SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

SV. This was done to obtain a similar SV ( y
) that would be 120
away from the phase-A
axis and that interpretation is valid. But now the more-correct explanation can be provided. It was
mentioned that given our choice of conventions the SV must be defined by Equation (3.69).
jj (3.69): x k xA1xBe xC e
Rotating the SV by 120
to obtain the phase-B projection was accomplished by multiply the
j120 SV by e
j
e
. Multiplying that factor through the SV definition yields Equation (3.101).
j j j j
x e k
xA1xBe xC e
e
j j j
x e k xAe xB1xC e
(3.101)
In Equation (3.101) we have done nothing to the definition of the complex plane (the Re/Im or
α/β axes) but it is clear that the phase variable axes have been rotated by 120
; for example, x A
is no longer acting in a direction coincident with the real axis. Using Equation (3.100) it would be
seen that in obtaining the phase-C projection, the phase axes are rotated another 120
(for a
total of 240 120
from the original positions). The action of rotating the SV to align with
the real axis is seen clearly below.
j j
j j j
j j j
xA Re xA1xBe xC e 1
xB Re
xA1xBe xC e
e
xC Re
xA1xBe xC e
e
1
j j
j 1
j
j j
1
xA Re xA xBe xC e
xB Re
xAe xB xC e
xC Re
xAe xBe x C
The apparent axes are shown in Figure 3.32 for the projection onto the phase –A, –B, and –C
axes.
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