Consideration of Hysteresis, Saturation, Fringing and Leakage Fluxes in
the Frequency-Dependent Analytical Model of Nonlaminated Cylindrical
Actuators
Abstract
Previous works have demonstrated that analytical high-fidelity models of
nonlaminated actuators and magnetic thrust bearings cannot just describe
the magnetic skin effect inside the solid core, but also be applied
directly within the control circuit. By an appropriate rational
approximation a digital implementation on a microcontroller becomes
possible. However, these approximated models neither considered
hysteresis and saturation nor frequency-dependent fringing and leakage
fluxes. This article elaborates whether or not these nonlinearities can
and should be included in real-time control systems. We present an
improved process to map an analytical hysteresis model to a limited
measured dataset and discuss the impact of the nonlinear magnetization
curve. It leads to a novel fractional-order all-pass filter, modeling
the frequency-dependent hysteresis angle for a single load point. Its
rational filter form is suitable for implementation in Matlab/Simulink
as well as real-time applications. Leakage and fringing fluxes, on the
other hand, can be considered with relatively low effort within the
original analytical models. The underlying reluctance network is
determined by a FE-analysis as well as analytically and reduced to a
highly simplified form. Depending on whether the total flux or the
force-dependent flux is of interest, the model order may increase
significantly and constant correction factors are preferable.