SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

3
KT Ke
2
(sinusoidal)
K 2 K (trapezoidal)
T e
(2.59)
Since there is no such thing as “overall” bEMF, there is no corresponding constant KE. However,
since the motor neutral is not usually available, only line-line parameters can be measured and the
bEMF constant is often specified as a line measurement, Ke,LL. Due to the way in which the two
motors are typically controlled, for the sinusoidal motor the line-line voltage is √3 larger than the
line-neutral voltage but for the trapezoidal motor the line-line voltage is twice as large as the lineneutral
voltage. Using these relationships and Equation (2.59), the torque constants in terms of
line quantities can be found and are given by Equation (2.60).
K
3
K
2
K K
T e, LL
T e, LL
(sinusoidal)
(trapezoidal)
(2.60)
These values of KT are valid when the proper type of current is fed to each motor. Later the case
will be examined when improper current is fed to the motors. Finally, it must be noted that there
are several variants of these values used throughout the literature and this seems to be a large
point of confusion. Those given here have been selected to provide technically-accurate
continuity between the per-phase and three-phase discussions. Most variants in the literature can
be resolved but there have been a few which the author could not decipher. [69] gives the most
detailed coverage of the subject of these constants.
Electronic Commutation
The trapezoidal motor can theoretically produce ripple-free torque when driven with ideal
rectangular currents, though this is not completely achievable in practice (discussed later). Since
the current in a trapezoidal motor is DC over the flat-topped bEMF, since it is switched full-on
over the commutation period, and since the polarity of the current is reversed once per electrical
cycle, this motor resembles a brush DC motor without the brushes. For this reason it is sometimes
called a Brushless DC Motor (BLDC), although claims in the literature that it is simply a brush
DC motor “turned inside out” are false, as should be apparent from prior discussion. Further,
since the current is controlled by only electronic means, it is sometimes referred to as an
Electrically-Commutated Motor (ECM) or electronically switched motor. As mentioned, the
process of controlling the current relative to shaft position is often called electronic (current)
commutation. For a trapezoidal motor the current changes only six times per revolution so Halleffect
sensors are often used with simple logic circuits to determine which windings should carry
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