Preprint 29-2013

Regularization and Numerical Simulation of Dynamical Systems Modeled with Modelica

Author(s) : Randolf Altmeyer , Andreas Steinbrecher

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 29-2013

MSC 2000

65L80 Methods for differential-algebraic equations

34A09 Implicit equations, differential-algebraic equations

Abstract :
Quasi-linear differential-algebraic equations (DAEs) are essential tools for modeling dynamical processes, e.g. for mechanical systems, electrical circuits or chemical reactions. These models are in general of higher index and contain so called hidden constraints which lead to instabilities and order reductions during numerical integration of the model equations. In this article we consider dynamical systems modeled with quasi-linear DAEs of higher index using Modelica. We investigate a regularization of model equations in the Modelica framework in view of an efficient and robust numerical simulation. We will present an approach for numerical integration of quasi-linear DAEs which is based on overdetermined DAEs obtained from dynamical models modeled with Modelica.

Keywords : dynamical systems, differential-algebraic equations, regularization, numerical integration, Modelica, QUALIDAES, MO2FOR