Supporting Infinitely Fast Processes in Continuous System Modeling

Abstract

In this article, we examine the consequences of introducing a new construct into an equation-based language to model infinitely fast processes. We do this by extending the equation-based language Modelica with a special time constant, Θ. Θ provides modelers with an additional language construct that they can utilize both to improve performance of numerical integration for existing models as well as formulating and simulating models that existing tools struggle with. We present two cases where clear net benefits of introducing this new operator are illustrated. The first being an artificial DAE-System using a monotonic function, the second being an electrical circuit with and without a parasitic capacitance Based on or observations we believe that by enabling modelers to express common idealizations using Θwe can improve both performance and maintainability, since idealizations made by the modeler are encoded explicitly in the model.