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UBC Theses and Dissertations

Modeling and stability analysis of structurally-varying dynamic systems with application to mechanical processing Peng, Jie


With the ever-increasing sophistication of engineering practices, more time-variant and structurally-varying dynamic systems are required to accomplish various demanding tasks. The research on various aspects of the dynamics of these complex systems is therefore becoming increasingly active. The current project, which is the modeling and stability analysis of structurally-varying dynamic system, is initiated in such a context. A structurally-varying system is defined as a dynamic system that consists of a number of structural subsystems and are interconnected together through a finite set of constraints, which are time varying. The dynamics of the overall system depends on not only the dynamics of the subsystems but also the interconnections between them. The focus of this research is the stability analysis of linear, structurally-varying dynamic systems. Since the system has a time-varying structure, the stability condition of the system is generally changing with time (or more accurately with the constraints between subsystems). For different situations, test criteria for evaluating the stability of structurally-varying systems are developed. The relationship between the system stability and time-varying constraints is investigated. The relationship of the subsystem dynamics and the overall system dynamics is also studied. The main purposes of this study can be summarized as follows: first is to evaluate the stability of the system under certain constraints, and second is to deliberately change these constraints according to a set of desired criteria (such as change the constraints of the system in order to stabilize it) to maintain the system within a desired operating region, which may serve design and development purposes.

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