Rational Approximation of the Analytical Model of Nonlaminated Cylindrical Magnetic Actuators for Flux Estimation and Control

Abstract

Eddy currents can significantly hamper the electromagnetic dynamics, especially those of nonlaminated actuators, and have thus been of great interest in actuator control for many years. Although there are high-fidelity models describing phenomena inside the solid core, such as the magnetic skin effect, these models have never been applied directly within the control circuit. The main reason for this is the lack of an appropriate approximation suitable for time-discrete digital implementation on a microcontroller. This article aims to provide a complete review about possible approaches to obtain a rational approximation of the frequency-dependent effective reluctance and inductance of an electromagnetic actuator. The rational approximation is then used to design a common infinite impulse response filter (IIR-filter). Using the example of a flux-controlled magnetic thrust bearing, we conclude with two novel approximations: a mathematically complex Pade approximation of a sum of continued fractions and a simple Matsuda approximation of an implicit equivalent fractional-order system. On the other hand, the former is the most accurate, and the latter allows wider approximation bandwidths. Depending on possible sampling and switching frequencies as well as the bandwidth of the actuator and computing capacity of the control unit, the most appropriate approximation for almost any use case can be selected.