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.