Hybrid Systems Modeling Manufacturing and Front Dynamics

Abstract

This thesis investigates the dynamics of a certain class of hybrid dynamical systems, so called switched tank systems. By applying switched tank systems as models for manufacturing systems and front dynamics in semiconductor superlattices new insights into the nature of dynamic behaviour in these systems are obtained.Hybrid dynamical systems are characterized by an interaction of continuous dynamical systems and an automaton, which changes parameters or the complete dynamics of the system according to logical rules, if the state reaches certain thresholds in state space.In the first part of this thesis the background of modeling and investigating hybrid systems as dynamical systems is explained on a more general level at the example of switched tank systems. Methods from automata theory (state transition graphs) and nonlinear dynamics are applied. It is shown that the dynamics is governed by the rich variety of border collision bifurcations, which are not obtained in usual dynamical systems.The second part of this thesis introduces and investigates two applications from distinct areas of science in detail.One application is the modeling of manufacturing systems. Basic layouts of manufacturing systems are investigated for their dynamics dependent logistic performance. It is shown that rule based switching processes in manufacturing systems in connection with too small (or too large) buffer capacities can cause chaotic behaviour, which implies significant performance reductions.In a second application a switched tank model is used to describe the dynamics of accumulation and depletion fronts in semiconductor superlattices. By approximating basically continuous processes of front generation and annihilation by instantaneous switching-like processes, a generic description for this spatio-temporal pattern forming process is found, which in certain parameter regions can be analyzed by means of a one-dimensional map. Altough a superlattice model is investigated the applied methods are very general and are expected to work for other pattern forming systems with similar characteristics.To summarize, the objective of this thesis is twofold. First, to show that even very simple hybrid systems can produce a very complicated dynamics and deserve attention in the theory of dynamical systems at their own right. Second, applications of hybrid models in two very distinct fields of modern science (engineering and semiconductor physics) are given, underlining the significance in science and engineering.