Application of synergetic control theory to non-sinusoidal PMSMs via multiple reference frame theory

Park equations in a rotor reference frame are used for sinusoidal back-electromotive force (EMF) permanent magnet synchronous machines (PMSMs) to eliminate the rotor-position dependency and create time-invariant model. However, Park equations are not suitable for non-sinusoidal back EMF cases. Instead, multiple reference frames are considered individually for each harmonic, with their rotation speed defined as multiples of the rotor electrical speeds. A nonlinear average-value model of the inverter-fed PMSMs is developed. A universal controller is designed for the resulting nonlinear model using a synergetic approach to control theory that does not require linearization. The controller is able to construct the desired input voltage for the 1st, 5th, and 7th harmonics in both direct and quadrature axes. The final model is verified with four-quadrant operation and locked rotor tests where speed and torque commands are closely tracked.

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