SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure 5.16 – Torque functions: (a) components; (b) combined.
This can also be seen by examining Equation (5.11). To produce positive mutual (magnet) torque,
i q should be positive as usual (for forward motoring operation). For the rotor of Figure 5.15-b, in
which Ld Lq,
it is clear that i d must have the same sign as i q (positive) in order for the
reluctance term to contribute positive torque. On the contrary, for the rotor of Figure 5.15-c, in
which Ld Lq,
it is clear that i d must have the opposite polarity as i q in order for the reluctance
term to contribute positive torque. In the dq rotor frame, when the current SV has a positive d-
component, it is less than 90° ahead of the rotor flux; when the component is negative, its lead is
greater than 90°. The relative location of the current SV required to produce maximum torque per
current is shown in Figure 5.17. This should make clear the direct correspondence between
Equation (5.11), Figure 5.15, Figure 5.16, and Figure 5.17.
Figure 5.17 – Required position of stator current SV for maximum torque.
223