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UBC Theses and Dissertations

New approaches to linear graph modeling of distributed-parameter systems Alipourazadi, Shahram


Analytical modeling is an important fundamental step in the development of procedures such as simulation, design, control, and health monitoring of engineering systems. Typically, physical properties such as inertia, flexibility (or stiffness), capacitance, inductance, and energy dissipation (mechanical damping or electrical resistance) are spatially distributed in a physical dynamic system. Often in dynamic models, these characteristics are approximated by spatially “lumped” elements. For better accuracy, however, the true distributed nature of these parameters has to be incorporated into the model. Distributed parameter (DP) models are important in this context. This thesis concerns the representation of distributed parameter engineering systems using linear graphs (LG). Among possible approaches for modeling of engineering systems, linear graphs are used in the present work due to its numerous advantages as discussed in the thesis. An engineering system may possess physical properties in many domains such as mechanical, electrical, thermal, and fluid. Mechatronic systems are multi-domain systems, which typically possess at least electro-mechanical characteristics. Linear graphs present a domain-independent unified approach for modeling multi-domain systems. Furthermore, linear graphs have beneficial features in the development of automatic procedures for modeling and designing engineering systems, which are long-term goals of the present work. In this thesis, approaches are developed for the representation of distributed-parameter systems as LG models. Different approaches are presented for this purpose and compared. The LG modeling approach enables one to visualize the system structure before formulating the dynamic equations of the system. For example, for a DP system the structure of its LG model may possess a well-defined pattern. In this work, vector linear graphs are introduced to take advantage of these patterns. General notations and elements are defined for vector linear graphs. As a result of this development a new single element is generated for use in the modeling of distributed-parameter systems, particularly in the mechanical domain. In this thesis, a software toolbox is enhanced and presented for LG modeling, which is able to automatically extract the state space equations of a mechatronic system. This software tool is provided free for academic use and is accessible through the Internet. Throughout the thesis many comprehensive examples are provided to illustrate the developed concepts and procedures and their application.

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