SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

the sinusoidal torque controller of Figure 5.3 is redrawn as Figure 5.10, where the triangle carrier
is represented by v T . 36 Filters on the phase current measurements are not shown.
Figure 5.10 – Torque control of sinusoidal motor; phase-variable form.
According to Figure 5.8-c, the PI controllers are required to regulate continuously-varying
signals. In addition, if the control system diagram were drawn it would be seen that the bEMF
acts as a periodic disturbance to the current loop. The primary limitation of this configuration is
the phase shift associated with the PI controllers operating at synchronous frequency [154]. In
steady state this phase shift causes the torque angle to decrease from the ideal 90° ( rin
Figure 5.5). In this configuration the current loop is responsible for controlling both the amplitude
and the phasing. In contrast the reference signal in Figure 5.6 is a DC quantity in steady state due
to the Park transform. (The controller in Figure 5.6 had no current loop because impressed stator
currents were assumed.) The way to fix the problem is to close the current loop around the stator
currents transformed to the rotor frame.
The first step toward this is to use the inverse Clarke transform as before to replace the threephase
sinusoidal commutator with the two-phase one and move the current loops from the phase-
36
In a wye-connected motor only two of the currents can be controlled independently. For this reason some
references (primarily from the popular literature) claim that it does not make sense to use the third current
loop (in that case the third PI compensator is not present and the phase-C current command is given by
* * *
iC iA iB
). The hysteresis controller has a phase interference problem because it does control all three
phases [132]. The issue is that controlling the voltage at terminal-A can be accomplished only by pulling
the terminal high or low. But each time this change is made to phase-A, it changes the state of the entire
inverter, which changes the line-neutral voltages of phase-B and phase-C, thus the phases cannot be
controlled independently. [78, p.335] confirms that it is not logical to use three regulators, and in addition
to solving the problem by slaving the third as above, another option is to generate a ZS signal to be fed
back to decouple the phase regulators. However, for some reason, the three-regulator variety seems most
prevalent in the literature concerning CRPWM, perhaps indicating that the effect may not be as pronounced
as in a hysteresis CRPWM. For simplicity all three regulators are shown here.
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