Modelling and simulation are key tools for analysis and design of systems and processes from almost any scientific or engineering discipline. Models of complex systems are typically built on acausal Differential-Algebraic Equations (DAE) and discrete events using Object-Oriented Modelling (OOM) languages, and some of their key concepts can be explained as symmetries. To obtain a computer executable version from the original model, several algorithms, based on bipartite symmetric graphs, must be applied for automatic equation generation, removing alias equations, computational causality assignment, equation sorting, discrete-event processing or index reduction. In this paper, an open source tool according to OOM paradigm and developed in MATLAB is introduced. It implements such algorithms adding an educational perspective about how they work, since the step by step results obtained after processing the model equations can be shown. The tool also allows to create models using its own OOM language and to simulate the final executable equation set. It was used by students in a modelling and simulation course of the Automatic Control and Industrial Electronics Engineering degree, showing a significant improvement in their understanding and learning of the abovementioned topics after their assessment.
This paper presents a new algorithm for the resolution of over-constrained lumped process systems, where partial differential equations of a continuous time and space model of the system are reduced into ordinary differential equations with a finite number of parameters and where the model equations outnumber the unknown model variables. Our proposal is aimed at the study and improvement of the algorithm proposed by Hangos-Szerkenyi-Tuza. This new algorithm improves the computational cost and solves some of the internal problems of the aforementioned algorithm in its original formulation. The proposed algorithm is based on parameter relaxation that can be modified easily. It retains the necessary information of the lumped process system to reduce the time cost after introducing changes during the system formulation. It also allows adjustment of the system formulations that change its differential index between simulations.
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