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Local and Global Stability and Dynamics of a Class of Nonlinear Time-Delayed One-Degree-of-Freedom SystemsNayfeh, Nader Ali 12 January 2007 (has links)
We investigate the dynamics and stability of nonlinear time-delayed one-degree-of-freedom systems possessing quadratic and cubic nonlinearities and subjected to external and parametric disturbances. Due to the time-delay terms, the trivial solution of the unforced system undergoes Hopf bifurcations. We use the method of multiple scales to determine the normal forms of the Hopf bifurcations and hence determine whether they are locally supercritical or subcritical. Then, we use a combination of a path following scheme, the normal forms, and the method of harmonic balance to calculate and trace small- and large-amplitude limit cycles and use Floquet theory to ascertain their stability and hence generate global bifurcation diagrams. We validate these diagrams using numerical simulations. We apply the results to two important physical problems: machine-tool chatter in lathes and control of the sway of container cranes using time-delayed position feedback. We find that the Hopf bifurcations in machine tools are globally subcritical even when they are locally supercritical. We find multiple large-amplitude solutions coexisting with the linearly stable trivial solution. Consequently, there are three operating regions for machine tools: an unconditionally stable region, an unconditionally unstable region, and a conditionally stable region. In the latter region, the multiple responses lead to hysteresis. Then, we investigate the use of bifurcation control to transform the subcritical bifurcations into supercritical ones. We find that cubic-velocity feedback with appropriate gains can shrink or even eliminate the conditionally stable region. Then, we find that time-delayed acceleration feedback with an appropriate gain can completely eliminate the linear instability region. In contrast, we find that the Hopf bifurcations in controlled cranes are locally and globally supercritical. Finally, we investigate the effectiveness of time-delayed position feedback in rejecting external and parametric disturbances in ship-mounted cranes. / Ph. D.
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Modeling and Stability Analysis of Thermoacoustic Instabilities in Gas Turbine Combustor SectionsLiljenberg, Scott Alan 24 October 2000 (has links)
In order to predict the linear stability of combustion systems in industrial-scale gas turbines, a stability analysis was completed using models generated for each of the major dynamic components. Changes in the combustion process of gas turbines to reduce emissions has resulted in large amplitude pressure oscillations associated with a coupling between the natural acoustic modes of the combustor and the unsteady heat release from the flame. Detailed models of the acoustics and the heat release processes were created and assembled, with a time delay element and the appropriate scaling, into a system block diagram to investigate the stability of the system using linear system theory. Wherever possible the analytical models were validated with experimental data. The main goal of this work was to create a design methodology which could be used by industry to predict where instabilities were likely to occur during the design phase. Results show that the system based stability analysis can predict some of the instability frequencies seen in the experimental data, but more refined models are needed to predict every instability. Future work will involve designing experiments to validate and refine the dynamic models already developed. / Master of Science
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Design and development of a one-degree-of-freedom force-reflecting manual controller prototype for teleoperationPuligari, Chandrasekar Reddy 22 November 2004 (has links)
The present research is carried out from the viewpoint of primarily space applications where human lives may be in danger if they are to work under these conditions. This work proposes to develop a one-degree-of-freedom (1-DOF) force-reflecting manual controller (FRMC) prototype for teleoperation, and address the effects of time delays commonly found in space applications where the control is accomplished via the earth-based control stations. To test the FRMC, a mobile robot (PPRK) and a slider-bar were developed and integrated to the 1-DOF FRMC. The software developed in Visual Basic is able to telecontrol any platform that uses an SV203 controller through the internet and it allows the remote system to send feedback information which may be in the form of visual or force signals. Time delay experiments were conducted on the platform and the effects of time delay on the FRMC system operation have been studied and delineated.
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The Effects of Constant Time Delay in Teaching Recognition of Braille WordsHardin, Toni R. 01 January 2016 (has links)
The purpose of the study was to evaluate the use of a constant time delay procedure to teach core content words in braille to a student with a visual impairment. A multiple probe (conditions) across behaviors design was used to evaluate the effectiveness of the training and follow-up sessions. The results showed the procedure was effective in teaching core content braille words within a resource setting and the student was able to generalize the information to an inclusive setting.
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Attitude dynamics stabilization with unknown delay in feedback control implementationChunodkar, Apurva Arvind 05 August 2010 (has links)
This work addresses the problem of stabilizing attitude dynamics with
an unknown delay in feedback. Two cases are considered: 1) constant time-delay 2) time-varying time-delay. This is to our best knowledge the first result
that provides asymptotically stable closed-loop control design for the attitude dynamics problem with an unknown delay in feedback. Strict upper bounds on the unknown delay are assumed to be known. The time-varying delay is assumed to be made of the constant unknown delay with a time-varying
perturbation. Upper bounds on the magnitude and rate of the time-varying part of the delay are assumed to be known. A novel modification to the concept
of the complete type Lyapunov-Krasovskii (L-K) functional plays a crucial
role in this analysis towards ensuring stability robustness to time-delay in the control design. The governing attitude dynamic equations are partitioned to
form a nominal system with a perturbation term. Frequency domain analysis is employed in order to construct necessary and sufficient stability conditions
for the nominal system. Consequently, a complete type L-K functional is constructed for stability analysis that includes the perturbation term. As an
intermediate step, an analytical solution for the underlying Lyapunov matrix is obtained. Departing from previous approaches, where controller parameter values are arbitrarily chosen to satisfy the sufficient conditions obtained from
robustness analysis, a systematic numerical optimization process is employed here to choose control parameters so that the region of attraction is maximized. The estimate of the region of attraction is directly related to the initial angular velocity norm and the closed-loop system is shown to be stable for a large set
of initial attitude orientations. / text
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The Human Immune System: A Challenging Control ProblemVale, Julie January 2004 (has links)
This work deals with the control of the human immune system. A standard immune system model is modified by introducing control signals corresponding to drug cocktail and immune suppressor treatments. The ultimate objective is to use these control signals to 'cure' a chronically-ill patient. Control is challenging for this system due to nonlinearities and time delays. In fact, it is shown that fundamental aspects of the system dynamics are lost when the system is linearised; hence, control approaches involving linearisation are fruitless. Feedback linearisation and some optimal control methods are also investigated and shown to be infeasible. However, it is shown that, for certain parameter values and initial conditions related to the virus and patient, a specific open-loop control scheme using only the drug cocktail achieves the objective. It is also proven that, unfortunately, this control scheme fails for other parameter values and initial conditions. A two-stage open-loop controller that uses both control inputs is then proposed. It is shown in simulation that the two-stage controller works over a larger set of parameters and initial conditions than the single-stage controller, but a rigorous analysis of the two-stage controller remains elusive.
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Nouvelles stratégies de contrôle avancé pour les procédés sidérurgiques / New Advanced Control Strategy for Steel Making ProcessAsghar, Mohamad Taki 03 May 2018 (has links)
L'industrie sidérurgique rencontre depuis des années un développement important. Les caractéristiques des produits destinés aux différents secteurs industriels deviennent de plus en plus exigeantes. Actuellement des régulateurs avancés de type PID sont utilisés avec une structure multi-boucles locales. Afin de traiter les cahiers des charges de plus en plus contraints, il devient intéressant de revoir cette stratégie de contrôle. Ce sujet de thèse CIFRE entre ArcelorMittal et le CRAN a pour objectif de proposer de nouvelles stratégies de contrôle avancé pour le laminage à froid des bandes d'acier de type tôle fine, notamment des stratégies centralisées de contrôle remplaçant des boucles de régulation locales et indépendantes, afin d'élargir le champ des matériaux traitables, d'augmenter et d'optimiser la productivité et les capabilités du procédé ainsi que de minimiser les coûts de production. Dans une première partie, une étude bibliographique sera effectuée afin de mieux cerner les différents modèles métallurgiques et dynamiques du système à piloter. Dans une seconde partie, le cahier des charges sera traduit en termes d'un problème d'optimisation dont la solution est un contrôleur de type retour d'état. Enfin dans une troisième et dernière partie, une synthèse de retour de sortie dynamique sera proposée pour résoudre le problème des mesures manquantes / The steel industry has been developing for years. The characteristics of the products intended for the various industrial sectors are becoming more and more demanded. Currently advanced PID controllers are used with a local multi-loop structure. In order to deal with the increasingly constrained specifications, it is interesting to review this control strategy. This CIFRE PhD thesis between ArcelorMittal and CRAN aims to propose new advanced control strategies for the cold rolling of thin sheet steel strips, including centralized control strategies replacing local and independent control loops, to broaden the scope of treatable materials, increase and optimize process productivity and capabilities, and minimize production costs. In a first part, a bibliographic study will be carried out in order to better define the various metallurgical and dynamic models of the system to be controlled. In a second part, the specifications will be translated in terms of an optimization problem whose solution is the state feedback controller. Finally, in a third and final part, a dynamic output feedback synthesis will be proposed to solve the problem of missing measurements
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Output Stability Analysis for Nonlinear Systems with Time DelaysUnknown Date (has links)
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
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Network-based Haptic Systems with Time-Delays / Systèmes haptiques en réseau avec retards de communicationLiacu, Bogdan Cristian 20 November 2012 (has links)
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.
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Uma contribuição ao estudo das redes mutuamente conectadas de DPLLs usando modelos de tempo discreto. / A contribution to study of mutually-connected DPLL networks using discrete time models.Unzueta, Marcus Vinícius Richardelle 07 July 2008 (has links)
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.
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