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Model electrical and torque characteristics of a universal (or series) motor
The Universal Motor block represents the electrical and torque characteristics of a universal (or series) motor using the following equivalent circuit model.
Where:
R_{a} is the armature resistance.
L_{a} is the armature inductance.
R_{f} is the field winding resistance.
L_{f} is the field winding inductance.
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_{b} in the armature:
$${v}_{b}={L}_{af}{i}_{f}\omega $$
where L_{af} is a constant of proportionality and 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_{f} and substitute this value into the equation for torque:
$$T={L}_{af}{\left(\frac{V}{{R}_{f}+{R}_{a}+{L}_{af}\omega}\right)}^{2}$$
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_{f}+R_{a} and 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 L_{f} in the model. This requires information about the RMS rated current and voltage for the total inductance.
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.
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 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.
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.
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.
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.
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 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 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.
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 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.
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. The default value is 2e-04 kg*m^{2}. The value can be zero.
Rotor damping. The default value is 1e-06 N*m/(rad/s). The value can be zero.
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.
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.
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.
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.
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.
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.
Mechanical rotational conserving port.
Mechanical rotational conserving port.
Field winding thermal port. For more information, see Thermal Ports.
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.