Model electrical and torque characteristics of shunt motor

Rotational Actuators

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:

*R*—_{a}**Armature resistance***L*—_{a}**Armature inductance***R*—_{f}**Field winding resistance***L*—_{f}**Field winding inductance**

The Shunt 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:

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

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:

For the steady-state torque-speed relationship,

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

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

Solve the preceding equations for

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

Substitute these values of

*i*and_{a}*i*into the equation for torque:_{f}$$T=\frac{{L}_{af}}{{R}_{a}{R}_{f}}\left(1-\frac{{L}_{af}\omega}{{R}_{f}}\right){V}^{2}$$

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

*R*and_{a}*L*. It uses the no-load speed at zero torque to get a second equation that relates these two quantities. Then, it solves for_{af}/R_{f}*R*and_{a}*L*._{af}/R_{f}

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

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

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. 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.**No-load speed**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.**Rated speed (at rated load)**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.**Rated load (mechanical power)**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.

**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.

**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 input.

`-`

Negative electrical input.

`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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