SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure 5.33 – Top-level model of rotor-oriented FOC (with decoupling).
The decoupling scheme is often presented without much discussion; the author’s present
understanding follows. Since the coupling exists because of the flux linkage, it is present in an R-
L load as well (the bEMF offset term would not be present). Both the cross-coupling and the
bEMF disturbance are multiplied by ω, which varies slowly compared to the possible rate of
change of the currents (and in steady-state operation i d and i q are relatively constant). As far the
as the steady-state cross-coupling of i d and i q is concerned (and as far as ω contributes to the
bEMF offset), the disturbances are nearly steady-state quantities. It therefore appears that the
decoupling serves to reduce the magnitude of the error (thus “unloading” the integrators) in order
to improve transient response. On the other hand, transients in i d and i q feed straight through and
are not steady-state disturbances, thus it appears that the decoupling also improves the transient
response. At least one reference [118] seems to confirm this understanding.
It is curious that most diagrams of FOC controllers do not include these decoupling terms. It is
certain that by injecting the bEMF offset term its disturbance on the current loop is eliminated
[158]. Since ω varies slowly compared to the bandwidth of the current loop the regulators can
handle the error, but as mentioned, [118] indicates that eliminating this offset does improve
response. The cross-coupling in the model is clear as well. However, if the synchronous
inductance is low the cross-coupling may not be significant enough to warrant the use of
decoupling.
At any rate, when the decoupling is not performed and the coupling in the motor model is
ignored, or when the decoupling is performed and assumed to be perfect, the BPMS model
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