# DC Machine

Implement wound-field or permanent magnet DC machine

**Libraries:**

Simscape /
Electrical /
Specialized Power Systems /
Electrical Machines

## Description

The DC Machine block implements a wound-field or permanent magnet DC machine.

For the wound-field DC machine, you can access the field
terminals (F+, F−) to use the machine model as a
shunt-connected or a series-connected DC machine.
The Simulink^{®} input T_{L}
provides the torque applied to the shaft.

The armature circuit (A+, A−) consists of an inductor La and resistor Ra in series with a counter-electromotive force (CEMF) E.

The CEMF is proportional to the machine speed.

E =
K_{E}ω | (1) |

*K _{E}* is the voltage
constant and

*ω*is the machine speed.

In a separately excited DC machine model, the voltage constant
K_{E} is proportional to the
field current
*I _{f}*:

K
=
_{E}L_{af}I,_{f} | (2) |

*L*_{af} is the
field-armature mutual inductance.

The electromechanical torque that the DC
Machine block develops is proportional to
the armature current
*I _{a}*.

T
=
_{e}K,_{T}I_{a} | (3) |

*K _{T}* is the torque
constant. The sign convention for

*T*and

_{e}*T*is:

_{L}T > 0: Motor
mode_{e} ,
T_{L}T < 0:
Generator mode_{e},
T_{L} | (4) |

The torque constant is equal to the voltage constant.

K
=
_{T}K._{E} | (5) |

The armature circuit is connected between the A+ and A− ports of the DC Machine block. It is represented by a series Ra La branch in series with a Controlled Voltage Source and a Current Measurement block.

In the wound-field DC machine model, the field circuit is represented by an RL circuit. It is connected between the F+ and F− ports of the DC Machine block.

In the permanent magnet DC machine model, there is no field
current as the magnets establish the excitation
flux. *K _{E}*
and

*K*are constants.

_{T}The mechanical part computes the speed of the DC machine from the net torque applied to the rotor. The block uses the speed to implement the CEMF voltage E of the armature circuit.

The mechanical part implements this equation:

$$J\frac{d\omega}{dt}={T}_{e}-{T}_{L}-{B}_{m}\omega -{T}_{f},$$

where *J* is the inertia,
*B _{m}* is
the viscous friction coefficient, and

*T*is the Coulomb friction torque.

_{f}## Examples

## Ports

### Input

### Output

### Conserving

## Parameters

## References

[1] * Analysis of
Electric Machinery,* Krause
et al., pp. 89–92.

## Extended Capabilities

## Version History

**Introduced before R2006a**