|Thesis abstract: |
In the last years equation-based languages straightened and simplified the way sophisticated models of complex physical systems are built. In particular, the object-oriented modelling paradigm allows to obtain such models in an affordable way by focusing on the development of single 'building blocks,' i.e., the objects, and connecting them so as to obtain the overall description of the physical system. This often results in large and complicated models, hard to simulate and, in general, to manage from a control-theoretical point of view. The aim of this work is to provide methodologies and (semi-)automatic techniques to cope with said complexity, in order to simplify and streamline the model analysis and simulation. In particular, the main methodological contributions of this research are: - the development of a simplification framework which includes most of the model manipulation techniques available in the literature and novel ones; - the development of a technique able to perform a structural analysis of a DAE system, called 'Cycle Analysis', and returning a dependency graph representing the way the dynamic variables are interacting, and associating with each dynamic variable a time scale; - some novel indices are introduced to characterise some structural properties of the system, e.g., the stiffness and a quantification of 'how much' a system is suited to be separated within different subsystems; - the results of the Cycle Analysis are used for improving the simulation efficiency by means of mixed-mode integration methods, and of a co-simulation (multi-rate) architecture, showing the effectiveness of the approach on some applications of interest; - a novel framework for model order reduction for hybrid systems is proposed.