A dq-axis framework for electrostatic synchronous machines and charge oriented control

Recently, innovations such as advanced dielectric liquids and additive manufacturing have enabled electrostatic machines at the fractional horsepower scale that have competitive performance with their conventional electromagnetic counterparts. The emergence highlights a need for circuit modeling that guides machine design and drive controls, rooted in the canon of well-established electromagnetic machinery practices. This paper combines prior approaches and expands upon them to form a unified electrostatic machine dq-axis framework capable of providing insight on the capacitances of interest for torque production as well as control. Maximum torque per volt and charge oriented control are presented with a torque equation whose terms are parsed into field, elastance, and induction torque mechanisms. Complex vector voltage regulators form the heart of drive controls. The model is confirmed with finite element analysis (FEA).