Multi-Mode DAE Systems with Varying Index

Sven Erik Mattsson
Dassault Systèmes, Sweden

Martin Otter
Institute of System Dynamics and Control, DLR, Germany

Hilding Elmqvist
Dassault Systèmes, Sweden

Ladda ner artikelhttp://dx.doi.org/10.3384/ecp1511889

Ingår i: Proceedings of the 11th International Modelica Conference, Versailles, France, September 21-23, 2015

Linköping Electronic Conference Proceedings 118:9, s. 89-98

Visa mer +

Publicerad: 2015-09-18

ISBN: 978-91-7685-955-1

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


This paper discusses an approach how to handle multi-mode DAE systems described by continuous-time state machines where mode-dependent state constraints are present. The goal is to perform static symbolic analysis and to generate efficient run-time code. This technique allows to extend the class of multi-mode systems that can be handled by Modelica tools.


Multi-mode; DAE; varying index; continuous-time state machine; variable structure system


Albert Benveniste, Timothy Bourke, Benoît Caillaud, Marc Pouzet (2014): On the index of multi-mode DAE Systems (also called Hybrid DAE Systems). [Research Report] RR-8630, Inria; ENS. <hal-01084069>. Download: https://hal.inria.fr/hal-01084069/document

Dassault Systèmes (2015): Dymola 2016. http://www.Dymola.com

Elmqvist H., Gaucher F., Mattsson S.E., Dupont F. (2012): State Machines in Modelica. Modelica’2012 Conference, Munich, Germany, Sept. 3-5, 2012. Download: http://www.ep.liu.se/ecp/076/003/ecp12076003.pdf

Elmqvist H., Mattsson S.E., Otter M. (2014): Modelica extensions for Multi-Mode DAE Systems. Proceedings of the 10th International Modelica Conference, March 10-12, Lund, Sweden, pp. 183-193. Download: http://www.ep.liu.se/ecp/096/019/ecp14096019.pdf

Höger C. (2014): Dynamic Structural Analysis for DAEs. Proceedings of the 2014 SCS Summer Simulation Multiconference. Download: http://dl.acm.org/ft_gateway.cfm?id=2685629&ftid=1511015&dwn=1&CFID=532067289&CFTOKEN=59766485

Mattsson, S.E. and G. Söderlind (1993): Index reduction in differential-algebraic equations using dummy derivatives. SIAM Journal of Scientific and Statistical Computing, Vol. 14, pp. 677-692.

Mattsson S.E., Olsson H., Elmqvist H. (2001): Methods and Algorithms for Varying Structure Hybrid DAE Simulation. EC IST Project Realsim. Contract number: IST-1999-11979, Internal Report 2.2, Dynasim, Lund, Sweden.

Modelica Association (2014): Modelica, A Unified Object-Oriented Language for Systems Modeling. Language Specification, Version 3.3, Revision 1. June 11. Download: https://www.modelica.org/documents/ModelicaSpec33Revision1.pdf

Pantelides C. (1988): The consistent initialization of differential-algebraic systems. SIAM Journal of Scientific and Statistical Computing, 9(2), pp. 213–231.

Pepper P., Mehlhase A., Höger C., Scholz L. (2011): A Compositional Semantics for Modelica-style Variablestructure Modeling. 4th International Workshop on Equation-Based Object-Oriented Modeling Languages and Tools. ETH Zürich, Switzerland. Download: http://www.ep.liu.se/ecp/056/006/ecp1105606.pdf

Pryce J.D. (2001): A simple structural analysis method for DAEs. BIT Numerical Mathematics, Vol. 41, No. 2, pp. 364–394.

Zimmer D. (2010): Equation-Based Modeling of Variable-Structure Systems. Dissertation, ETH Zürich, No. 18924. Download:

Citeringar i Crossref