if current in the stator
• rf resistance of stator winding
• lambda f flux in the stator
• va voltage at the terminals of the rotor winding
• ia current in the rotor
• ra resistance of the rotor winding
• lambda a flux in the rotor

The fluxes can be expressed as follows:

where:

• Lff inductance in the stator winding
• Laa inductance in the rotor winding
• Laf et Lfa mutual inductances between the rotor and the stator

Also the mutual inductances can be estimated by a sinusoidal function of the angular speed of the motor theta c:

where L is a constant

The action of the switch allows the rotor winding to be perceived as a stationary winding with a magnetic axis perpendicular to the axis of the winding field. There is no induced voltage in one of the windings because of the variation of the current crossing the other winding. Consequently, the voltage equations can be reduced to a matrix in a Laplace domain, as follows:

It is useful to represent the electromagnetic torque equation that follows:

And finally using the equation linking the angular speed omega r, a complete relation can be set and allows users to form the representative block diagram.

where:

• J moment of inertia of rotor
• Bm damping coefficient associated to the mechanical rotation movement
• Tl load torque
• Usually the damping coefficient Bm is not considered.

The DC motor is often represented by figure 9-13. According to the type of motor, the rotoric circuit can be connected in parallel with the statoric circuit, thus Vf=Va in the case of a shunt motor.

A motor that uses two distinct circuits is referred to as a separately excited motor. The stator has to be supplied with another circuit since the rotor is connected to the power network. The stator can be supplied using different methods, either using a constant source or with Simulink.

Motor Parameters

• R rotor: (ra) resistance of rotoric winding (ohm)
• L rotor: (Laa) inductance of rotoric winding (henry)
• R stator: (rf) resistance of statoric winding (ohm)
• L stator: (Lff) inductance of statoric winding (henry)
• L mutual: (Laf) mutual inductance between the stator and the rotor (henry)

Mechanical Load Parameters

• Load Torque: mechanical torque of the load driven by the motor (N.m)
• Moment of inertia: the value of total inertia driven by the motor. This value consists of the inertia of the motor and the inertia of the driven mechanical load (kg.m2)
• Viscous friction: value of viscous friction or damping. This corresponds to a friction loss varying with the speed (N.m.s)
• Dry friction: value of dry friction. This corresponds to constant friction loss (N.m)

D.C. Motor Type
Allows users to specify the origin of the statoric circuit power supply:

• Shunt connection: the stator voltage is the same as the rotor voltage since both are connected in parallel.
• Internal: separately excited motor, the stator is supplied by a constant internal source.
• External: separately excited motor, the stator is supplied by an external source originating from an A/D.
• Simulink: separately excited motor, the stator is supplied by a source originating from Simulink.

List of Available Signals
At acquisition, the following signals are made available by the sensors:

• I_label: total current of the D.C. motor (A)
• E_label: voltage generated by the armature circuit as a counter electromotive force (V)
• wr_label: speed of the D.C. motor rotor (rad/s)
• Vp_label: voltage at the positive terminal of the motor with respect to the ground (V)
• Vn_label: voltage at the negative terminal of the motor with respect to the ground (V)
• V_ext_label: voltage of the D.C. motor, or voltage of armature Va (V)
• Vf_label: excitation voltage at the terminals of stator (rf+Lff) (V)
• Vlink_label: voltage originating from Simulink to supply the stator, in the case of a separately excited motor supplied by a Simulink circuit (V)
• Tm_label: mechanical torque of the motor load (N.m)
• If_label: current in the stator circuit or field current.

D.C. Motor Control Panel
Figure 9 - 14 shows the control panel of a D.C. motor.

Figure 9 - 15 shows typical example using a DC Motor.

Figure 9 - 15 Example using a D.C. motor