The Use of Physical Knowledge to Guide Formula Manipulation in System Modelling

Very often, systems consist of subsystems which may be independently described. Object oriented modelling languages, as Dymola and Omola, allow models to be structured in independent submodels as systems are structured in subsystems. However, it is not an easy task to derive a mathematical model, suitable for simulation environments, from such a representation. Algebraic problems arise when the modelling tool attempts to solve the computational causality assignment in the equations. This paper discusses the advantages of physical causality analysis in object oriented modelling. A new representation, which adds a layer of physical knowledge, is proposed in order to analyze the physical behaviour of models described in a modular way. The physical interactions in the model are derived before computational causality assignment is undertaken. An automated procedure to find the adequate mathematical representation of coupling phenomena is developed by means of a symbolic formula manipulation kernel. The proposed methodology allows object oriented and modular modelling, preserving the system model structure analogy. The algorithms developed could be applied to support well established object oriented modelling languages as Dymola and Omola.