SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure 6.9 – FOC block diagram.
The motor and inverter (and Clarke transform) can be modeled in state-space as shown in Figure
6.10. This figure simply represents the way that the state-space model fits into FOC; it uses the
non-linearized version of the model, thus the state vector is [ , , , ] T
x i i
. Therefore the
function that gives rotor position in the model is simply g( x ) x4r. Figure 6.10 – State-space model of motor and inverter.
By definition, sensorless FOC cannot measure position or speed, thus the full state vector is not
available. As mentioned, some observers do estimate the full state vector but that requires the
mechanical parameters to be known. Instead, the pseudo state vector [ , , , ] T
x i i e e is
r
estimated as shown in Figure 6.11. From the last two estimated states the rotor angle may be
calculated using the function f x ˆ , which will be discussed shortly.
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