Selected numerical methods to model the fractional-order system behavior of nonlaminated magnetic actuators
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Robert Seifert
Robert Seifert received the Dipl.-Ing. degree in electrical engineering from TU Dresden, Germany in 2014. Since 2015, he has been research associate and doctoral candidate at the Chair of Electrical Machines and Drives of Prof. W. Hofmann at TU Dresden. His research involves linear drives and magnetic bearings, for which he studies the application of soft magnetic composites and new control strategies, with a special focus on fractional–order systems and their application in digital actuator control.
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Martin Hecht
Martin Hecht received the B. Sc. degree in electrical engineering and information technology at ETH Zurich, Switzerland in 2021. Since 2021, he has been attending a master program at the Department of Information Technology and Electrical Engineering at ETH Zurich, with focus on power electronic systems In 2020 he undertook an internship at the Chair of Electrical Machines and Drives of Prof. Hofmann at TU Dresden.
Prof. Dr.-Ing. Wilfried Hofmann received the Dipl.-Ing. and Dr.-Ing. degrees in electrical engineering from TU Dresden, Germany, in 1978 and 1984, respectively. Since 2007, he has held the Chair of Electrical Machines and Drives at TU Dresden. He published over 360 papers, 60 patents and four books. His main research areas are energy conversion, mechatronics and motion control as well as control of ac machines and power electronics. Prof. W. Hofmann is member of the German Academy of Science and Engineering (acatech) and the Saxon Academy of Sciences. He is a member of IEEE IES EMTC, VDE/VDI and the steering committees of the EPE, ISMB and SPEEDAM.
Abstract
Nonlaminated magnetic actuators are highly influenced by eddy currents and minor perturbations like e. g. hysteresis. Known analytical models lead to trans-cendental system descriptions with fractional-order characteristics, not suited for the actuator control. Although analytical approximations resolve the issue, the inclusion of minor perturbations leads to impractical model orders, which require simplifications and compromise the model accuracy. This article studies numerical methods to directly approximate the transcendental systems or measurement data, allowing for a high accuracy with sufficiently low orders. We improve existing approaches like Levy’s method and vector fitting and apply them to a fractional-order system. Using measurement data, a comparison shows that the numerical approaches match or excel our previously studied analytical approximations.
Zusammenfassung
Die Kraftdynamik ungeblechter magnetischer Aktoren ist insbesondere von Wirbelströmen aber auch von anderen Störgrößen, wie z. B. Hysterese beeinträchtigt. Bekannte analytische Modelle führen zu komplexen transzendenten Systembeschreibungen basierend auf fraktionalen Systemen, ungeeignet für die Aktorregelung. Analytische Approximationen lösen das Problem für das Wirbelstrommodell, führen jedoch bei Berücksichtigung anderer Störgrößen zu impraktikablen Systemordnungen. Die folglich notwendigen Ver-einfachungen verschlechtern die Modellgenauigkeit. Diese Arbeit untersucht numerische Methoden, um die transzendenten Systeme oder Messdaten mit hoher Genauigkeit bei hinreichend kleinen Ordnungen direkt zu approximieren. Bekannte Ansätze wie Levys Methode oder das Vector Fitting werden verbessert und auf fraktionale Systeme angewandt. Ein Vergleich anhand von Messdaten zeigt, dass die numerischen den analytischen Ansätzen gleichgestellt oder überlegen sind.
About the authors
Robert Seifert received the Dipl.-Ing. degree in electrical engineering from TU Dresden, Germany in 2014. Since 2015, he has been research associate and doctoral candidate at the Chair of Electrical Machines and Drives of Prof. W. Hofmann at TU Dresden. His research involves linear drives and magnetic bearings, for which he studies the application of soft magnetic composites and new control strategies, with a special focus on fractional–order systems and their application in digital actuator control.
Martin Hecht received the B. Sc. degree in electrical engineering and information technology at ETH Zurich, Switzerland in 2021. Since 2021, he has been attending a master program at the Department of Information Technology and Electrical Engineering at ETH Zurich, with focus on power electronic systems In 2020 he undertook an internship at the Chair of Electrical Machines and Drives of Prof. Hofmann at TU Dresden.
Prof. Dr.-Ing. Wilfried Hofmann received the Dipl.-Ing. and Dr.-Ing. degrees in electrical engineering from TU Dresden, Germany, in 1978 and 1984, respectively. Since 2007, he has held the Chair of Electrical Machines and Drives at TU Dresden. He published over 360 papers, 60 patents and four books. His main research areas are energy conversion, mechatronics and motion control as well as control of ac machines and power electronics. Prof. W. Hofmann is member of the German Academy of Science and Engineering (acatech) and the Saxon Academy of Sciences. He is a member of IEEE IES EMTC, VDE/VDI and the steering committees of the EPE, ISMB and SPEEDAM.
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This work was supported by the German Research Foundation (DFG) under Grant HO 1483/78-1. We thank the German Academic Exchange Service (DAAD) for funding the internship of M. Hecht.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Methoden
- Simplified MIMO design of observer-based PI control in view of input saturation
- Selected numerical methods to model the fractional-order system behavior of nonlaminated magnetic actuators
- Enhancements in formal process description by using a formal method
- Identifikation auslösender Umstände von SOTIF-Gefährdungen durch systemtheoretische Prozessanalyse
- Anwendungen
- Machine learning for the perception of autonomous construction machinery
- Beiträge zur Regelung des VGF-Kristallzüchtungsprozesses
- Dissertations
- Prediction based activation of vehicle safety systems – a contribution to improve to occupant safety by validation of pre-crash information and crash severity plus restraint strategy prediction
- Informations
- Obituary Prof. Dr. Hans-Michael Hanisch
Articles in the same Issue
- Frontmatter
- Methoden
- Simplified MIMO design of observer-based PI control in view of input saturation
- Selected numerical methods to model the fractional-order system behavior of nonlaminated magnetic actuators
- Enhancements in formal process description by using a formal method
- Identifikation auslösender Umstände von SOTIF-Gefährdungen durch systemtheoretische Prozessanalyse
- Anwendungen
- Machine learning for the perception of autonomous construction machinery
- Beiträge zur Regelung des VGF-Kristallzüchtungsprozesses
- Dissertations
- Prediction based activation of vehicle safety systems – a contribution to improve to occupant safety by validation of pre-crash information and crash severity plus restraint strategy prediction
- Informations
- Obituary Prof. Dr. Hans-Michael Hanisch
