This block implements a brushless DC machine.
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where Labc is the time-varying inductance matrix (global inductance for DQ and VDQ models), Iabc is the stator current inside the winding, R is the stator resistance and Vabc is the voltage across the stator windings. As for ψabc, it defines the magnet flux linked into the stator windings (for DQ and VDQ models), or the total flux (for the SH model),
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It is important to note that there are many different types of Park transforms and this often leads to confusion when interpreting the motor states inside the D-Q frame. The one used here presents the advantage of being orthonormal (notice the √3/2 factor). This particular Park orthonormal transform is power-invariant which means that the power computed in the D-Q frame by performing a dot product of currents and voltages will be numerically equal to the one computed in the phase domain. With this transform (and only this transform) the PMSM torque can be expressed by (3), where pp is the number of pole pairs.
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One may notice the absence of the 3/2 factor in (3), which is usually present in the PMSM torque equation when using non-orthonormal transforms. This is, again, because this model uses the orthonormal Park transform. Figure 1 explains the principle of the Park transform. Considering fixed ABC referential with all quantities ( Vbemf, motor current I) rotating at the electric frequency ω, if we observe these quantities in a D-Q frame turning at the same speed we can see that the motor quantities will be constant.
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The main difference between the PMSM and the BLDC lies in the shape of the Back EMF voltage. The BLDC has a trapezoidal back EMF shape that is parametrized with λm the permanent flux linkage and H the back EMF flat area in degree.
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Symbol | Name | Description | Unit | Type |
|---|---|---|---|---|
R | Stator resistances | Resistances of the stator windings specified for every phase, A, B and C. | Ω | Input |
Ls | Stator inductance | Phase to neutral winding inductance | H | Input |
λm | Permanent magnet flux linkage | Amplitude of the rotor permanent magnet flux | Wb | Input |
δΦ/δθ | Back EMF profile | Profile of the back EMF, either Trapezoidal or User defined | Input | |
EMFfile | Back EMF profile table | Field only visible in User defined mode. Allows to import a back EMF resource file. | Input | |
H | Back EMF flat area | Field only visible in Trapezoidal mode. Flat section width in degree of the back EMF voltage | ° | Input |
pp | Number of pole pairs | Number of pole pairs | Input | |
is | Stator currents | Currents measured at phases A, B and C of the stator | A | Measurement |
isdq | Stator currents (DQ) | Currents measured of axis d and q | A | Measurement |
Vs | Stator voltages | Voltages measured at phases A, B and C of the stator | V | Measurement |
Bemf | Back EMF voltages | Phase to neutral voltage generated from the permanent magnet flux linkage | V | Measurement |
P | Active power (3ph, instantaneous) | Instantaneous electrical active power | W | Measurement |
Q | Reactive power (3ph, instantaneous) | Instantaneous electrical reactive power | var | Measurement |
θe | Electrical rotor position | Position of the rotor from 0 to 360 degrees | ° | Measurement |
Rs | Snubber resistance | Resistances of the snubber on phase A, B and C | Ω | Input |
Cs | Snubber capacitance | Capacitance of the snubber on phase A, B and C | F | Input |
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Symbol | Name | Description | Unit | Type |
|---|---|---|---|---|
J | Rotor inertia | Moment of inertia of the rotor | kg*m2 | Input |
Fv | Viscous friction coefficient | Viscous friction | N*m*s/rad | Input |
Fs | Static friction torque | Static friction | N*m | Input |
ctrl | Mechanical control mode | Control mode of the mechanical model. Has two possible values: speed or torque. In speed mode, the mechanical model is bypassed and the speed command is sent directly. In torque mode, the torque command is used to measure the speed using the mechanical parameters of the machine. | Input | |
T | Torque command | Torque command sent to the mechanical model | N*m | Input |
ωrc | Rotor speed command | Speed command sent to the mechanical model | rpm | Input |
ωr | Rotor speed | Speed of the rotor | rpm | Measurement |
Te | Electromagnetic torque | Torque measured at the rotor | N*m | Measurement |
θ0 | Initial rotor angle | Rotor position at time t = 0 | ° | Input |
θ | Rotor angle | Rotor position from 0 to 360 degrees | ° | Measurement |
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Resolver Parameters & Measurements
Symbol | Name | Description | Unit | Type |
|---|---|---|---|---|
Ren | Enable resolver | Whether or not to enable the resolver | N/A | Input |
Rsc | Resolver feedback signals | The two two-phase windings producing a sine and cosine feedback current proportional to the sine and cosine of the angle of the motor | N/A | Measurement |
Rpp | Number of resolver pole pairs | Number of pole pairs of the resolver | N/A | Input |
Rdir | Direction of the sensor rotation | Direction in which the sensor is turning, either clockwise or counterclockwise | N/A | Input |
Rθ | Angle offset Δθ ( Sensor- Rotor ) | Angle offset between the resolver and the rotor position from 0 to 360 degrees | ° | Input |
Rk | Resolver sine cosine gains | The sine/cosine modulation output sine/cosine component amplitude. Default value are 1, 0, 0 and 1 | N/A | Input |
Etype | Excitation source type | The source from which the excitation of the resolver is generated. Can either be AC, which is generated inside the FPGA with the specified frequency, DC, which is generated with a 90° from the rotor and External, which is generated from outside the model | N/A | Input |
Ef | Excitation frequency | Frequency of the excitation when in AC mode | Hz | Input |
Esrc | Excitation source | Source of the external excitation source when in External mode | N/A | Input |
Ets | Excitation time shift | This parameter is used to compensate the time offset between the carrier generation's input in the system and modulated signals' output | s | Input |
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Where Sin.Sin, Sin.Cos, Cos.Sin, and Cos.Cos represent gains that are applied to simulate a non-ideal resolver. To simulate an ideal resolver, set the Sin.Sin and Cos.Cos gains to 1, set the Sin.Cos and Cos.Sin gains to 0, set the pp to 1, and set the θOffset to 0. This results in the following equations:
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Encoder Parameters & Measurements
Symbol | Name | Description | Unit | Type |
|---|---|---|---|---|
Encen | Enable encoder | Whether or not to enable the encoder | N/A | Input |
Enctype | Encoder type | Encoder type, either Quadrature or Hall Effect | N/A | Input |
QABZ | A B Z encoder signals | A B and Z signals of the encoder | N/A | Measurement |
Qppr | Number of pulses per revolution | Number of pulses in one full revolution of the encoder | N/A | Input |
Qdir | Direction of the sensor rotation | Direction in which the sensor is turning, either A leads B or B leads A | N/A | Input |
Qθ | Angle offset Δθ ( Sensor - Rotor ) | Angle offset between the encoder and the rotor position from 0 to 360 degrees | ° | Input |
Qrat | Encoder speed ratio ( sensor to mechanical position ) | Mechanical to encoder ratio. Angle of Encoder = Qrat * machine mechanical angle. | N/A | Input |
Hθ | Hall effect sensor position | Position of sensor phases A, B and C in Hall effect mode | ° | Input |
Hrat | Hall effect sensor speed ratio ( sensor to mechanical position ) | Mechanical to encoder ratio. Angle of Encoder = Hrat * machine mechanical angle in Hall effect mode | N/A | Input |
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Visualization of Resolver Encoder Parameters Effects
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