SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

more correct yet is to acknowledge that the components in the rotor reference frame are real and
imaginary (Equation 3.106) just as they are in the αβ plane. Instead of thinking about rotating a
space vector or rotating a coordinate system, simply think of the SV as existing in the rotor
reference frame originally. Given Equation (3.106) and the definition of the complex plane, the
rotor reference frame is always in the same position shown in Figure 3.38. The αβ axes (not
labeled) would be rotating in the CW direction. In the rotor reference frame we are not concerned
with where the SV may lie in the αβ plane; we look at the position of the SV relative to the rotor
position only. Since this is the meaning of the rotor reference frame, it is also the best way to
visualize the result of the Park transformation.
Figure 3.38 – Park transform: rotor reference frame perspective.
The Park transform allows us to continue to refine our understanding of SV- and reference frame
theory. In Part I when the stator MMF was developed, the argument of the cosine was briefly
discussed and it was said that the current position ωt (an electrical quantity) shares the same
angular space as the MMF position (a mechanical quantity). Then in Part II (in the section “The
SV as a Distribution”) a potential discrepancy was examined to reveal the meaning of reference
frame theory (and the Part I discussion was revisited in this light). Now the earlier Part II
discussion will be revisited and finalized.
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