Solving Sensorless IPMSM Equations

We show that the two equations of interior permanent magnet synchronous motors always satisfy four (speed, position) solution pairs, predetermining where sensorless algorithms will end up. With such finiteness, we see a silver lining in establishing theoretical basics for the open problem of startup with an unknown initial position. We reveal normal-reversal duality that demystifies the familiar binary behavior of sensorless field-oriented …