SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

more widely understood theory (such as single-phase equivalent analysis), but such is not the case
(for students and engineers outside of the motor control field).
On the other end of the spectrum are works that rely entirely on the use of space vector theory. If
connections between space vector theory and traditional theory are presented, they are usually
based on the fully-general six-variable nonlinear time-varying coefficient models, which are
difficult to grasp upon first encountering (these models absent in many undergraduate texts).
Discussion of the meaning of the space vector and the nuances of its theory are generally minimal
or absent entirely. It is the author’s perception that most texts employing space vector theory are
written above the graduate level. The application to the general machine is very generalized.
Handling the rotor and stator quantities expressed in different reference frames requires bulky
notation (such as variables laden with simultaneous superscripts and compound subscripts). It is
time consuming and difficult to learn a notation and different texts use entirely different notation.
The meaning and usefulness of the theory can be buried in the mathematics or it can be easily lost
in the drudgery of keeping track of symbols. In addition, many texts are rooted in induction motor
analysis and treat synchronous machines by issuing a statement along the lines of, “to be
completely general, the theory has been developed in general terms of the induction motor but it
is easily adapted for the synchronous machine.” While this is a valid approach, it is very time
consuming to work through induction motor literature in order to follow the specialization of an
induction motor model to describe the synchronous machine.
Fortunately, references in between these extremes [42], [78], [88], [73] generally attempt (with
varied success) to explain the theory in simple terms; these are of the most value to the
newcomer. Nonetheless, it may still be difficult to bridge understanding between different
resources, especially between works on opposite ends of the spectrum described above. The
theory and its application are multifaceted and most unfortunately, while a particular reference
may succeed at emphasizing a certain simplified understanding, other important aspects may be
unintentionally minimized or ignored completely.
The author has found that the perspective most useful in learning space vector theory is found in
the more theoretical texts (the perspective is called reference frame theory). Since they are written
at an advanced level, it is necessary to have a fair grasp of traditional machine theory in order to
understand them. The aim of Part II is to introduce and utilize space vector theory where
necessary to develop the linear transformation of variables and the concept of reference frames,
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