SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

stationary regulator had. For completeness the synchronous regulator can be transformed to the
stationary frame. The math [154] is again omitted and the result is shown in Figure 5.29.
Figure 5.29 – Synchronous regulator in stationary frame.
Now the polarities of the cross-coupling terms are such that with increasing ω the α-component is
decreased and the β-component is increased, resulting in a phase lead. As with the stationary
regulator in the synchronous frame, examining the synchronous regulator in the stationary frame
like this is simply a demonstration from a different viewpoint of what we already know to be true.
In this case, the oscillator is active and is more complicated to analyze: it produces output signals
even with zero error [78, p. 344] but of course errors are required to adjust the phase of the output
to that of the command [158]. Figure 5.29 also demonstrates that a regulator with the
performance benefits of the synchronous regulator can be implemented in the stationary frame;
this was the original concept presented by Rowan and Kerkman [154]. It can be implemented
more simply than a regulator in the synchronous frame (though with modern hardware this is no
longer an issue).
In summary, the synchronous regulator is superior to the stationary regulator. It has become the
standard for current regulation in polyphase AC machines [157]. Since FOC inherently
implements synchronous (rotor) frame current regulation, it inherits the same benefits. Now
current control of a motor under FOC will be investigated further.
FOC/Synchronous Current Regulation
Rotor-oriented FOC was shown in Figure 5.14. As before, the blocks in can be bent into the form
of Figure 5.24. When the inverter is assumed ideal, then control system reduces to that shown in
Figure 5.30. Notice that the rotor position is not relevant—the transformations autonomously
handle the current phasing in both command and feedback signals.
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