Modeling the impact of discretizing rotor angular position on computation of field-oriented current components in high speed electric drives

Modern drives consist of alternating current electric motors, and the field-oriented control (FOC) of such motors enables fast, precise, and robust regulation of a drive's mechanical variables such as torque, speed, and position. The control algorithm, implemented in a microprocessor, requires feedback from motor currents, and the quality of this feedback is essential to a drive's control properties. Motor phase currents are sampled and processed in order to extract their mean over a digital control interval. Afterwards, the mean phase currents are transformed into a rotating field-oriented reference frame to enable controlling the mechanical variables. The field-oriented frame rotates continuously, but in practice the transformation is carried out using a discrete angular position. This paper investigates how the discretization impacts the computed field-oriented currents in high speed drives, where the rotor displacement during a control interval is substantial. A continuous-time model of field-oriented currents is indicated as a reference to quantify errors. An original approach to normalize variables and to solve the model analytically is proposed in order to investigate how the errors related to rotor position discretization are influenced by drive operating conditions. The analytical solution is validated by computer simulation. The results show that the currently applied methodology of computing field-oriented current components, due to an invalid assumption, introduces errors of a few percent when a drive operates at high speed. These errors can be compensated using the presented solution.