Consideration of Hysteresis, Saturation, Fringing and Leakage Fluxes in the Frequency-Dependent Analytical Model of Nonlaminated Cylindrical Actuators

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.