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Model electrical and torque characteristics of a universal (or series) motor

Rotational Actuators

The Universal Motor block represents the electrical and torque characteristics of a universal (or series) motor using the following equivalent circuit model.

Where:

*R*is the armature resistance._{a}*L*is the armature inductance._{a}*R*is the field winding resistance._{f}*L*is the field winding inductance._{f}

When you set the **Model parameterization** parameter
to `By equivalent circuit parameters`

, you
specify the equivalent circuit parameters for this model. The Universal
Motor block computes the motor torque as follows:

The magnetic field in the motor induces the following back emf

*v*in the armature:_{b}$${v}_{b}={L}_{af}{i}_{f}\omega $$

where

*L*is a constant of proportionality and_{af}*ω*is the angular velocity.The mechanical power is equal to the power reacted by the back emf:

$$P={v}_{b}{i}_{f}={L}_{af}{i}_{f}{}^{2}\omega $$

The motor torque is:

$$T=P/\omega ={L}_{af}{i}_{f}{}^{2}$$

The torque-speed characteristic for the Universal Motor block
model is related to the parameters in the preceding figure. When you
set the **Model parameterization** parameter to ```
By
DC rated power, rated speed & maximum torque
```

or ```
By
DC rated power, rated speed & electrical power
```

,
the block solves for the equivalent circuit parameters as follows:

For the steady-state torque-speed relationship when using a DC supply,

*L*has no effect.Sum the voltages around the loop:

$$V=({R}_{f}+{R}_{a}){i}_{f}+{v}_{b}=({R}_{f}+{R}_{a}+{L}_{af}\omega ){i}_{f}$$

Solve the preceding equation for

*i*and substitute this value into the equation for torque:_{f}$$T={L}_{af}{\left(\frac{V}{{R}_{f}+{R}_{a}+{L}_{af}\omega}\right)}^{2}$$

The block uses the rated speed and power to calculate the rated torque. The block uses the rated torque and rated speed values in the preceding equation plus the corresponding electrical power to determine values for

*R*and_{f}+R_{a}*L*._{af}

When you set the **Model parameterization** parameter
to ```
By AC rated power, rated speed, current & electrical
power
```

, then the block must include the inductive terms *L _{a}* and

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

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

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

**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.`By DC rated power, rated speed & maximum torque`

— Provide DC power and speed parameters that the block converts to an equivalent circuit model of the motor. This is the default method.`By DC rated power, rated speed & electrical power`

— Provide AC power and speed parameters that the block converts to an equivalent circuit model of the motor.`By AC rated power, rated speed, current & electrical power`

— Provide AC power and speed parameters that the block converts to an equivalent circuit model of the motor.

**Total armature and field winding resistance**Total resistance of the armature and field winding. This parameter is only visible when you select

`By equivalent circuit parameters`

for the**Model parameterization**parameter. The default value is`132.8`

Ω.**Rated speed (at rated load)**Motor speed at the rated mechanical load. This parameter is only visible when you select

`By DC rated power, rated speed & maximum torque`

,`By DC rated power, rated speed & electrical power`

, or`By AC rated power, rated speed, current & electrical power`

for the**Model parameterization**parameter. The default value is`6.5e+03`

rpm.**Rated load (mechanical power)**The mechanical load for which the motor is rated to operate. This parameter is only visible when you select

`By DC rated power, rated speed & maximum torque`

,`By DC rated power, rated speed & electrical power`

, or`By AC rated power, rated speed, current & electrical power`

for the**Model parameterization**parameter. The default value is`75`

W.**Rated DC supply voltage**The DC voltage at which the motor is rated to operate. This parameter is only visible when you select

`By DC rated power, rated speed & maximum torque`

or`By DC rated power, rated speed & electrical power`

for the**Model parameterization**parameter. The default value is`200`

V.**Electrical power in at rated load**The amount of electrical power the motor uses at the rated mechanical power. This parameter is only visible when you select

`By DC rated power, rated speed & electrical power`

or`By AC rated power, rated speed, current & electrical power`

for the**Model parameterization**parameter. The default value is`160`

W.**Maximum (starting) torque**Maximum torque the motor produces. This parameter is only visible when you select

`By DC rated power, rated speed & maximum torque`

for the**Model parameterization**parameter. The default value is`0.39`

N*m.**Total armature and field winding inductance**Total inductance of the armature and field winding. If you do not have information about this inductance, set the value of this parameter to a small, nonzero number. This parameter is only visible when you select

`By equivalent circuit parameters`

,`By DC rated power, rated speed & maximum torque`

, or`By DC rated power, rated speed & electrical power`

for the**Model parameterization**parameter. The default value is`0.525`

H.**Note:**You can set the**Total armature and field winding inductance**value to zero, but this only makes sense if you are driving the motor with a DC source.**RMS rated voltage**RMS supply voltage when the motor operates on AC power. This parameter is only visible when you select

`By AC rated power, rated speed, current & electrical power`

for the**Model parameterization**parameter. The default value is`240`

V.**RMS current at rated load**RMS current when the motor operates on AC power at the rated load. This parameter is only visible when you select

`By AC rated power, rated speed, current & electrical power`

for the**Model parameterization**parameter. The default value is`0.8`

A.**AC frequency**Frequency of the AC supply voltage. This parameter is only visible when you select

`By AC rated power, rated speed, current & electrical power`

for the**Model parameterization**parameter. The default value is`50`

Hz.

**Rotor inertia**Rotor inertia. The default value is

`2e-04`

kg*m^{2}. 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.

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

**Field to armature resistance ratio, Rf/Ra**The ratio of the field to the armature resistance. This parameter is required only when showing the field and armature thermal ports. It is used to determine individual resistance values for the field and armature windings so that the thermal heat generated by the two resistors can be apportioned correctly. The default value is

`1`

.**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.

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.

The block has the following ports:

`+`

Positive electrical port.

`-`

Negative electrical port.

`C`

Mechanical rotational conserving port.

`R`

Mechanical rotational conserving port.

`Hf`

Field winding thermal port. For more information, see Thermal Ports.

`Ha`

Armature winding thermal port. For more information, see Thermal Ports.

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

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