SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

clear the meaning, but the reader is cautioned that there are many different terms used to describe
a voltage induced in a coil and the various components of that voltage. Some of the common
terms are: speed voltage, transformer voltage, motional EMF, counter-EMF, back-EMF,
rotational voltage, armature reaction voltage, magnetizing EMF, airgap voltage. While there is
some common agreement as to the specific meaning of each term they are often used
interchangeably, especially back-EMF. In the sense that all components of an induced voltage act
to counter changes in flux, identifying any of them as the back-EMF or counter-EMF could be
etymologically reasonable. But to be clear, this report defines back-EMF to be the component of
induced stator voltage produced only by a change in the stator flux linkage due to the position of
the rotor. This means that any change in the stator circuit that occurs while the rotor is locked
cannot be called the bEMF. This approach has some circuit-theory appeal in that the distributed
inductance of a real winding can be modeled as a lumped element in series with an ideal voltage
source. On the other hand, the entire stator flux linkage plays an important role in the modeling
presented in the next chapter, thus the total induced voltage g(t) is often used. In addition, g(t) has
a physical meaning that will be examined in the next chapter.
The KVL equations for the circuits shown in Figure 2.18 and Figure 2.19 are Equations (2.25)
and (2.26), respectively, with the stator flux linkage is defined as Equation (2.27). It should now
be clear that when Equation (2.27) is substituted into Equation (2.26), the result is equivalent to
Equation (2.25). The distinction between e(t) and g(t) and the connection between these equations
will be revisited in the next chapter and should become clearer at that time.
d R
di(
t)
d
R
v(
t)
i(
t)
R L , where
dt dt
dt
e(t)
(2.25)
d
v(
t)
i(
t)
R
dt
(2.26)
Li
(2.27)
R
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