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 control (FOC) scheme with the genuine/specious pair, and devise a detection-quit mechanism to help FOC systems flee the specious pair using the knowledge of motor/generator mode. These two ingredients enable a tailored sensorless algorithm that can obviate the need for initial position detection.