SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

eluctance for compatibility with the derivation but it is known as the internal or leakage
permeance of the magnet [69, p.4.12]. The flux shown in Figure 2.14 corresponds to the flux path
in the center of Figure 2.13.
Figure 2.14 – Magnetic circuit of Figure 2.12.
The two magnets can be combined ( R 2R
) and the two airgap reluctances can be combined
m m
as R 2 Rag
. Per the assumptions given earlier the rotor and stator reluctances are ignored. The
reduction yields the circuit shown in Figure 2.15.
Figure 2.15 – Simplified magnetic circuit of Figure 2.12.
The flux linking the turns of the coil is from two sources: the coil ( C ) and the permanent
magnet ( M ). Ignoring hysteresis, superposition applies and the total flux ( T ) is given by
Equation (2.14). Since leakage flux is ignored here, this total flux crosses the airgap, thus it could
be called the airgap flux.
(2.14)
T
C
M
C and M are found by standard circuit analysis techniques using the circuits shown in Figure
2.16Figure 2.16 and are given by Equation (2.15) and Equation (2.16).
N i
C
R R
(2.15)
m
R
m
M r
(2.16)
R Rm
30