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 1
^st
, 5
^th
, and 7
^th
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.