Emil Fredriksson
Modelon AB, Sweden/
Christian Andersson
Modelon AB, Sweden/Department of Numerical Analysis, Lund Unversity, Sweden
Johan Åkesson
Modelon AB, Sweden/Department of Automatic Control, Lund University, Sweden
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http://dx.doi.org/10.3384/ecp14096827Published in: Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden
Linköping Electronic Conference Proceedings 96:86, p. 827-836
Published: 2014-03-10
ISBN: 978-91-7519-380-9
ISSN: 1650-3686 (print), 1650-3740 (online)
Often integrating ordinary differential equations or differential algebraic equations (DAE) do not constitute the problem alone. A common complement is finding the root of an algebraic function (an event function) that depends on the states of the problem. This formulation of a model enables the possibility of including discontinuities; an important part of the Functional Mock-up Interface standard which allows hybrid models of differential algebraic equations. The problem of root-finding during integration is however difficult. Both in a theoretical aspect and as a software problem.
An implementation of software for root-finding is done in Assimulo; a Python/Cython wrapper for integrators. The implementation takes the Functional Mock-up Interface standard into consideration. The implementation is made usable for a wide variety of integration algorithms and is also verified and benchmarked with advanced industrial models; showing good indications of being robust and scaling well for large systems.
FMI; JModelica.org; Assimulo; events; discontinuities; Illinois algorithm; safeguard
