SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure 6.11 – Sensorless FOC using observer.
There are several things that must be understood about the diagram in Figure 6.11. The plant is
representative of the motor, inverter, and Clarke transform. The plant is the only power-
conversion part of the control system. However, it is modeled in the stationary (αβ) reference
frame, which does not physically exist. This means that the input vector u v
is a software
variable. It could be the Clarke transform of the measured phase voltages but is often the αβ
y
commands given to the SVM inverter. 43 This also means that the measured output vector i
is a software variable as well (the Clarke transform on phase-variable currents measured using a
current transducer); since it is a measurement the vector is shown in blue. The current loops, PI
compensators, Park and inverse-Park transforms, observer and its compensator, and the rotor
angle calculation all exist in software. This is made clear by reexamining Figure 6.1.
In the simplest case, the function f x ˆ used to calculate the rotor angle could be the two-
argument arctangent function mentioned earlier. A few articles in the popular literature insinuate
that this function is only valid for sinusoidal motors but it is valid regardless of the waveshape—
the arctangent is operating on the αβ components. One disadvantage of using the function is the
required division. Another potential disadvantage may be the susceptibility to noise unless a
digital filter is used (the observer states and rotor angle are calculated each cycle of the current
43 The αβ commands will result in errors because they do not account for bus voltage variations, voltage
drop in the transistors, and dead-time effects. There are any number of ways to correct for these
deficiencies; the severity of the problem depends greatly on the power transistors, bus voltage, and load.
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