Hybrid Semantics in Equation-Based Modeling

Sammanfattning: Equation-based object-oriented modeling languages represent a highly composable class of modeling languages. In these languages models are expressed as differential-algebraic equations with no explicit causal relation between variables. Modeling of structurally varying systems in such languages is typically done by defining modes that describe the continuous evolution of the system, coupled with modeswitches describing structural changes. Specifically, structural changes can give rise to discontinuities and impulses, which can result in additional changes to the system. This thesis formalizes semantics for the treatment of structurally varying systems in such languages, including automatic handling of discontinuities and impulses from the theory of non-linear circuits. The semantics are implemented as part of an equation-based modeling language, where the treatment of impulses is based on backwards-Euler. The expressiveness of the implementation is evaluated on a number of structurally varying systems, both in the electrical and mechanical domains. We conclude that the semantics are expressive enough to describe some structurally varying systems, but are sensitive to numerical errors. Furthermore, more work is needed to allow the semantics to express inelastic collision in a satisfactory man-ner.