DC motor

Armature resistance and inductance coupled to a rotational shaft.

  • electrical
  • rotational
  • Gradara equations
  • 3 ports
  • 3 parameters
BlockDC motorKindmotorLibraryElectrical

Description

A permanent-magnet DC motor: armature resistance and inductance in series with a back-EMF proportional to shaft speed. The same constant k gives torque per ampere.

Example

Motor speed control

Speed referencePI controllerVoltage driveDC motorInertia & loadSpeed sensorGround
In Gradara, select a DC motor block and press F1, then choose Open example. It opens as a new model in My models, ready to run.

Also in this example:StepPI controllerVoltage driveInertia & loadSpeed sensorGround

Ports

Conserving terminals 3

  • +pelectrical

    Positive armature terminal. Current into p is the armature current i.

  • −nelectrical

    Negative armature terminal.

  • shaftflangerotational

    Rotor shaft. The motor applies torque k · i to what is connected; w is its speed.

Parameters

  • ResistanceR1.2 Ω

    ≥ 0.001

    Armature resistance, in ohms.

  • InductanceL0.02 H

    ≥ 0.00001

    Armature inductance, in henries.

  • Motor constantk0.15 N·m/A

    ≥ 0.0001

    Motor constant: torque per ampere in N·m/A, equal to back-EMF per rad/s in V·s/rad.

Equations

Modelica
v = p.v − n.v, i = p.i, p.i + n.i = 0
w = d(flange.phi)/dt
L · di/dt = v − R · i − k · w, i(0) = 0
torque on the load = k · i (flange.tau = −k · i)

Implementation

The block’s Modelica model
L*der(i) = v - R*i - k*w;
tau = k*i;

Assumptions and limitations

  • No rotor inertia, friction, brush drop, or saturation. Connect an inertia to the shaft; without one the shaft has no mass.
  • The armature starts with zero current.

Used in

These larger examples use it too. Open them from Examples in the app.

  • Motor speed control
  • EV drivetrain
  • Servo position control

See also

Select a block in Gradara and press F1 to open its page offline.