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Regularization and Numerical Simulation of Dynamical Systems Modeled with Modelica

Altmeyer, Randolf; Steinbrecher, Andreas

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

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.