Application of Selected Numerical Methods to Model the Fractional-Order System Behavior of Nonlaminated Magnetic Actuators

The electromagnetic dynamics of nonlaminated magnetic actuators are highly influenced by eddy currents and minor perturbations like core saturation, hysteresis as well as fringing and leakage fluxes. In the literature, analytical high-fidelity models describing these phenomena are known, which lead to complex reluctance networks or transcendental system descriptions with fractional-order characteristics. Therefore, they are not suitable for a direct implementation within the actuator control. Previously, we provided appropriate analytical rational approximations that allow a digital real-time implementation of these models on a microcontroller. However, the inclusion of the minor perturbations, if possible, leads to impractical model orders requiring simplifications, which compromise the model accuracy. This article studies numerical methods to reduce high model orders or directly approximate the transcendental systems or empirical measurement data. The greater degree of freedom allows for a possible higher model accuracy with sufficiently low orders. We review and improve existing approaches like Levy's method and Vector Fitting and apply them to the frequency response of the underlying fractional-order system. Furthermore we propose an order reduction algorithm based on a pole-zero-cancellation with tracking error compensation. Using measurement data, a comparison shows that the numerical approaches match or excel our previously studied analytical approximation.