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

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung


Eddy currents can significantly hamper the electromagnetic dynamics especially 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 Padé approximation of a sum of continued fractions and a simple Matsuda approximation of an implicit equivalent fractional-order system. Whereas the former is the most accurate, 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.


Seiten (von - bis)1-16
FachzeitschriftIEEE Transactions on Magnetics
PublikationsstatusVeröffentlicht - Dez. 2019

Externe IDs

Scopus 85077497402
ORCID /0000-0002-3347-0864/work/142255169



  • Actuators, magnetic bearings, eddy currents, rational approximation, analytical modeling