SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure 6.6 – Full state feedback (open-loop estimator).
The estimated state would be in error if they were not initialized to the initial states of the plant or
if the model was not exact (which it can never be). Further, the rate at which the error exx ˆ
tends to zero is determined by the plant dynamics (thus the estimate could not be used for
control); the math that shows this is found in any of the references cited at the end of this chapter.
To solve these problems the estimator can be made to be closed-loop. There seems to be only one
sensible way to do this and it is shown in Figure 6.7. The topology is generally called a
Luenberger observer (named after its inventor, David Luenberger). The estimated output is
compared with the actual output and the error is multiplied by a ( n m)
gain matrix L . This
allows the error dynamics to be controlled, eliminates the error due to incorrect initial state
estimates, and should hedge against errors caused by the difference between the plant and the
observer model.
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