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Symbolic Techniques in MathModelica System Designer

Peter Aronsson
Organization: Wolfram Research, inc.
Department: MathCore

2006 Wolfram Technology Conference
Conference location

Champaign IL

MathModelica System Designer is a modeling and simulation environment that allows creation of mathematical models in an intuitive and easy manner by using the object-oriented, equation-based language Modelica. This is achieved in a graphical model editor where components are connected together to form models of systems. Since Modelica is equation based, it is suitable for any domain, and it is therefore also possible to mix components of different domains in the same model, like for instance mechanical, electrical, or discrete controller components. A Modelica translator is used to translate a Modelica model description into a set of differential and algebraic equations with discrete events, a so-called hybrid DAE system. Due to the object-oriented nature of the Modelica models, such DAE systems are typically sparse and often have high index. The index of a DAE corresponds to how many times certain equations must be differentiated in order to transform the DAE into explicit ODE form. In order to achieve efficient simulation of such models, it is often required to symbolically simplify the equation system and reduce its size. Also, to be able to use an arbitrary numerical solver for the model, it is also required to reduce the index of the system by a technique called index reduction.

In this presentation we show how these techniques are used in MathModelica System Designer to achieve efficient simulation of hybrid DAEs. We also present how to utilize this to be able to solve hybrid DAE systems in Mathematica by using the Mathematica connection in MathModelica System Designer.

*Mathematics > Calculus and Analysis > Differential Equations
*Wolfram Technology > Application Packages > Additional Applications > MathModelica

DAE, differential-algebraic equation, hybrid DAE system, MathModelica, discrete controller components
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MathModelica Symbolic Techniques_NoOutputs.nb (1.7 MB) - Mathematica Notebook [for Mathematica 5.2]