SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure 4.30 – Synthesis of SV by time-averaging base SVs.
Each base SV Si
is asserted for a certain fraction σi of the modulation period T. The time-
average SV is the sum of these products and is given by Equation (4.7), where the subscripts ‘x’
and ‘y’ indicate active base SVs and the subscript ‘N’ represents a null base SV. (In Figure 4.30,
the active base SVs are 1 S
and 2 S
and the null SV is arbitrary.)
S S S
S
(4.7)
x x y y N N
MUST
Since σi is the fraction of the modulation period for which Si
is asserted, i 1.
The
“maximum” static output would correspond to a single base SV being asserted continuously as
we have already seen. The “maximum” output of a moving SV would be whatever SV is
generated when only active base SVs are used ( N 0 ). Using simple trigonometry it can be
shown that the locus of all possible “maximum” ( N 0 ) SVs is identically the hexagon that
connects the tips of the base SVs, as shown in Figure 4.31.
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