Thesis (M. Ed.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 27-31).

Not available / text

published_or_final_version / Mathematics / Master / Master of Philosophy

Thesis (Ph. D.)--University of Hong Kong, 2008. / Includes bibliographical references (leaf 238-259) Also available in print.

Thesis (M.Sc)(Chemical Technology, Engineering and Technology Management)--University of Pretoria, 2005. / Includes summary. Includes bibliographical references (leaves 75-80).

Thesis (Ph. D.)--Ohio State University, 2004. / Title from first page of PDF file. Document formatted into pages; contains xiii, 96 p.; also includes graphics Includes bibliographical references (p. 92-96). Available online via OhioLINK's ETD Center

Thesis (M.Eng.)(Chemical)--University of Pretoria, 2004. / Includes summary. Includes bibliographical references.

Systems with time delays have a broad range of applications not only in control systems but also in many other disciplines such as mathematical biology, financial economics, etc. The time delays cause more complex behaviours of the systems. It requires more sophisticated analysis due to the infinite dimensional structure of the space spaces. In this thesis we investigate stability properties associated with output functions of delay systems. Our primary target is the equivalent Lyapunov characterization of input-tooutput stability (ios). A main approach used in this work is the Lyapuno Krasovskii functional method. The Lyapunov characterization of the so called output-Lagrange stability is technically the backbone of this work, as it induces a Lyapunov description for all the other output stability properties, in particular for ios. In the study, we consider two types of output functions. The first type is defined in between Banach spaces, whereas the second type is defined between Euclidean spaces. The Lyapunov characterization for the first type of output maps provides equivalence between the stability properties and the existence of the Lyapunov-Krasovskii functionals. On the other hand, as a special case of the first type, the second type output renders flexible Lyapunov descriptions that are more efficient in applications. In the special case when the output variables represent the complete collection of the state variables, our Lyapunov work lead to Lyapunov characterizations of iss, complementing the current iss theory with some novel results. We also aim at understanding how output stability are affected by the initial data and the external signals. Since the output variables are in general not a full collection of the state variables, the overshoots and decay properties may be affected in different ways by the initial data of either the state variables or just only the output variables. Accordingly, there are different ways of defining notions on output stability, making them mathematically precisely. After presenting the definitions, we explore the connections of these notions. Understanding the relation among the notions is not only mathematically necessary, it also provides guidelines in system control and design. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2017. / FAU Electronic Theses and Dissertations Collection

Au cours des dernières décennies, les environnements virtuels se sont de plus en plus répandus et sont largement utilisés dans de nombreux domaines comme, par exemple, le prototypage, la formation à l’utilisation de différents outils/appareils, l’aide à la réalisation de tâches difficiles, etc. L’interaction avec la réalité virtuelle, ainsi que le retour d’effort, sont assurés par des interfaces haptiques. En général, ces systèmes sont affectés par des retards de communication et de traitement, entraînant une détérioration des performances. Dans cette thèse, une étude complète des méthodes existantes, les outils théoriques et de nouvelles solutions sont proposés dans le cadre de l’haptique. Dans un premier temps, une étude comparative, fondée sur des résultats expérimentaux obtenus sur un système haptique à un degré de liberté, met en évidence les avantages et les inconvénients des algorithmes de commande les plus classiques, transposés du domaine de la téléopération à l’haptique. Sont ensuite examinés les outils théoriques nécessaires à l’analyse de la stabilité des systèmes à retard selon différentes situations, tenant compte des limites physiques des plates-formes expérimentales considérées. En plus du cas classique du retard constant, des incertitudes sont également considérées et modélisées par plusieurs types de distributions (distribution uniforme, normale et gamma avec gap). Finalement, pour surmonter les inconvénients liés aux retards, deux nouvelles approches sont proposées. Tout d’abord, la commande de type prédicteur de Smith est reprise et une solution spécifique pour les systèmes haptiques est mise en oeuvre. L’idée principale consiste à introduire dans le prédicteur de Smith les forces liées à l’environnement en utilisant les informations complémentaires issues de la réalité virtuelle, en ce qui concerne les distances entre l’objet virtuel piloté et d’autres objets présents dans la scène. Pour surmonter la perte de performances induite par l’utilisation d’un gain fixe dans les correcteurs, commun à toutes les situations (mouvements libres ou restreints), la seconde approche propose un correcteur Proportionnel Dérivé incluant une stratégie de séquencement de gain en fonction de la distance jusqu’à une éventuelle collision. Les deux approches sont validées expérimentalement sur une plateforme haptique à trois degrés de liberté, pour différents scénarios de complexité progressive, partant de situations avec des mouvements simples - libre et restreints, des contacts avec des objets en mouvement, pour arriver à des situations plus complexes - boîte virtuelle avec des murs fixes ou mobiles. / During the last decades, virtual environments have become very popular and are largely used in many domains as, for example, prototyping, trainings for different devices, assistance in completing difficult tasks, etc. The interaction with the virtual reality, as well as the feedback force, is assured by haptic interfaces. Generally, such systems are affected by communication and processing time-delays, resulting in a deterioration of performances. In this thesis, a complete study of the existing methods, as well as theoretical tools and new solutions, are proposed for the haptic framework. First, a comparative study, based on the experimental results obtained on a 1-dof haptic system, highlights the advantages and drawbacks of the most common control algorithms ported from teleoperation to haptics. Next, the theoretical tools needed in analyzing the stability of the delayed systems in different situations, as well as the physical limitations of the experimental platforms considered, are examined. Besides the standard case of constant time-delays, uncertainties are also considered and modeled by different types of distributions (uniform, normal and gamma distribution with gap). In the sequel, for overcoming the drawback of time-delays, two new approaches are proposed. First, the use of Smith predictor-based control is addressed and a specific solution for haptic systems is developed and discussed. The main idea is to introduce into the Smith predictor the environmental forces by using the additional information from the virtual reality regarding the distances between the controlled virtual object and other objects in the scene. To overcome the loss of performances induced by using a fixed gain in the controllers for all situations (free or restricted motions), the second approach proposes a gain-scheduling Proportional Derivative control strategy depending on the distance until a possible collision. Both approaches are experimentally validated on a 3-dof haptic platform, under different scenarios elaborated gradually from simple situations - free and restricted motion, contacts with moving objects, to more complex situations - virtual box with fixed or moving sides.

Este trabalho tem por objetivo apresentar uma nova forma de analisar as redes de sincronismo de fase mutuamente conectadas. Estas redes são formadas por Phase-Locked Loops digitais ou DPLLs. O sinal gerado por cada DPLL é enviado a todos os demais dispositivos, formando a rede mutuamente conectada. Parte-se do pressuposto de que as ligações entre os dispositivos são dotadas de atrasos, o que dificulta o tratamento do problema. No entanto, é apresentado aqui um método para análise das malhas de sincronismo via discretização do modelo de tempo contínuo, objetivando dirimir essa dificuldade, já que atrasos são facilmente representados em modelos de tempo discreto. Para tanto, o modelo da rede no espaço de estados é equacionado a partir da rede. Esse modelo no espaço de estados é, então, discretizado e, enfim, pode-se determinar o estado síncrono da rede incluindo a freqüência de sincronismo e analisar sua estabilidade. Como se poderá constatar, escolhendo um período de amostragem adequado, pode-se representar o comportamento das redes de sincronismo com modelos discretos, obtendo elevado grau de precisão. / This work introduces a new method for studying a mutually-delayed-connected network of Digital Phase-Locked Loops DPLLs. The signal generated by a DPLL in the network is sent to all other devices in this same network. Because of delayed signals, it is difficult to treat this problem. So, its shown here a method for analyzing the networks via discretization of continuous time delay model in order to deal with this issue easily, considering that delays are naturally represented in discrete time models. First of all, a continuous state space model is obtained from mutually-connected network. Then, this model is discretized and, finally, the synchronous state can be determined and the stability can be analyzed. As shown below, choosing a proper time sample, the behavior of mutually-delayed-connected networks can be approximately represented by a discrete time model.