SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure 2.31 – Back-EMF and drive current for trapezoidal BPMS motor.
Unlike the sinusoidal motor, it is seen that the trapezoidal motor is driven with discontinuous
currents, again with magnitude Ip. This current control scheme goes by various names (such as
trapezoidal drive, six-step commutation, squarewave current drive) but these are all misleading
because each can carry several different meanings depending on context. Thus, this report will
call this 120° six-step commutation. Torque is produced by a phase winding only when the bEMF
and current are both nonzero, thus we do not need any analytical expression for the bEMF—as
long as it is constant over the 120° “commutation period” it can be considered a DC value in the
torque equation. This is why the trapezoidal motor described earlier in the chapter was called an
“arbitrary” trapezoidal motor—in the ideal case it does not really matter what shape the bEMF
takes on between commutation periods as long as there is at least 120° of flat-topped bEMF. 9
Only two windings contribute to torque at any given instant, thus the torque can be expressed as
Equation (2.58).
2Ke Ip
(2.58)
The per-phase torque and total torque for a trapezoidal motor are shown in Figure 2.32. Similar to
the sine motor, it makes sense that the per-phase torque is equal to Ke·i(t).
9 Real trapezoidal motors rarely achieve this 120° flat top. Additionally, when a trapezoidal motor is driven
with non-ideal currents (whether intentionally or as a result of operation with motor-drive mismatch or at
the edge of normal operation) the waveshape between the flat segments does matter because it interacts
with the bEMF to produce torque ripple.
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