Nonlinear order reduction in dynamic magnetic equivalent circuits of electromechanic actuators: Incorporating relative motion and back EMF

Physics-based modeling of electromechanical actuators driven by power electronics converters is highly desired for precise dynamics representations of magnetic components. In this paper, a very detailed dynamic magnetic-equivalent circuit of an actuator is set forth that is based on geometrical and material characteristics, and avoids conventional geometrical simplifications and uniform flux-density assumptions. In general, the presence of eddy currents in dynamic physics-based models significantly increases the model order. The computational intensity is further pronounced when considering the nonlinearity associated with relative motion. Automated linear and nonlinear order-reduction techniques are introduced to numerically extract the essential system dynamics in the desired bandwidth, thus preserving both dynamic accuracy and computational efficiency. In particular, the original high-order model is replaced with piecewise linear reduced- order models that are expressed as numerical functions of the mechanical position and speed. The model order is successfully reduced from 300 to only 5 state variables, thus significantly cutting the execution time. The resulting reduced-order model is verified with the original full-order model in predicting time-domain transients as well as frequency-domain characteristics, which is important for converter-driven actuators.