Controlled synchronization of mechanical systems with a unilateral constraint

Conference paper (2016)

Authors

Michael Baumann ETH Zürich
J. J Benjamin Biemond Katholieke Universiteit Leuven
Remco I. Leine University of Stuttgart
N. van de Wouw Team Bart De Schutter - Mechanical, Maritime and Materials Engineering , Eindhoven University of Technology, University of Minnesota
Research Group
Team Bart De Schutter (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2016 Michael Baumann, J. J Benjamin Biemond, Remco I. Leine, N. van de Wouw
DOI
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https://doi.org/10.1016/j.ifacol.2016.10.188
Synchronization Hybrid systems Lyapunov stability Measure differential inclusions Unilateral constraints
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Published Date

2016

Language

English

Reuse Rights

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Bart De Schutter

Abstract

This paper addresses the controlled synchronization problem of mechanical systems subjected to a geometric unilateral constraint as well as the design of a switching coupling law to obtain synchronization. To define the synchronization problem, we propose a distance function induced by the quotient metric, which is based on an equivalence relation using the impact map. A Lyapunov function is constructed to investigate the synchronization problem for two identical one-dimensional mechanical systems. Sufficient conditions for the individual systems and their controlled interaction are provided under which synchronization can be ensured. We present a (coupling) control law which ensures global synchronization, also in the presence of grazing trajectories and accumulation points (Zeno behavior). The results are illustrated using a numerical example.