# Shunt Motor

Model electrical and torque characteristics of shunt motor

## Library

Rotational Actuators

## Description

The Shunt Motor block represents the electrical and torque characteristics of a shunt motor using the following equivalent circuit model.

When you set the Model parameterization parameter to `By equivalent circuit parameters`, you specify the equivalent circuit parameters for this model:

• RaArmature resistance

• LaArmature inductance

• RfField winding resistance

• LfField winding inductance

The Shunt Motor block computes the motor torque as follows:

1. The magnetic field in the motor induces the following back emf vb in the armature:

${v}_{b}={L}_{af}{i}_{f}\omega$

where Laf is a constant of proportionality and ω is the angular velocity.

2. The mechanical power is equal to the power reacted by the back emf:

$P={v}_{b}{i}_{a}={L}_{af}{i}_{f}{i}_{a}\omega$

3. The motor torque is:

$T=P/\omega ={L}_{af}{i}_{f}{i}_{a}$

The torque-speed characteristic for the Shunt Motor block model is related to the parameters in the preceding figure. When you set the Model parameterization parameter to ```By rated power, rated speed & no-load speed```, the block solves for the equivalent circuit parameters as follows:

1. For the steady-state torque-speed relationship, L has no effect.

2. Sum the voltages around the loop:

$\begin{array}{l}V={i}_{a}{R}_{a}+{L}_{af}{i}_{f}\omega \\ V={i}_{f}{R}_{f}\end{array}$

3. Solve the preceding equations for ia and if:

$\begin{array}{l}{i}_{f}=\frac{V}{{R}_{f}}\\ {i}_{a}=\frac{V}{{R}_{a}}\left(1-\frac{{L}_{af}w}{{R}_{f}}\right)\end{array}$

4. Substitute these values of ia and if into the equation for torque:

$T=\frac{{L}_{af}}{{R}_{a}{R}_{f}}\left(1-\frac{{L}_{af}\omega }{{R}_{f}}\right){V}^{2}$

The block uses the rated speed and power to calculate the rated torque. The block uses the rated torque and no-load speed values to get one equation that relates Ra and Laf/Rf. It uses the no-load speed at zero torque to get a second equation that relates these two quantities. Then, it solves for Ra and Laf/Rf.

The block models motor inertia J and damping B for all values of the Model parameterization parameter. The output torque is:

${T}_{load}=\frac{{L}_{af}}{{R}_{a}{R}_{f}}\left(1-\frac{{L}_{af}\omega }{{R}_{f}}\right){V}^{2}-J\stackrel{˙}{\omega }-B\omega$

The block produces a positive torque acting from the mechanical C to R ports.

### Thermal Ports

The block has two optional thermal ports, one per winding, hidden by default. To expose the thermal ports, right-click the block in your model, and then from the context menu select Simscape > Block choices > Show thermal port. This action displays the thermal ports on the block icon, and adds the Temperature Dependence and Thermal Port tabs to the block dialog box. These tabs are described further on this reference page.

Use the thermal ports to simulate the effects of copper resistance losses that convert electrical power to heat. For more information on using thermal ports in actuator blocks, see Simulating Thermal Effects in Rotational and Translational Actuators.

## Dialog Box and Parameters

### Electrical Torque Tab

Model parameterization

Select one of the following methods for block parameterization:

• `By equivalent circuit parameters` — Provide electrical parameters for an equivalent circuit model of the motor. This is the default method.

• ```By rated power, rated speed & no-load speed``` — Provide power and speed parameters that the block converts to an equivalent circuit model of the motor.

Armature resistance

Resistance of the armature. This parameter is only visible when you select `By equivalent circuit parameters` for the Model parameterization parameter. The default value is `110` Ω.

Field winding resistance

Resistance of the field winding. This parameter is only visible when you select `By equivalent circuit parameters` for the Model parameterization parameter. The default value is `2.5e+03` Ω.

Back-emf constant

The ratio of the voltage generated by the motor to the motor speed. The default value is `5.11` s*V/rad/A.

Armature inductance

Inductance of the armature. If you do not have information about this inductance, set the value of this parameter to a small, nonzero number. The default value is `0.1` H. The value can be zero.

Field winding inductance

Inductance of the field winding. If you do not have information about this inductance, set the value of this parameter to a small, nonzero number. The default value is `0.1` H. The value can be zero.

Speed of the motor when no load is applied. This parameter is only visible when you select ```By rated power, rated speed & no-load speed``` for the Model parameterization parameter. The default value is `4.6e+03` rpm.

Motor speed at the rated load. This parameter is only visible when you select ```By rated power, rated speed & no-load speed``` for the Model parameterization parameter. The default value is `4e+03` rpm.

The mechanical load for which the motor is rated to operate. This parameter is only visible when you select ```By rated power, rated speed & no-load speed``` for the Model parameterization parameter. The default value is `50` W.

Rated DC supply voltage

The voltage at which the motor is rated to operate. This parameter is only visible when you select ```By rated power, rated speed & no-load speed``` for the Model parameterization parameter. The default value is `220` V.

Starting current at rated DC supply voltage

The initial current when starting the motor with the rated DC supply voltage. This parameter is only visible when you select ```By rated power, rated speed & no-load speed``` for the Model parameterization parameter. The default value is `2.09` A.

### Mechanical Tab

Rotor inertia

Rotor inertia. The default value is `2e-04` kg*m2. The value can be zero.

Rotor damping

Rotor damping. The default value is `1e-06` N*m/(rad/s). The value can be zero.

Initial rotor speed

Speed of the rotor at the start of the simulation. The default value is `0` rpm.

### Temperature Dependence Tab

This tab appears only for blocks with exposed thermal ports. For more information, see Thermal Ports.

Resistance temperature coefficients, [alpha_f alpha_a]

A 1 by 2 row vector defining the coefficient α in the equation relating resistance to temperature, as described in Thermal Model for Actuator Blocks. The first element corresponds to the field winding, and the second to the armature. The default value is for copper, and is ```[ 0.00393 0.00393 ]``` 1/K.

Measurement temperature

The temperature for which motor parameters are defined. The default value is `25` C.

### Thermal Port Tab

This tab appears only for blocks with exposed thermal ports. For more information, see Thermal Ports.

Thermal masses, [Mf Ma]

A 1 by 2 row vector defining the thermal mass for the field and armature windings. The thermal mass is the energy required to raise the temperature by one degree. The default value is ```[ 100 100 ]``` J/K.

Initial temperatures, [Tf Ta]

A 1 by 2 row vector defining the temperature of the field and armature thermal ports at the start of simulation. The default value is `[ 25 25 ]` C.

## Ports

The block has the following ports:

`+`

Positive electrical input.

`-`

Negative electrical input.

`C`

Mechanical rotational conserving port.

`R`

Mechanical rotational conserving port.

`Hf`

`Ha`

## References

[1] Bolton, W. Mechatronics: Electronic Control Systems in Mechanical and Electrical Engineering, 3rd edition Pearson Education, 2004.