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Unipolar Stepper Motor

Model stepper motor with center taps on phase windings

Library

Rotational Actuators

Description

The Unipolar Stepper Motor block represents a stepper motor that has center taps on the two phase windings. The winding currents and mechanical output are defined by the following equations:

where:

  • eA+ is the back emf induced across the A+ to A0 half-winding.

  • eA- is the back emf induced across the A- to A0 half-winding.

  • eB+ is the back emf induced across the B+ to B0 half-winding.

  • eB- is the back emf induced across the B- to B0 half-winding.

  • iA+ is the current flowing from the A+ port to the A0 center tap port.

  • iA- is the current flowing from the A- port to the A0 center tap port.

  • iB+ is the current flowing from the B+ port to the B0 center tap port.

  • iB- is the current flowing from the B- port to the B0 center tap port.

  • vA+ is the voltage at the A+ port relative to the A0 center tap port.

  • vA- is the voltage at the A- port relative to the A0 center tap port.

  • vB+ is the voltage at the B+ port relative to the B0 center tap port.

  • vB- is the voltage at the B- port relative to the B0 center tap port.

  • Km is the motor torque constant.

  • Nr is the number of teeth on each of the two rotor poles. The Full step size parameter is (π/2)/Nr.

  • R is the half-winding resistance. For example, it is the resistance between A+ and A0 ports.

  • L is the half-winding inductance. For example, it is the inductance between A+ and A0 ports.

  • Rm is the magnetizing resistance.

  • B is the rotational damping.

  • J is the inertia.

  • ω is the rotor speed.

  • Θ is the rotor angle.

  • Td is the detent torque amplitude.

If the initial rotor is zero or some multiple of (π/2)/Nr, the rotor is aligned with the A-phase winding. If a positive current flows from the A+ port to the A0 center tap port, then the stepper acts to stay aligned with the A-phase. Equivalently, a positive current flowing from the A0 center tap port to the A- port also acts on the rotor to stay aligned with the A-phase.

The Unipolar Stepper Motor block produces a positive torque acting from the mechanical C to R ports for either of the following sequences. Both sequences assume the rotor initial angle is zero or some multiple of (π/2)/Nr.

SequenceCenter taps connected to groundCenter taps connected to positive supply
1Positive current from A+ to A0Positive current from A0 to A-
2Positive current from B+ to B0Positive current from B0 to B-
3Positive current from A- to A0Positive current from A0 to A-
4Positive current from B- to B0Positive current from B0 to B-

Thermal Ports

The block has five optional thermal ports, one for each of the four half-windings and one for the rotor. These ports are 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 and iron 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.

Basic Assumptions and Limitations

The model is based on the following assumptions:

  • This model neglects magnetic saturation effects and any magnetic coupling between phases.

  • When you select the Start simulation from steady state check box in the Simscape™ Solver Configuration block, this block will not initialize an Initial rotor angle value between –π and π.

  • All four half-windings are assumed to be identical, and therefore have the same resistance temperature coefficient, alpha, and the same thermal mass.

Dialog Box and Parameters

Electrical Torque Tab

Half-winding resistance

Half of the resistance of the A and B phase windings as measured between the A+ and A-, and the B+ and B- ports. The default value is 0.55 Ω.

Half-winding inductance

Half of the inductance of the A and B phase windings as measured between the A+ and A-, and the B+ and B- ports. The default value is 0.0015 H.

Motor torque constant

Motor torque constant Km. The default value is 0.19 N*m/A.

Detent torque

The amplitude of the sinusoidal torque variation observed when rotating the shaft of the unpowered motor. The default value is 0 N*m.

Magnetizing resistance

The total magnetizing resistance seen from each of the phase windings, for example across A+ and A0. The value must be greater than zero. The default value is Inf, which implies that there are no iron losses.

Full step size

Step size when changing the polarity of either the A or B phase current. The default value is 1.8°.

Mechanical Tab

Rotor inertia

Resistance of the rotor to change in motor motion. The default value is 4.5e-05 kg*m2. The value can be zero.

Rotor damping

Energy dissipated by the rotor. The default value is 8e-04 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.

Initial rotor angle

Angle of the rotor at the start of the simulation. The default value is 0 rad.

Temperature Dependence Tab

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

Resistance temperature coefficient

Parameter α in the equation defining resistance as a function of temperature, as described in Thermal Model for Actuator Blocks. It is assumed that all windings are made of the same material, and therefore have the same resistance temperature coefficient. The default value is for copper, and is 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.

Half-winding thermal mass

The thermal mass for half of either the A or B winding. The thermal mass is the energy required to raise the temperature by one degree. It is assumed that all four half-windings have the same thermal mass. The default value is 100 J/K.

Half-winding initial temperatures, [T_A+ T_A- T_B+ T_B-]

A 1 by 4 row vector defining the temperature of the four half-windings at the start of simulation. The default value is [ 25 25 25 25 ] C.

Rotor thermal mass

The thermal mass of the rotor, that is, the energy required to raise the temperature of the rotor by one degree. The default value is 50 J/K.

Rotor initial temperature

The temperature of the rotor at the start of simulation. The default value is 25 C.

Percentage of magnetizing resistance associated with the rotor

The percentage of the magnetizing resistance associated with the magnetic path through the rotor. It determines how much of the iron loss heating is attributed to the rotor thermal port HR, and how much is attributed to the four winding thermal ports. The default value is 90%.

Ports

The block has the following ports:

A+

Top A-phase electrical connection

A0

A-phase center tap connection

A-

Lower A-phase electrical connection

B+

Top B-phase electrical connection.

B0

B-phase center tap connection

B-

Lower B-phase electrical connection

C

Mechanical rotational conserving port

R

Mechanical rotational conserving port

HA+

Thermal port for winding between A+ and A0. For more information, see Thermal Ports.

HA-

Thermal port for winding between A- and A0. For more information, see Thermal Ports.

HB+

Thermal port for winding between B+ and B0. For more information, see Thermal Ports.

HB-

Thermal port for winding between B- and B0. For more information, see Thermal Ports.

HR

Thermal port for rotor. For more information, see Thermal Ports.

References

[1] M. Bodson, J. N. Chiasson, R. T. Novotnak and R. B. Rekowski. "High-Performance Nonlinear Feedback Control of a Permanent Magnet Stepper Motor." IEEE Transactions on Control Systems Technology, Vol. 1, No. 1, March 1993.

[2] P. P. Acarnley. Stepping Motors: A Guide to Modern Theory and Practice. New York: Peregrinus, 1982.

[3] S.E. Lyshevski. Electromechanical Systems, Electric Machines, and Applied Mechatronics. CRC, 1999.

See Also

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