Symbolic manipulation techniques for model simplification in object-oriented modelling of large scale continuous systems

Abstract

In the present work, techniques for the symbolic manipulation of general nonlinear differential algebraic equation (DAE) systems are presented, and used for model simplification purposes, to support efficient simulation of large scale continuous systems in an object-oriented modelling environment. The specific problems addressed are efficient elimination of trivial equations by means of substitution, system block lower triangular (BLT) partitioning, and tearing, i.e. hiding of algebraic variables. Moreover, the weakening heuristic criterion for decoupling of large systems, via dynamic approximation, is studied. All these techniques have been successfully implemented and tested in MOSES (modular object-oriented software environment for simulation), in order to define a complete model simplification process. The results achieved by applying the discussed algorithms and criteria on serial multibody systems are illustrated. A brief overview on further known symbolic manipulation techniques is also given, comparing them with the proposed ones, throughout the paper.