Abstract
The class of hybrid systems describes most technical systems in great detail. However, the respective models and their behavior tend to be very complex. Recently, a new subclass of hybrid automata has been introduced, the Flat Hybrid Automata (FHA) that relies on the concepts of differential flatness for the continuous parts, and strongly connected automaton graphs for the discrete event part, in order to deal with the complexity from a design perspective. Therefore, we introduce in the present paper an approach to reduce the automaton graph of an FHA in a systematic way by removing edges from the adjacency matrix. The main contribution of the paper is twofold: Firstly, based on practical considerations we develop a heuristic algorithm to reduce the automaton graph. Secondly, we present possible ways to include knowledge about the system in the reduction.
Zusammenfassung
Das dynamische Verhalten vieler technischer Systeme lässt sich durch hybride Systeme gut beschreiben. Allerdings können die Modelle und deren dynamisches Verhalten einen hohen Komplexitätsgrad aufweisen. Zur Handhabung der Komplexität beim Systementwurf wurden kürzlich Flache Hybride Automaten (FHA) als neue Subklasse hybrider Automaten vorgestellt. Das Konzept basiert auf der differentiellen Flachheit der kontinuierlichen Teilsysteme und auf streng zusammenhängenden Automatengraphen der ereignisdiskreten Teilsysteme. Im vorliegenden Beitrag wird ein Ansatz zur systematischen Reduktion des ereignisdiskreten Subsystems eines FHA für den Systementwurf vorgestellt, basierend auf dem Entfernen von Kanten aus dem Automatengraphen. Dazu wird zum einen ein parametrierbarer, heuristischer Algorithmus zur schrittweisen Anpassung der Transitionsmatrix vorgestellt und zum anderen werden mögliche Ansätze zur Nutzung von Strukturinformation über das System aufgezeigt.
This contribution is dedicated to Prof. Dr.-Ing. Dr. h.c. Michael Zeitz on the occasion of his 80th birthday.
About the authors
Tobias Kleinert graduated in Mechanical Engineering in 1999 at RWTH Aachen University and completed his PhD in 2005 at the Chair of Automation and Computer Control of Prof. Jan Lunze at Ruhr-Universität Bochum. His career led him to BASF SE where he worked in the areas of Advanced Process Control, Production Technology Propylene Oxide, Regulated Automation Solutions, Digital Control Systems, Manufacturing Execution Solutions and Smart Manufacturing. As senior manager automation and digitalization he had assignments at the BASF sites in Ludwigshafen/D, Antwerp/B and Schwarzheide/D. In 2020, he assumed the professorship in information and automation systems for process and material technology at the Chair of Process Control Engineering at RWTH Aachen University.
Frederik Zahn received a Bachelor of Science in Engineering Science from Technical University of Munich in 2016 and a Master of Science in Mechanical Engineering from Karlsruhe Institute of Technology in 2019. He is currently pursuing doctoral studies in the fields of hybrid systems and control at the Institute for Automation and Applied Informatics, Karlsruhe Institute of Technology.
Prof. Dr. Veit Hagenmeyer is the Director of the Institute for Automation and Applied Informatics (IAI) at Karlsruhe Institute of Technology (KIT). Main fields of interest: automation, control, energy informatics, mechatronics.
Acknowledgment
We want to thank the anonymous reviewers who provided valuable remarks that improved the quality of the present paper considerably.
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