SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

The number of closed-loop schemes is large. The methods differ primarily in the type of
estimator and the type of correction used, although there are variations as to which signals are
measured. A sizeable portion of the literature concerns the sensorless control of induction
machines, which is a technical challenge that is very different in nature than the sensorless control
of a BPMS motor. Due to different terminology in use is at times difficult to identify which type
of estimator is used. For example, some references state a Luenberger observer is a structure
applicable to only linear systems while other references claim otherwise. A full-order linear
observer may be called a Luenberger observer, while a reduced-order linear observer may be
called a Gopinath observer; another reference will reverse the names. Often an “extended”
Luenberger observer is mentioned but the author has yet to find the subject treated in a control
system text. Further, there are different structures identified as “extended” Luenberger or Kalman
filters (ELO and EKF)—an EKF in one reference may simply estimate states, while an EKF in
another reference may be used for simultaneous state estimation and parameter identification. In
addition to the large variation in terminology and structure of the “simple” linear Luenberger and
Kalman filters (and their extended varieties), nonlinear observers are reported, as is nonlinear
compensation of a linear observer. It is also popular to combine adaptive schemes with the
observers; there are simply too many possibilities to categorize.
A cursory examination of the literature on sensorless control will reveal that much of it requires a
graduate- or post-graduate understanding of mathematical control theory to understand the
operation of the system. Even if one had such training, conducting a literature review would be a
formidable task. According to [93], “…for the two year period 2005-2006 over 120 papers
featuring [sensorless control] were published in IEEE Transactions and Institution of Engineering
and Technology Proceedings alone.” Even if one were to read and comprehend all of them, it is
difficult to make any performance comparisons because the different schemes are not evaluated
according to a standard (though some have recently been proposed) [93]. For these reasons and
others, this report presents only a simple linearized Luenberger-style observer (closed-loop, full
order).
Luenberger Observer
The sensorless scheme just presented was given as a set of equations that could be solved
numerically in software. Another popular alternative is to utilize the state-space form. In this
242