SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

emphasize that vt () is the applied voltage (not a modeled source) it will be indicated by a
polarity instead of a source.)
Figure 2.17 – Per-phase electrical model of general brushless PM motor; explicit inductor.
Readers familiar with the synchronous machine will likely identify the last term in Equation
(2.24)—which corresponds to the voltage source in Figure 2.17—as the back-EMF (bEMF). In
this report this bEMF term will be labeled e(t) as shown in Figure 2.18.
Figure 2.18 – Per-phase electrical model of general brushless PM motor; explicit inductor.
In much of the literature, the total induced voltage is represented as a voltage source equal to the
time derivative of the flux linkage as shown in Figure 2.19.
Figure 2.19 – Per-phase electrical model of general brushless PM motor; implicit inductor.
The circuits in Figure 2.18 and Figure 2.19 are the two most prevalent models for an armature
winding in a non-salient-pole synchronous machine. (At this point we have still neglected the
effects of the other windings and the effect of flux leakage; later it will be shown that both of
these effects can be accounted for by modifying the simple inductance defined earlier.) This
discussion has made careful distinction between g(t) and e(t), but much of the literature uses the
explicit “e(t)” to mean what has here been denoted g(t). The context of an article should make
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