Conference article

Co-simulation with communication step size control in an FMI compatible master algorithm

Tom Schierz
Martin Luther University Halle-Wittenberg, NWF II - Institute of Mathematics, Halle (Saale), Germany

Martin Arnold
Martin Luther University Halle-Wittenberg, NWF II - Institute of Mathematics, Halle (Saale), Germany

Christoph Clauß
Fraunhofer Institute for Integrated Circuits IIS, Design Automation Division EAS, Dresden, Germany

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Published in: Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany

Linköping Electronic Conference Proceedings 76:20, p. 205-214

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Published: 2012-11-19

ISBN: 978-91-7519-826-2

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


Complex multi-disciplinary models in system dynamics are typically composed of subsystems. This modular structure of the model reflects the modular structure of complex engineering systems. In industrial applications; the individual subsystems are often modeled separately in different mono-disciplinary simulation tools. The Functional Mock-Up Interface (FMI) provides an interface standard for coupling physical models from different domains and addresses problems like export and import of model components in industrial simulation tools (FMI for Model Exchange) and the standardization of co-simulation interfaces in nonlinear system dynamics (FMI for Co-Simulation). In November 2011; the third beta version of FMI for Model Exchange and Co-Simulation v2.0 was released that supports advanced numerical techniques in co-simulation like higher order extrapolation and interpolation of subsystem inputs; step size control including step rejection and Jacobian based linearly implicit stabilization techniques. Well known industrial simulation tools for applied dynamics support Version 1.0 of this standard and plan to support the forthcoming Version 2.0 in the near future; see the "Tools" tab of website for up-to-date information. The renewed interest in algorithmic and numerical aspects of co-simulation inspired some new investigations on error estimation and stabilization techniques in FMI for Model Exchange and Co-Simulation v2.0 compatible co-simulation environments. The present paper extends recent results from [ArnoldClaussSchierz12] on reliable error estimation and communication step size control in the framework of FMI for Model Exchange and Co-Simulation v2.0. Based on a strict mathematical analysis; we study the asymptotic behaviour of the local error and two error estimates that may be used to adapt the communication step size automatically to the changing solution behaviour during time integration. These theoretical results are illustrated by numerical tests for a (linear) quarter car model and provide a basis for future investigations with more complex coupled engineering systems.


FMI; error estimation; step size control


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