SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

One final connection will be made between the graphical and mathematical derivations. Equation
(3.2) clearly shows the component MMF produced by each phase and the action of these standing
waves is seen clearly in Figure 3.7 and Figure 3.8 where the instantaneous distributions are
compared to their maximum unit values (the dashed lines). Equation (3.7) clearly shows the total
MMF, and the action of this traveling wave is made clear by Figure 3.9. Each standing wave
(component MMF) could be represented as an MMF phasor in the traditional manner, but
abstracting to phasors just to have to project them back onto the real axis does nothing to aid the
visualization. If instead the instantaneous value of each standing wave (component MMF) is
drawn coincident with the axis along which it acts, it is possible to visualize that component’s
contribution to the total. This is shown in Figure 3.11, where the two figures correspond to
current positions of zero and thirty electrical degrees—the same electrical position as in Figure
3.7 and Figure 3.8.
Figure 3.11 – Instantaneous values of component and total MMFs; (c.f. Figure 3.7, Figure 3.8).
Examining the component contributions shows the standing wave action—the contribution of
each phase increases and decreases as a function of current but is always oriented in the same
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