Conference article

Chattering-Free Simulation of Hybrid Dynamical Systems with the Function Mock-Up Interface 2.0

Ayman Aljarbouh
Centre de Recherche INRIA-IRISA, Campus de Beaulieu, France

Benoit Caillaud
Centre de Recherche INRIA-IRISA, Campus de Beaulieu, France

Download articlehttp://dx.doi.org/10.3384/ecp1612495

Published in: The First Japanese Modelica Conferences, May 23-24, Tokyo, Japan

Linköping Electronic Conference Proceedings 124:13, p. 95-105

Show more +

Published: 2016-05-18

ISBN: 978-91-7685-749-6

ISSN: 1650-3686 (print), 1650-3740 (online)

Abstract

The numerical simulation of non-smooth hybrid systems exhibiting chattering behavior requires high computational costs. In the worst case, the simulation appears to come to a halt, since infinitely many discrete transitions would need to be simulated. In this paper we present an FMI-based framework and prototypical implementation for robust and reliable detection and elimination “On the Fly” of chattering behavior in run-time simulation of non-smooth hybrid systems. The main benefit of the developed framework is that it establishes solvability requirements and theorems for simulating hybrid systems while performing the chattering path avoidance internally in the master algorithm of the interface. This increases the efficiency of the chattering-free simulation as no enumeration of modes is required during the chattering detection and elimination process. The developed FMI-based framework can generate a chattering-free simulation for any generic chattering Functional Mockup Unit (FMU) conforming to the FMI standard v2.0 Specification for model exchange.

Keywords

Functional Mockup Interface (FMI), Functional Mockup Unit (FMU), Non-smooth Hybrid systems, Discontinuity mappings, Chattering

References

Ayman Aljarbouh and Benoit Caillaud. On the regularization of chattering executions in real time simulation of hybrid systems. Baltic Young Scientists Conference Proceedings, pages 49–66, 2015a. URL https://hal.archives-ouvertes.fr/hal-01246853v2.

Ayman Aljarbouh and Benoit Caillaud. Robust simulation for hybrid systems: Chattering path avoidance. Linköping Electronic Conference Proceedings, 119(018):175–185, 2015b. ISSN 1650-3686. doi: 10.3384/ecp15119175. URL http://www.ep.liu.se/ecp/119/018/ecp15119018.pdf.

Martin Biák, Tomáš Hanus, and Drahoslava Janovská. Some applications of filippov’s dynamical systems. Journal of Computational and Applied Mathematics, 254:132–143, 2013. ISSN 0377-0427. doi: http://dx.doi.org/10.1016/j.cam.2013.03.034. URL http://www.sciencedirect.com/science/article/pii/S0377042713001428.

Torsten Blochwitz, Martin Otter, Johan Akesson, Martin Arnold, Christoph ClauB, Hilding Elmqvist, Markus Friedrich, Andreas Junghanns, Jakob Mauss, Dietmar Neumerkel, Hans Olsson, and Antoine Viel. Functional mockup interface 2.0: The standard for tool independent exchange of simulation models. In Pro ceedings of 9th International Modelica Conference, Munich, Germany, 076(017):173–184, 2012. ISSN 1650-3686. doi: 10.3384/ecp12076173. URL http://www.ep.liu.se/ecp/076/017/ecp12076017.pdf.

Chaohong Cai, Rafal Goebel, Ricardo Sanfelice, and Andrew Teel. Hybrid systems: limit sets and zero dynamics with a view toward output regulation. Springer-
Verlag, 2008. URL https://hybrid.soe.ucsc.edu/files/preprints/21.pdf.

Mario di Bernardo, Chris J. Budd, Alan R. Champneys, Piotr Kowalczyk, Arne B. Nordmark, Gerard Olivar Tost, and Petri T. Piiroinen. Bifurcations in nonsmooth dynamical systems. SIAM Review, 50(4):629–701, 2008. doi: 10.1137/050625060. URL http://dx.doi.org/10.1137/050625060.

A.F. Filippov. Differential Equations with Discontinuous Righthand Sides. Springer Netherlands, 1988. ISBN 978-94-015-7793-9.

K.H. Johansson, A.E. Barabanov, and K.J. Astrom. Limit cycles with chattering in relay feedback systems. Automatic Control, IEEE Transactions on, 9(018):1414–1423, 2002. ISSN 0018-9286. doi: 10.1109/TAC.2002.802770. URL http://www.ep.liu.se/ecp/119/018/ecp15119018.pdf.

Remco I. Leine and Henk Nijmeijer. Dynamics and Bifurcations of Non-Smooth Mechanical Systems. Springer Berlin Heidelberg, 2004. ISBN 978-3-642-06029-8.

John Lygeros, Claire Tomlin, and Shankar Sastry. Hybrid Systems: Modeling, Analysis and Control. Lecture Notes on Hybrid Systems, 2008. URL
http://inst.cs.berkeley.edu/~ee291e/sp09/handouts/book.pdf.

Peter Schrammel. Logico-Numerical Verification Methods for Discrete and Hybrid Systems. PhD dissertation, 2012.

Vadim I. Utkin. Sliding Mode in Control and Optimization. Springer Berlin Heidelberg, 1992. ISBN 978-3-642-84379-2.

D. Weiss, T. Küpper, and H.A. Hosham. Invariant manifolds for nonsmooth systems with sliding mode. Mathematics and Computers in Simulation, 110:15–32, 2015. doi: http://dx.doi.org/10.1016/j.matcom.2014.02.004. URL http://www.sciencedirect.com/science/article/pii/S037847541400041X.

Jun Zhang, Karl Henrik Johansson, John Lygeros, and Shankar Sastry. Zeno hybrid systems. International Journal of Robust and Nonlinear Control, 11(5):435–451, 2001. ISSN 1099-1239. doi: 10.1002/rnc.592. URL http://dx.doi.org/10.1002/rnc.592.

Citations in Crossref