SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure 3.14 – Cross section of two pole motor.
Now the stator and rotor quantities are shown together in the developed view of Figure 3.15. The
rotor is still positioned at 30° and the stator MMF is that which would result if the stator currents
were at 120° in Figure 3.6.
Figure 3.15 – Developed view showing rotor flux density and stator MMF.
There are a number of methods to derive the torque produced. Using coenergy it is possible to
show that the torque produced in a non-salient machine with sinusoidally-distributed magnetic
fields on the rotor and stator can be described in terms of the peaks of these distributions and the
spatial angle between them [27, pp.117-121]. These cosine waves exist in space and can be
described by phasors. Since this is a phasor analysis it only holds for sinusoidal quantities under
steady-state.
It is easiest to begin with the MMF waves. In this case the torque is given by Equation (3.12),
where c1 is a constant, FR and FS are the amplitudes of the sinusoidal MMF waves of the rotor and
stator, and δ is the angle (called the load angle or torque angle) measured from the peak of the
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