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PISANO, FABIO. "Analysis and synthesis techniques of nonlinear dynamical systems with applications to diagnostic of controlled thermonuclear fusion reactors." Doctoral thesis, Università degli Studi di Cagliari, 2013. http://hdl.handle.net/11584/266202.
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Nonlinear dynamical systems are of wide interest to engineers, physicists and mathematicians, and this is due to the fact that most of physical systems in nature are inherently non-linear. The nonlinearity of these systems has consequences on their time-evolution, which in some cases can be completely unpredictable, apparently random, although fundamentally deterministic. Chaotic systems are striking examples of this.
In most cases, there are no hard and fast rules to analyse these systems. Often, their solutions cannot be obtained in closed form, and it is necessary to resort to numerical integration techniques, which, in case of high sensitivity to initial conditions, lead to ill-conditioning problems and high computational costs.
The dynamical system theory, the branch of mathematics used to describe the behaviour of these systems, focuses not on finding exact solutions to the equations describing the dynamical system, but rather on knowing if the system stabilises to a steady state in the long term, and what are the possible attractors, e.g. a quasi-periodic or chaotic attractors.
Regarding the synthesis, from both a practical and a theoretical standpoint, it is very desirable to develop methods of synthesizing these systems. Although extensive theory has been developed for linear systems, no complete formulation for nonlinear systems synthesis is present today.
The main topic of this thesis is the solution of engineering problems related to the analysis and synthesis of nonlinear and chaotic systems.
In particular, a new algorithm which optimizes Lyapunov exponents estimation in piecewise linear systems has been applied to PWL and polynomial chaotic systems. In the field of complex systems synthesis, a systematic method to project systems of order 2n characterized by two positive Lyapunov exponents, has been proposed. This procedure couples nth-order chaotic systems with a suitable nonlinear coupling function. Furthermore, a method for the fault detection has been developed. In the field of time series analysis, a new denoising method, based on the wavelet transform of the noisy signal, has been described. The method implements a variable thresholding, whose optimal value is determined by analysing the cross-correlation between the denoised signal and the residuals and by applying different criteria depending on the particular decomposition level. Finally, a study of dynamical behaviour of Type I ELMs has been performed for a future modelization of the phenomenon. In this context, a statistical analysis of time intervals between successive Type I ELMs has been proposed.---------------------------------- Il tema principale di questa tesi è la soluzione di problemi ingegneristici legati all’analisi e alla sintesi di sistemi dinamici non lineari. I sistemi dinamici non lineari sono di largo interesse per ingegneri, fisici e matematici, e questo è dovuto al fatto che la maggior parte dei sistemi fisici in natura è intrinsecamente non lineare.
La non linearità di questi sistemi ha conseguenze sulla loro evoluzione temporale, che in certi casi può rivelarsi del tutto imprevedibile, apparentemente casuale, seppure fondamentalmente deterministica. I sistemi caotici sono un esempio lampante di questo comportamento. Nella maggior parte dei casi non esistono delle regole standard per l’analisi di questi sistemi. Spesso, le soluzioni non possono essere ottenute in forma chiusa, ed è necessario ricorrere a tecniche di integrazione numerica, che, in caso di elevata sensibilità alle condizioni iniziali, portano a problemi di mal condizionamento e di elevato costo computazionale.
La teoria dei sistemi dinamici, la branca della matematica usata per descrivere il comportamento di questi sistemi, non si concentra sulla ricerca di soluzioni esatte per le equazioni che descrivono il sistema dinamico, ma piuttosto sull’analisi del comportamento a lungo termine del sistema, per sapere se questo si stabilizzi in uno stato stabile e per sapere quali siano i possibili attrattori, ad esempio, attrattori quasi-periodici o caotici.
Per quanto riguarda la sintesi, sia da un punto di vista pratico che teorico, è molto importante lo sviluppo di metodi in grado di sintetizzare questi sistemi. Sebbene per i sistemi lineari sia stata sviluppata una teoria ampia e esaustiva, al momento non esiste alcuna formulazione completa per la sintesi di sistemi non lineari.
In questa tesi saranno affrontati problemi di caratterizzazione, analisi e sintesi, legati allo studio di sistemi non lineari e caotici.
La caratterizzazione dinamica di un sistema non lineare permette di individuarne il comportamento qualitativo a lungo termine. Gli esponenti di Lyapunov sono degli strumenti che permettono di determinare il comportamento asintotico di un sistema dinamico. Essi danno informazioni circa il tasso di divergenza di traiettorie vicine, caratteristica chiave delle dinamiche caotiche. Le tecniche esistenti per il calcolo degli esponenti di Lyapunov sono computazionalmente costose, e questo fatto ha in qualche modo precluso l’uso estensivo di questi strumenti in problemi di grandi dimensioni. Inoltre, durante il calcolo degli esponenti sorgono dei problemi di tipo numerico, per ciò il calcolo deve essere affrontato con cautela. L’implementazione di algoritmi veloci e accurati per il calcolo degli esponenti di Lyapunov è un problema di interesse attuale.
In molti casi pratici il vettore di stato del sistema non è disponibile, e una serie temporale rappresenta l’unica informazione a disposizione. L’analisi di serie storiche è un metodo di analisi dei dati provenienti da serie temporali che ha lo scopo di estrarre delle statistiche significative e altre caratteristiche dei dati, e di ottenere una comprensione della struttura e dei fattori fondamentali che hanno prodotto i dati osservati. Per esempio, un problema dei reattori a fusione termonucleare controllata è l’analisi di serie storiche della radiazione Dα, caratteristica del fenomeno chiamato Edge Localized Modes (ELMs). La comprensione e il
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controllo degli ELMs sono problemi cruciali per il funzionamento di ITER, in cui il type-I ELMy H-mode è stato scelto come scenario di funzionamento standard. Determinare se la dinamica degli ELM sia caotica o casuale è cruciale per la corretta descrizione dell’ELM cycle. La caratterizzazione dinamica effettuata sulle serie temporali ricorrendo al cosiddetto spazio di embedding, può essere utilizzata per distinguere serie random da serie caotiche.
Uno dei problemi più frequenti che si incontra nell’analisi di serie storiche sperimentali è la presenza di rumore, che in alcuni casi può raggiungere anche il 10% o il 20% del segnale. È quindi essenziale , prima di ogni analisi, sviluppare una tecnica appropriata e robusta per il denosing.
Quando il modello del sistema è noto, l’analisi di serie storiche può essere applicata al rilevamento di guasti. Questo problema può essere formalizzato come un problema di identificazione dei parametri. In questi casi, la teorie dell’algebra differenziale fornisce utili informazioni circa la natura dei rapporti fra l’osservabile scalare, le variabili di stato e gli altri parametri del sistema.
La sintesi di sistemi caotici è un problema fondamentale e interessante. Questi sistemi non implicano soltanto un metodo di realizzazione di modelli matematici esistenti ma anche di importanti sistemi fisici reali. La maggior parte dei metodi presentati in letteratura dimostra numericamente la presenza di dinamiche caotiche, per mezzo del calcolo degli esponenti di Lyapunov. In particolare, le dinamiche ipercaotiche sono identificate dalla presenza di due esponenti di Lyapunov positivi.
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Taylor, Christopher Trevor. "Enhancement of imagery from passive millimetre-wave systems for security scanning." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/enhancement-of-imagery-from-passive-millimetrewave-systems-for-security-scanning(7011ec7c-86ee-4770-b637-7ffe4909b241).html.
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This thesis concerns methods to enhance current and explore future radiometric imaging systems for security screening. Its main focus is on the test and calibration procedures for the BorderWatch system – an established 33 GHz passive millimetre-wave imager developed by QinetiQ PLC as an outdoor security scanning portal for soft-sided heavy goods vehicles at ports of entry. The effects of the limited size of the sky background reflector of the operational system are addressed and modifications to mitigate these effects are proposed. Systematic diurnal and seasonal variations in the receiver output powers are characterised and strongly linked with variations in the physical temperature of the RF components. The proposed BorderWatch temperature calibration subsystem requires a reliable cold sky temperature reference point; the aim being to reduce the level of fixed pattern noise in present-day imagery and allow for post-processing methods requiring absolute temperature values. Cost considerations rule out independent millimetre-wave radiometers at each site so a proposed alternative is to use infra-red measurements as a proxy. A literature investigation is made into the millimetre-wave and infrared atmospheric opacities for a variety of meteorological conditions. The design, calibration and operation of a 35 GHz switching radiometer is described together with a comparison of the millimetre-wave radiometric brightness temperature measurements against the data from a low cost commercial infra-red sensor and from a nearby meteorological station. The results show an excellent correlation between the zenith sky temperatures in the infrared and millimetre-wave bands but only in clear sky conditions – as anticipated the presence of clouds affects the infra-red brightness distribution much more strongly than that of the millimetre-wave. Future security imagers may well incorporate interferometric arrays. An extensive simulation programme has been carried out to explore appropriate numbers of antennas and whether radio astronomy configurations and post-processing techniques can offer cost-effective routes to high image fidelity. The results of a quantitative analysis are promising and array configurations and techniques appropriate for potential future security imagers are suggested.
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Besançon, Gildas. "Contributions à l'étude et à l'observation des systèmes non linéaires avec recours au calcul formel." Grenoble INPG, 1996. http://www.theses.fr/1996INPG0152.
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Ce travail s'inscrit principalement dans le domaine de synthese d'observateurs pour systemes non lineaires et participe d'une double preoccupation: d'une part le developpement de nouvelles methodes pour l'observation des systemes, et d'autre part l'applicabilite des resultats, via quelques exemples et le recours au calcul formel. La premiere partie est plus directement dediee aux problemes d'observabilite et d'observateurs. En distinguant non uniformite et uniformite (par rapport a l'entree) des syntheses, nous proposons d'abord un observateur (non uniforme) pour une classe de systemes triangulaires, puis des conditions d'observation reduite uniforme de systemes non uniformement observables. Enfin, nous etendons ces resultats par l'etude d'une synthese decentralisee d'observateur pour systemes interconnectes, illustree par l'estimation des flux et vitesse d'une machine asynchrone. Dans une deuxieme partie, nous proposons d'etendre les syntheses disponibles pour des systemes sous formes particulieres, aux systemes qui leur sont equivalents par transformation d'etat, sur la base des resultats d'equivalence avec un systeme affine en l'etat modulo injection d'entree/sortie (e/s). En particulier, un recours au calcul formel pour le test d'une telle equivalence est propose, completant une bibliotheque plus generale d'aide a l'etude des systemes non lineaires, programmee sous mathematica (et utilisee par exemple pour une etude de stabilite d'une machine asynchrone). Des conditions d'equivalence avec une forme triangulaire particuliere sont alors proposees, ainsi qu'une procedure de test, illustrees sur un exemple petrochimique. Ce type de caracterisation est etendu a une plus large classe de systemes de type affine dans les cas mono ou multi-sorties et cascade, illustree par les systemes de type euler-lagrange. Enfin l'equivalence avec une forme affine modulo injection d'e/s avec transformation de sortie est examinee. La derniere partie est consacree a l'observation de systemes discrets affines en l'etat modulo injection d'e/s, et aux conditions d'equivalence avec cette forme
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Zerrougui, Mohamed. "Observation et commande des systèmes singuliers non linéaires." Phd thesis, Université Henri Poincaré - Nancy I, 2011. http://tel.archives-ouvertes.fr/tel-00705339.
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Les travaux présentés dans cette thèse ont été effectués au Centre de Recherche en Automatique de Nancy (CRAN). Ils portent sur l'observation et la commande des systèmes singuliers non linéaires. Dans un premier temps nous nous sommes intéressés à la synthèse d'observateur et au filtrage H infini des systèmes singuliers bilinéaires. Dans un deuxième temps, nous avons étudié la synthèse d'observateur pour les systèmes singuliers non linéaires Lipschitziens. La dernière partie de ce travail concerne la stabilisation et la commande basée observateurs des systèmes singuliers non linéaires. L'objectif de ce travail a été de proposer des résultats facilement implémentables et de couvrir une large classe de systèmes non linéaires. La contribution principale de ce mémoire a été de proposer des observateurs H infini pour les systèmes singuliers non linéaires, en utilisant le non biais de l'erreur d'estimation. Les paramètres de ces observateurs sont obtenus par la résolution des inégalités matricielles linéaires (LMIs). Le deuxième apport concerne la synthèse de commande stabilisante et l'utilisation d'un des observateurs proposés dans cette thèse pour la synthèse d'une commande basée observateur pour les systèmes singuliers non linéaires. Cette dernière est réalisée grâce à la réécriture des fonctions non linéaires sous des formes adéquates à l'application de la commande des systèmes.
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Hajraoui, Abderrahmane. "Architecture multi-processeurs en automatisme non linéaire." Rouen, 1989. http://www.theses.fr/1989ROUES023.
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Wasik, Valentine. "Analyse de la précision d’estimation de deux systèmes d’imagerie polarimétrique." Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4348.
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L’imagerie polarimétrique permet d’estimer certaines caractéristiques d’un milieu qui peuvent ne pas être révélées par imagerie d’intensité standard. Cependant, les mesures effectuées peuvent être fortement perturbées par des fluctuations inhérentes aux processus physiques d’acquisition. Ces fluctuations sont difficiles à atténuer, notamment à cause de la fragilité des milieux observés ou de l’inhomogénéité des images acquises. Il est alors utile de caractériser la précision des estimations qu’il est possible d’obtenir. Dans cette thèse, cette question est abordée au travers de deux applications d’imagerie polarimétrique : la microscopie non-linéaire de second harmonique résolue en polarisation (PSHG) pour l’analyse de l’organisation structurale d’objets biomoléculaires, et l’imagerie radar polarimétrique interférométrique à synthèse d’ouverture (PolInSAR) pour l’estimation des paramètres du couvert forestier. Pour la première application, la précision d’estimation en présence de bruit de Poisson est caractérisée pour l’ensemble des assemblages moléculaires présentant une symétrie cylindrique, ce qui permet notamment d'aboutir à une procédure de détection des mesures qui ne permettent pas d’atteindre une précision d’estimation requise. Pour l’imagerie PolInSAR, on analyse une modalité d'acquisition intéressante pour les futures missions satellitaires. En particulier, on étudie dans ce contexte la précision d'estimation de la hauteur de végétation en présence de bruit de speckle en s'appuyant sur l'analyse du contraste polarimétrique. Une interprétation simple des comportements de cette modalité d'acquisition est obtenue dans la sphère de PoincaréPolarimetric imaging allows one to estimate some characteristics of a medium which might not be revealed by standard intensity imaging. However, the measurements can be strongly perturbed by fluctuations that are inherent in the physical acquisition processes. These fluctuations are difficult to attenuate, for instance because of the fragility of the observed media or because of the inhomogeneity of the obtained images. It is then useful to characterize the estimation precision that can be reached. In this thesis, this question is addressed through two polarimetric imaging applications: polarized-resolved second-harmonic generation non-linear microscopy (PSHG) for the analysis of the structural organization of biomolecular objects, and polarimetric interferometric synthetic aperture radar imaging (PolInSAR) for the estimation of vegetation parameters. For the first application, the estimation precision in the presence of Poisson noise is characterized for any molecular assembly that presents a cylindrical symmetry. This study results in particular in a procedure to detect the measurements that do not lead to a required precision. For PolInSAR imaging, we analyze an acquisition system that is interesting for future spatial missions. In particular, the estimation precision of the vegetation height is studied in this context in the presence of speckle noise by relying on the analysis of the polarimetric contrast. A simple interpretation of the behavior of this acquisition system is obtained in the Poincaré sphere
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Mhana, Khalid Jalal. "Optimal control of non-linear systems." Thesis, University of Sheffield, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.412720.
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Shearer, J. M. "Interval methods for non-linear systems." Thesis, University of St Andrews, 1986. http://hdl.handle.net/10023/13779.
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In numerical mathematics, there is a need for methods which provide a user with the solution to his problem without requiring him to understand the mathematics underlying the method of solution. Such a method involves computable tests to determine whether or not a solution exists in a given region, and whether, if it exists, such a solution may be found by using the given method. Two valuable tools for the implementation of such methods are interval mathematics and symbolic computation. In. practice all computers have memories of finite size and cannot perform exact arithmetic. Therefore, in addition to the error which is inherent in a given numerical method, namely truncation error, there is also the error due to rounding. Using interval arithmetic, computable tests which guarantee the existence of a solution to a given problem in a given region, and the convergence of a particular iterative method to this solution, become practically realizable. This is not possible using real arithmetic due to the accumulation of rounding error on a computer. The advent of packages which allow symbolic computations to be carried out on a given computer is an important advance for computational numerical mathematics. In particular, the ability to compute derivatives automatically removes the need for a user to supply them, thus eliminating a major source of error in the use of methods requiring first or higher derivatives. In this thesis some methods which use interval arithmetic and symbolic computation for the solution of systems of nonlinear algebraic equations are presented. Some algorithms based on the symmetric single-step algorithm are described. These methods however do not possess computable existence, uniqueness, and convergence tests. Algorithms which do possess such tests, based on the Krawczyk-Moore algorithm are also presented. A simple package which allows symbolic computations to be carried out is described. Several applications for such a package are given. In particular, an interval form of Brown's method is presented.
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Wilson, Jonathan P. "Non-linear dynamics and power systems." Thesis, University of Bath, 2000. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341136.
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Pechev, Alexandre Nikolov. "Robust linear and non-linear control of magnetically levitated systems." Thesis, Cardiff University, 2004. http://orca.cf.ac.uk/55944/.
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The two most advanced applications of contactless magnetic levitation are high-speed magnetic bearings and magnetically levitated vehicles (Maglev) for ground transportation using superconducting magnets and controlled d.c. electromagnets. The repulsion force from superconducting magnets provide stable levitation with low damping, while the suspension force generated by electromagnets is inherently unstable. This instability, due to the in verse force-distance relationship, requires the addition of feedback controllers to sustain stable suspension. The problem of controlling magnetically levitated systems using d.c. electromagnets under different operating conditions has been studied in this thesis with a design process primarily driven by experimental results from a representative single-magnet test rig and a multi-magnet vehicle. The controller-design stages are presented in detail and close relationships have been constructed between selection of performance criteria for the derivation process and desired suspension characteristics. Both linear and nonlinear stabilising compensators have been developed. Simulation and experimental results have been studied in parallel to assess operational stability and the main emphasis has been given to assessing performance under different operational conditions. For the experimental work, a new digital signal processor-based hardware platform has been designed, built with interface to Matlab/Simulink. The controller design methods and algorithmic work presented in this thesis can be divided into: non-adaptive, adaptive, optimal linear and nonlinear. Adaptive algorithms based on model reference control have been developed to improve the performance of the suspension system in the presence of considerable variations in external payload and force disturbances. New design methods for Maglev suspension have been developed using robust control theory (%oo and fi synthesis). Single- and multi-magnet control problems have been treated using the same framework. A solution to the Hoo controller-optimisation problem has been derived and applied to Maglev control. The sensitivity to robustness has been discussed and tools for assessing the robustness of the closed-loop system in terms of sustaining stability and performance in the presence of uncertainties in the suspension model have been presented. Multivariable controllers based on %00 and /i synthesis have been developed for a laboratory scale experimental vehicle weighing 88 kg with four suspension magnets, and experimental results have been derived to show superiority of the proposed design methods in terms of ability to deal with external disturbances. The concept of Hoo control has been extended to the nonlinear setting using the concepts of energy and dissipativity, and nonlinear state-feedback and out put-feed back controllers for Maglev have been developed and reported. Simulation and experimental results have been presented to show the improved performance of these controllers to attenuate guideway-induced disturbances while maintaining acceptable suspension qualities and larger operational bandwidth.
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López, Suárez Miquel. "Non-linear nanoelectromechanical systems for energy harvesting." Doctoral thesis, Universitat Autònoma de Barcelona, 2014. http://hdl.handle.net/10803/283731.
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Les Tecnologies de la Informació i la Comunicació (TICs) es troben arreu i experimenten un creixement del 5% cada any amb aplicacions en diverses àrees que comprenen des de la telefonia mòbil al control mèdic de la salut. Les TICs són, en part, responsables de l'extraordinari increment en la quantitat d'informació intercanviada en tot el món contribuint considerablement al que es coneix com la petjada de CO2. Avui dia, es dediquen molts esforços en disminuir dràsticament la potència elèctrica necessària per a la computació d'un bit d'informació amb l'objectiu d'assolir el límit de Landauer que estableix el mínim d'energia requerida en 2.85 zJ: el límit físic per a la unitat d'informació. El ràpid desenvolupament de l'electrònica de baix consum i la seva miniaturització ha obert la porta a la possibilitat de dissenyar tecnologies portàtils i autoalimentades. A més a més, el desenvolupament d'aquest tipus de dispositius representa un punt clau de cara a evitar el recanvi o recàrrega de les bateries convencionals. La recol·lecció d'energia provinent de vibracions mecàniques representa una opció molt atractiva per a l'alimentació d'aquest tipus de dispositius en termes de disponibilitat i densitat de potència.
L'objectiu de la present tesi és proporcionar una revisió de l'estat de l'art i trobar noves estratègies per incrementar el rendiment de les tecnologies de recol·lecció d'energia de les vibracions mecàniques. L'increment de la potència generada mitjançant la inducció d'un comportament biestable és estudiat a la micro i a la nanoescala, quan les vibracions presents en l'ambient venen caracteritzades pel seu extens ample de banda i la seva baixa intensitat, en comparació al rendiment proporcionat per les estratègies estàndards basades en l'ús de ressonadors.
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Zhou, Yimin. "Fault identificaiton in non-linear dynamic systems." Thesis, University of Oxford, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.494397.
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A fuzzy relational sliding mode observer (FRSMO) and proportional integral observer (FRPIO) are proposed to estimate the magnitude of slowly evolving faults in information-poor, i.e., difficult to model and non-linear systems. Where there is no fault in the system, the mismatch between the actual output and the model output can be shown to be zero. When the fault occurs in the system, the error is not zero, which is called a residual and can be used to diagnose the fault. In the fuzzy PI observer, the size of the fault can be obtained from the error passing the PI feedback compensation. In the fuzzy sliding mode observer, the equivalent injection signal is used to compensate for the fault thus obtaining the magnitude of the fault. To reduce modelling errors, an on-line learning fault identification scheme (OLFIS) is used to update the model and identify the fault in a periodical mode with different time intervals during the whole procedure. The selection of the intervals between model update and fault identification, convergence and speed of the scheme are investigated. The performance of the proposed methods is evaluated using a cooling-coil subsystem of an air-conditioning plant in a simulation environment. An actuator fault in the valve and a flow reduction fault are two typical incipient faults in the cooling coil system. The results of the actuator fault estimation and flow reduction fault estimation confirm the effectiveness of the methods.
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Abbs, Charlotte. "Quantum dynamics of non-linear optomechanical systems." Thesis, University of Nottingham, 2014. http://eprints.nottingham.ac.uk/27692/.
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This thesis explores the dynamics of optomechanical systems, which use radiation pressure to couple together optical and mechanical modes. Such systems display dynamics ranging from the quantum to the classical, with a variety of applications including ground state cooling and precision measurements. In this thesis two different geometries are presented for such a system in the form of the ‘reflective’ and ‘dispersive’ systems. Different aspects of the dynamics are investigated numerically and analytically. Firstly the reflective system is introduced, which consists of a cavity formed from a fixed and a moveable mirror. The optical frequency of the cavity couples linearly to the moveable mirror’s position. This geometry is explored as the cavity is driven by a laser, revealing a range of dynamical states in the mirror as the drive frequency is varied. An alternative geometry is presented in the form of the dispersive optomechanical system. Two fixed mirrors with a partially transmitting membrane at the centre provide a cavity supporting two optical modes, that couple approximately linearly or quadratically to the membrane position, depending on where the membrane is fixed. The system is explored in both linear and quadratic coupling regimes. Quadratic coupling is explored for a single optical mode by selecting a high tunnelling rate through the membrane. The dynamics of the membrane are explored via a similar set of techniques to those applied to the reflective system. Linear coupling for two optical modes is explored in the regimes of blue and red detuning. First resolved sideband cooling is explored, providing an alternative approach ground state cooling (which has been explored for the reflective case). Finally, strongly driving the system over a range of coupling strengths induces classical behaviour, extending from limit cycle oscillations to chaotic motion.
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Kahraman, Ahmet. "Non-linear dynamic analysis of geared systems /." The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487676847117141.
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Lam, Woon-Kwan. "Pattern formation in non-linear chemical systems." Ann Arbor, Mich. : ProQuest, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3288932.
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Thesis (Ph.D. in Applied Mathematics)--S.M.U., 2007.Title from PDF title page (viewed Nov. 19, 2009). Source: Dissertation Abstracts International, Volume: 68-11, Section: B, page: 7376. Adviser: Peter K. Moore. Includes bibliographical references.
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Sammarco, Elisa. "Non linear response of planar asymmetric systems." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/6492/.
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The seismic behaviour of one-storey asymmetric structures has been studied since 1970s by a number of researches studies which identified the coupled nature of the translational-to-torsional response of those class of systems leading to severe displacement magnifications at the perimeter frames and therefore to significant increase of local peak seismic demand to the structural elements with respect to those of equivalent not-eccentric systems (Kan and Chopra 1987). These studies identified the fundamental parameters (such as the fundamental period TL normalized eccentricity e and the torsional-to-lateral frequency ratio Ωϑ) governing the torsional behavior of in-plan asymmetric structures and trends of behavior. It has been clearly recognized that asymmetric structures characterized by Ωϑ >1, referred to as torsionally-stiff systems, behave quite different form structures with Ωϑ <1, referred to as torsionally-flexible systems. Previous research works by some of the authors proposed a simple closed-form estimation of the maximum torsional response of one-storey elastic systems (Trombetti et al. 2005 and Palermo et al. 2010) leading to the so called “Alpha-method” for the evaluation of the displacement magnification factors at the corner sides.
The present paper provides an upgrade of the “Alpha Method” removing the assumption of linear elastic response of the system. The main objective is to evaluate how the excursion of the structural elements in the inelastic field (due to the reaching of yield strength) affects the displacement demand of one-storey in-plan asymmetric structures. The system proposed by Chopra and Goel in 2007, which is claimed to be able to capture the main features of the non-linear response of in-plan asymmetric system, is used to perform a large parametric analysis varying all the fundamental parameters of the system, including the inelastic demand by varying the force reduction factor from 2 to 5. Magnification factors for different force reduction factor are proposed and comparisons with the results obtained from linear analysis are provided.
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Sun, Yi. "Non-linear hierarchical visualisation." Thesis, Aston University, 2002. http://publications.aston.ac.uk/13263/.
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This thesis applies a hierarchical latent trait model system to a large quantity of data. The motivation for it was lack of viable approaches to analyse High Throughput Screening datasets which maybe include thousands of data points with high dimensions. We believe that a latent variable model (LTM) with a non-linear mapping from the latent space to the data space is a preferred choice for visualising a complex high-dimensional data set. As a type of latent variable model, the latent trait model can deal with either continuous data or discrete data, which makes it particularly useful in this domain. In addition, with the aid of differential geometry, we can imagine that distribution of data from magnification factor and curvature plots. Rather than obtaining the useful information just from a single plot, a hierarchical LTM arranges a set of LTMs and their corresponding plots in a tree structure. We model the whole data set with a LTM at the top level, which is broken down into clusters at deeper levels of the hierarchy. In this manner, the refined visualisation plots can be displayed in deeper levels and sub-clusters may be found. Hierarchy of LTMs is trained using expectation-maximisation (EM) algorithm to maximise its likelihood with respect to the data sample. Training proceeds interactively in a recursive fashion (top-down). The user subjectively identifies interesting regions on the visualisation plot that they would like to model in a greater detail. At each stage of hierarchical LTM construction, the EM algorithm alternates between the E - and M - step. Another problem that can occur when visualising a large data set is that there may be significant overlaps of data clusters. It is very difficult for the user to judge where centres of regions of interest should be put. We address this problem by employing the minimum message length technique, which can help the user to decide the optimal structure of the model.
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Pechenik, Leonid. "Pattern formation and non-linear dynamics of non-equilibrium systems /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC IP addresses, 2000. http://wwwlib.umi.com/cr/ucsd/fullcit?p9970653.
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Chadwick, Mark Anthony. "Identification and analysis of linear and non-linear fast-sampled systems." Thesis, University of Sheffield, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.489362.
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This thesis presents an investigation into the identification and analysis of and non-linear fast-sampled systems. Traditionally, discrete-time sampled-data systems are represented using shift-operator parameterisations utilising the d-operator. An alternative parameterisation using the q-operator is explored and shown to maintain a close correspondence to the continuous-time. This approach offers the ability to unify discrete and continuous-time theory as each can be considered a special case of the d-operator approach. In addition, these parameterisations possess numerical advantages when compared to the shift-operator representations.
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Townsend, Shane Martin Joseph. "Non-linear model predictive control." Thesis, Queen's University Belfast, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.301061.
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Lawrence, Heather Bunting Elizabeth. "Organometallic compounds with non-linear optical properties." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.276835.
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Lampakis, Elias G. "Algebraic synthesis methods for linear multivariable control systems." Thesis, City, University of London, 1995. http://openaccess.city.ac.uk/19007/.
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The mathematical formulation of various control synthesis problems (such as Decentralized Stabilization Problem (DSP), Total Finite Settling Time Stabilization for discrete time linear systems (TFSTS), Exact Model Matching Problem (EMMP), Decoupling and Noninteracting Control Problems) via the algebraic framework of Matrix Fractional Representation (MFR) - i.e. the representation of the transfer matrices of the system as matrix fractions over the ring of interest - results to the study of matrix equations over rings, such as : A . X + B . Y = C , (X. A + Y . B =C) (1) A· X = B , (y. A = B) (2) A·X·B = C (3) A·X + Y·B = C, X·A + B·Y = C, A·X·B + C·Y·D = E (4). The main objective of this dissertation is to further investigate conditions for existence and characterization of certain types of solutions of equation (1) ; develop a unifying algebraic approach for solvability and characterization of solutions of equations (1) - (4), based on structural properties of the given matrices, over the ring of interest. The standard matrix Diophantine equation (1) is associated with the TFSTS for discrete time linear systems and issues concerning the characterization of solutions according to the Extended McMillan Degree (EMD) (minimum EMD, or fixed EMD) of the stabilizing controllers they define, are studied. A link between the issues in question and topological properties of certain families of solutions of (1) is established . Equation (1) is also studied in association with the DSP and Diagonal DSP (DDSP) for continuous time linear systems. Conditions for characterizing block diagonal solutions of (1) (which define decentralized stabilizing controllers) are derived and a closed form description of the families of diagonal and two blocks diagonal decentralized stabilizing controllers is introduced. The set of matrix equations (1) - (4) is assumed over the field of fractions of the ring of interest , ℛ , (mainly a Euclidean Domain (ED) and thus a Principal Ideal Domain (PID)) and solvability as well as parametrization of solutions over ℛ is investigated under the unifying algebraic framework of extended non square matrix divisors, projectors and annihilators of the known matrices over ℛ . In practice the ring of interest is either the ring of polynomials ℝ [s] , or the rings of proper ℝ_pr(s) and especially proper and stable rational functions R_op(s). The importance of R_op(s) is highlighted early in the thesis and further computational issues arising from its structure as an ED are considered.
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Tarr, C. A. Blair. "Intelligent controller for non-linear time lagged systems." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape17/PQDD_0026/MQ33279.pdf.
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Peng, Wei. "Non-linear detection algorithms for MIMO multiplexing systems." Click to view the E-thesis via HKUTO, 2007. http://sunzi.lib.hku.hk/HKUTO/record/B39558563.
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Fontes, Fernando Armenio Da Costa Castro. "Optimisation-based control of constrained non linear systems." Thesis, Imperial College London, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299453.
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Bell, S. C. "Scaling theory of non-linear and incommensurate systems." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376893.
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Tan, Woei Wan. "Self-learning neurofuzzy control of non-linear systems." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364037.
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Peng, Wei, and 彭薇. "Non-linear detection algorithms for MIMO multiplexing systems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B39558563.
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Sorour, Ahmed El-Sayed. "Some problems in non-linear open loop systems." Thesis, University of Kent, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.279420.
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Gotthans, Tomas. "Advanced methods for analyzing non-linear dynamical systems." Thesis, Paris Est, 2014. http://www.theses.fr/2014PEST1020/document.
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L'augmentation des performances des futurs systèmes dynamiques nécessite la prise en compte des phénomènes physiques non linéaires. Cette thèse apporte un éclairage et des contributions sur deux sujets complémentaires liés aux phénomènes dynamiques non linéaires. Le mémoire de thèse est divisé en deux parties.La première partie porte sur les non-linéarités des amplificateurs de puissance dans le cadre d'applications destinées aux télécommunications ou à la diffusion audio-visuelle. Plusieurs méthodes de modélisation et de linéarisation des amplificateurs de puissance ont été conçues et discutées. Un banc de test a été développé afin d'évaluer les méthodes sur des amplificateurs réels. La robustesse de ces techniques à un mauvais alignement temporel des signaux ainsi que leur capacité à faire face à des artefacts spectraux ont été évaluées. Par ailleurs, nous avons effectué une étude théorique sur l'existence et la prise en compte de solutions multiples dans l'approche adaptative par apprentissage indirect. La deuxième partie traite des systèmes dynamiques non linéaires qui présentent des solutions chaotiques. Ces systèmes sont bien connus, mais les techniques d'identification de ces solutions manquent de fiabilité ou nécessitent une puissance de calcul importante. Dans cette thèse, plusieurs méthodes utilisant également le calcul parallèle sont présentées. Les systèmes à commande différentielle fractionnaire sont brièvement discutés. Il est aussi montré, qu'il existe des systèmes liés à des fonctions de transfert non linéaires avec quantification pour lesquels les méthodes d'analyse classiques échouentIn order to achieve better performance of modern communication devices, that have to be operated on its physical limits, the nonlinear phenomena need to be taken into the account. This thesis brings insight into two different subjects related with nonlinear dynamical phenomena. The thesis itself is divided into two parts : the first part is focused on the domain of nonlinear power amplifiers from the system point of view. Several methods for modelization and linearization of power amplifiers have been designed and discussed. A test-bench has been assembled in order to evaluate the proposed methods on real power amplifiers. Then the robustness to time misalignment in the system and the ability to deal with spectral artifacts in the system of presented methods have been evaluated. Also a theoretical study has been conducted on the existence and management of multiple solutions in the frame of adaptive indirect learning approach. The second part deals with nonlinear dynamical systems that are exhibiting chaotic solutions. Such systems are well known, but techniques for identifying reliable such solutions are either missing or are computational intense. In this thesis several methods using also parallel computing are presented. Systems with fractional differential order are briefly discussed. It is as well shown, that there exists systems related with quantified nonlinear transfer functions for which the standard analyzing methods fails
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Chen, Hao. "Real time model adaptation for non-linear and non-stationary systems." Thesis, University of Reading, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.630445.
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This thesis studies the modelling for the non-linear and non-stationary systems. In a highly non-stationary environment, not only the model coefficients but also the model structure should be adapted with time. A number of novel on-line modeling approaches are proposed in this thesis. The proposed approaches are validated using several benchmark signal processing applications including time series prediction, noise cancellation and channel equalization. First, a novel tunable radial basis function network is proposed. in which the number of nodes (or the model size) of the network is fixed and a new structured node is used to replace the worst performing node whenever the current network does not fit the input data. Two schemes are proposed to optimize t.he structure of the new node: a powerful version based on the quantum particle swarm optimization algorithm and a fast version based on the "gradient search" approach. Secondly, a new online multiple modelling approach is proposed for nonstationary systems. The proposed multimodel approach is based on two level structures of linear sub-models. The advantage of the proposed method is that it is very fast, making it particularly suitable for real time applications. Finally a new adaptive channel equalizer is developed based on minimum biterror- rate. A key issue in the minimum bit-error-rate equalizer is how the probability density function of an associated signed decision variable can be estimated on-line. In the proposed equalizer, a novel online probability density function based on Gaussian mixture model is derived, which has significant better performance than existing approaches.
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Mahmood, Khalid. "Constrained linear and non-linear adaptive equalization techniques for MIMO-CDMA systems." Thesis, De Montfort University, 2013. http://hdl.handle.net/2086/10203.
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Researchers have shown that by combining multiple input multiple output (MIMO) techniques with CDMA then higher gains in capacity, reliability and data transmission speed can be attained. But a major drawback of MIMO-CDMA systems is multiple access interference (MAI) which can reduce the capacity and increase the bit error rate (BER), so statistical analysis of MAI becomes a very important factor in the performance analysis of these systems. In this thesis, a detailed analysis of MAI is performed for binary phase-shift keying (BPSK) signals with random signature sequence in Raleigh fading environment and closed from expressions for the probability density function of MAI and MAI with noise are derived. Further, probability of error is derived for the maximum Likelihood receiver. These derivations are verified through simulations and are found to reinforce the theoretical results. Since the performance of MIMO suffers significantly from MAI and inter-symbol interference (ISI), equalization is needed to mitigate these effects. It is well known from the theory of constrained optimization that the learning speed of any adaptive filtering algorithm can be increased by adding a constraint to it, as in the case of the normalized least mean squared (NLMS) algorithm. Thus, in this work both linear and non-linear decision feedback (DFE) equalizers for MIMO systems with least mean square (LMS) based constrained stochastic gradient algorithm have been designed. More specifically, an LMS algorithm has been developed , which was equipped with the knowledge of number of users, spreading sequence (SS) length, additive noise variance as well as MAI with noise (new constraint) and is named MIMO-CDMA MAI with noise constrained (MNCLMS) algorithm. Convergence and tracking analysis of the proposed algorithm are carried out in the scenario of interference and noise limited systems, and simulation results are presented to compare the performance of MIMO-CDMA MNCLMS algorithm with other adaptive algorithms.
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Lutz, Malinda Kay 1974. "Study of work flow in piezoelectrically driven linear and non-linear systems." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/50536.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1999.Includes bibliographical references (p. 159-160).
Standard assumptions about the efficiency of active systems working against a load neglect the load coupling inherent in these systems. This thesis contains a derivation for finding the actuation efficiency and work output in electro-mechanically coupled systems working against a load. This general derivation is for fully coupled, non-linear systems working against a generalized load. Three example cases are then shown to demonstrate several key aspects of the general derivation. The first example case is a one-dimensional, linear discrete actuator working against a one-dimensional, linear spring load. This example shows the effects of electro-mechanical coupling on the actuation efficiency. The second example case is of a piezoelectric bender first presented by Lesieutre and Davis[l] in their derivation of the device coupling coefficient. The bender example demonstrates the differences between the device coupling coefficient and actuation efficiency as well as the use of the generalized derivation in mechanically complex problems. The final example presented is a one-dimensional, linear discrete actuator working against a one-dimensional, non-linear load in order to demonstrate the possibility of increasing the work output of a system through the use of non-linear loading functions. To test the theoretical derivation presented, a custom built testing facility was designed and built to measure the work output and actuation efficiency of a discrete actuator working against both linear and non-linear loads. The testing facility was designed for load application with programmable impedances and closed loop testing at frequencies up to 1 kHz. The complete design of the testing facility is presented with an overview of the rationale behind the design decisions made. Finally, tests were performed on a discrete actuator working against linear and non-linear loading functions. The tests performed on a discrete actuator working against a linear load match the expected work output predicted by the theory. Tests performed on a discrete actuator working against a non-linear load validate that increases in the mechanical work out of the actuator are possible by using non-linear loads instead of linear loads. To illustrate that this is a practical result, the design of a loading device that loads a material non-linearly while loading a spring linearly is presented with its theoretical performance. Recommendations on ways to improve the model, testing methodology, and testing machine concludes the document.
by Malinda Kay Lutz.
S.M.
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Wilson, David R. "Algebraic synthesis methods for linear multivariable systems : decentralized stabilization." Thesis, City University London, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.292684.
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Lutz, Collin C. "Switched Markov Jump Linear Systems: Analysis and Control Synthesis." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/50859.
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Markov jump linear systems find application in many areas including economics, fault-tolerant control, and networked control. Despite significant attention paid to Markov jump linear systems in the literature, few authors have investigated Markov jump linear systems with time-inhomogeneous Markov chains (Markov chains with time-varying transition probabilities), and even fewer authors have considered time-inhomogeneous Markov chains with a priori unknown transition probabilities. This dissertation provides a formal stability and disturbance attenuation analysis for a Markov jump linear system where the underlying Markov chain is characterized by an a priori unknown sequence of transition probability matrices that assumes one of finitely-many values at each time instant. Necessary and sufficient conditions for uniform stochastic stability and uniform stochastic disturbance attenuation are reported. In both cases, conditions are expressed as a set of finite-dimensional linear matrix inequalities (LMIs) that can be solved efficiently. These finite-dimensional LMI analysis results lead to nonconservative LMI formulations for optimal controller synthesis with respect to disturbance attenuation. As a special case, the analysis also applies to a Markov jump linear system with known transition probabilities that vary in a finite set.Ph. D.
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Wang, Kon-King. "Complete synthesis of optimal control (single input linear systems)." Case Western Reserve University School of Graduate Studies / OhioLINK, 1993. http://rave.ohiolink.edu/etdc/view?acc_num=case1057165454.
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Zhao, Shenglin. "Analytical and numerical investigations of linear and non-linear beam-water interaction systems." Thesis, University of Southampton, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427332.
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Shi, Yong 1965. "Actuation efficiency and work flow in piezoelectrically driven linear and non-linear systems." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/82203.
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Castaneda, Veimar Yobany Moreno. "Transmission line modelling applied to non-linear control systems." Thesis, University of Huddersfield, 2006. http://eprints.hud.ac.uk/id/eprint/17872/.
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Yousif, Dafalla Mohamed. "Application of non-linear optimisation to multipurpose reservoir systems." Thesis, Loughborough University, 1999. https://dspace.lboro.ac.uk/2134/7154.
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The aim of this research is to investigate the application of nonlinear programming techniques to multipurpose reservoir systems. A multipurpose multiple reservoir operation problem is a typical nonlinear large scale optimization problem. The currently applied techniques overcome the nonlinearity and dimensionality problems through simplification. To model the problem more closely, a successful trial is made in this study to apply the most efficient and suitable nonlinear programming techniques. Although research in large scale nonlinear optimization has been in recent'years a major subject of interest within the mathematical programming community, its application to reservoir systems is very limited. As a result of these activities software packages, as Lancelot, have been developed. Lancelot is a general purpose software package designed for solving large-scale nonlinear optimization problems. It uses Augmented Lagrangian and Conjugate Gradient methods. This software is used here successfully to solve an optimization problem formulated for a major river system, the Blue Nile in Sudan. The system has two in series reservoirs used for hydropower generation, maintaining minimum downstream flows and irrigation. For optimization, some features of the system have been modelled. These are sedimentation, evaporation, demand and flow. To represent the effect of sedimentation a model is fitted and verified. To include the effect of evaporation a model that estimates the total evaporation losses is fitted using Penman approach and verified using water balance. To cope with flow uncertainty the Blue Nile flow has been modelled. ARMA(1,1) has given the best fitting. Irrigation requirements have been estimated using Penman- Monteith approach. Efficiency of water use has been investigated and other possible demand scenarios resulting from efficient water use are obtained. The results of flow and demand modelling are used as direct input to the optimization model while sedimentation and evaporation models are incorporated in the model. The objective of this model is to maximise power benefits on condition that certain irrigation and downstream requirements be met. To solve this problem a double precision version of Lancelot was installed in a hp-UNIX system. For the problem a specification and a standard input format, SEF, files were written and put under the same directory with Lancelot to run the program. The problem was solved successfully in few minutes. The solution includes values for the objective function, decision variables (releases and storage volumes), penalty parameter, Lagrange multipliers and slack variables. The optimization output is affected by reservoir sedimentation. Therefore the developed optimization and sedimentation models have been linked to investigate sedimentation effect on optimization on output along the course of reservoir operation. Results have shown that this approach can be used to investigate the effect of sedimentation on reservoir optimum output. In, a multipurpose reservoir system, the optimization output for one purpose is affected by the efficiency of water use for other purposes. Therefore the effect of efficient water use in irrigation on power benefits is investigated. Results have shown an increment in benefits due to using irrigation water efficiently. This approach can be applied to systems where priority is given for one purpose over the others.
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Haynes, Barry P. "A neural network adaptive controller for non-linear systems." Thesis, University of Portsmouth, 1997. https://researchportal.port.ac.uk/portal/en/theses/a-neural-network-adaptive-controller-for-nonlinear-systems(19584462-246e-4de3-9e80-cda4923a38c1).html.
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Gu, D. W. "Design of non-linear control systems via mathematical programming." Thesis, Imperial College London, 1985. http://hdl.handle.net/10044/1/37714.
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Benomair, Abdollha. "Non-linear observer based control of magnetic levitation systems." Thesis, University of Sheffield, 2018. http://etheses.whiterose.ac.uk/20582/.
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Active magnetic levitation AML systems have been widely used in magnetic levitation vehicles, wind turbine, medical applications, micro robot actuation and turbo-machinery. Contactless support of objects continues to be a fantasy for several centuries. The utilization of magnetic forces seems to be the ideal solution in many situations to such a goal. Using magnetic forces to support an object without any mechanical contact is constrained by the laws of magnetism. Earnshaw’s theorem states that when the inverse-square-law forces govern several charged particles, they can never be within a stable equilibrium. The interaction between ferromagnetic objects and electromagnets of either the active or passive type, is associated with an unstable nature. This unstable behaviour can be represented by highly non-linear differential equations. In the literature many researches are based on linearised models around a specific nominal operating point then linear controller is utilized to control the system. The associated problem with the linear control technique is that the system only be adequately controlled in a small region around the equilibrium point but the variation of operating regions in such non-linear system is wide following a major disturbance. In this research, two kinds of non-linear observer-based excitation controller are proposed for Maglev to ensure the stability of non-linear system in the presence of large disturbance and over larger operation regions. A combination of full-order Nonlinear high-gain observer (NHGO) with LQR-feedback linearisation is considered as first proposal. Second proposed controller is based on the Lyapunov stability theorems, and a further non-linear full-order observer-based controller via a non-linear fuzzy sliding mode controller is developed for Maglev system. The proposed control approaches are tested and validated through simulated exercises of a magnetic levitation system. Comparative assessments of the approaches are presented and discussed through the thesis.
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Roberts, Ian. "Analysis of non-linear aeroelastic systems using numerical continuation." Thesis, University of Bristol, 2004. http://hdl.handle.net/1983/f03bc690-1738-4b5d-9ef5-d0d4ecad09a9.
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Non-linearities within structures often present difficulties when developing algorithms to analyse their dynamic properties. Developing a combined aerodynamic and structural- aeroelastic - code is an example where non-linearities can induce particular characteristics as the presence of aerodynamic non-linearities can compound the complexity of the analysis. Furthermore, when non-linearities occur within actuation devices the impact of coupling control systems with the aeroelastic algorithms - aeroservoelastic - must also be considered. In this work, new methods of analysing aero(servo)elastic systems containing various structural non-linearities are studied. The first technique is used to analyse piecewise linear systems. In this method, aeroelastic equations are recast in a form where the independent variable is the time at which the system reaches a discontinuity, sets of these equations are then combined to form an algebraic set of equations describing a Limit-Cycle Oscillation (LCO). The second technique is applied to more general non-linearities by approximating any discrete non-linearities with trigonometric functions, creating a set of continuous Ordinary Differential Equations (ODEs). For both methods, computational efficiency is achieved by applying numerical continuation to track solution branches. The models analysed in this work are two and three degree-of-freedom aerofoil sections containing non-linearities in their heave, pitch and/or flap freedoms. Four different aerodynamic representations are used, two incompressible codes establish the accuracy of the new methods. The other codes are used to study transonic flows and show good agreement with work based on aeroelastic systems with both linear and non-linear structures. Three different control laws - fixed gain, optimal and adaptive - are also investigated to assess their ability to delay flutter onset and suppress LCOs. Optimal control showed the best overall ability to achieve these aims, although it was found that care must be taken not to destabilise areas below the flutter boundary. Finally, a method of analysing fatigue due to structural non-linearities is investigated. The analysis combines the numerical continuation techniques with the Rainflow method to quantify damage due to simple acceleration-deceleration profiles.
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Vaudrey, Michael Allen. "Adaptive Control Methods for Non-Linear Self-Excited Systems." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/28884.
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Self-excited systems are open loop unstable plants having a nonlinearity that prevents an exponentially increasing time response. The resulting limit cycle is induced by any slight disturbance that causes the response of the system to grow to the saturation level of the nonlinearity. Because there is no external disturbance, control of these self-excited systems requires that the open loop system dynamics are altered so that any unstable open loop poles are stabilized in the closed loop.
This work examines a variety of adaptive control approaches for controlling a thermoacoustic instability, a physical self-excited system. Initially, a static feedback controller loopshaping design and associated system identification method is presented. This design approach is shown to effectively stabilize an unstable Rijke tube combustor while preventing the creation of additional controller induced instabilities. The loopshaping design method is then used in conjunction with a trained artificial neural network to demonstrate stabilizing control in the presence of changing plant dynamics over a wide variety of operating conditions. However, because the ANN is designed specifically for a single combustor/actuator arrangement, its limited portability is a distinct disadvantage.
Filtered-X least mean squares (LMS) adaptive feedback control approaches are examined when applied to both stable and unstable plants. An identification method for approximating the relevant plant dynamics to be modeled is proposed and shown to effectively stabilize the self-excited system in simulations and experiments. The adaptive feedback controller is further analyzed for robust performance when applied to the stable, disturbance rejection control problem. It is shown that robust stability cannot be guaranteed because arbitrarily small errors in the plant model can generate gradient divergence and unstable feedback loops.
Finally, a time-averaged-gradient (TAG) algorithm is investigated for use in controlling self-excited systems such as the thermoacoustic instability. The TAG algorithm is shown to be very effective in stabilizing the unstable dynamics using a variety of controller parameterizations, without the need for plant estimation information from the system to be controlled.Ph. D.
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Nilsson, Albin. "Sensor fusion and fault diagnosticsin non-linear dynamical systems." Thesis, Uppsala universitet, Avdelningen för systemteknik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-428958.
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Sensors are highly essential components in most modern control systems and are used in increasingly complex ways to improve system precision and reliability. Since they are generally susceptible to faults it is common to perform on-line fault diagnostics on sensor data to verify nominal behavior. This is especially important for safety critical systems where it can be imperative to identify, and react to, a fault before it increases in severity. An example of such a safety critical system is the propulsion control of a vehicle. In this thesis, three different model-based methods for Fault Detection and Isolation (FDI) are developed and tested with the aim of detecting and isolating sensor faults in the powertrain of an electric, center articulated, four-wheel-drive vehicle. First, kinematic models are derived that combine sensor data from all sensors related to propulsion. Second, the kinematic models are implemented in system observers to produce fault sensitive zero-mean residuals. Finally, fault isolation algorithms are derived, which detect and indicate different types of faults via evaluation of the observer residuals. The results show that all FDI methods can detect and isolate stochastic faults with high certainty, but that offset-type faults are hard to distinguish from modeling errors and are therefore easily attenuated by the system observers. Faults in accelerometer sensors need extra measures to be detectable, owing to the environment where the vehicle is typically operated. A nonlinear system model shows good conformity to the vehicle system, lending confidence to its further use as a driver for propulsion control.
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Hua, Yunjie. "State estimation for a class of non-linear systems." Université Louis Pasteur (Strasbourg) (1971-2008), 2008. https://publication-theses.unistra.fr/public/theses_doctorat/2008/HUA_Yunjie_2008.pdf.
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En raison du fait que des nombreux processus et systèmes du monde réel peuvent être modélisés comme des systèmes commutés ou des systèmes multi-modèles, la synthèse d'observateurs pour ce type de systèmes a suscité un intérêt croissant ces dernières décennies. Une deuxième raison qui justifie cet intérêt vient du fait que les observateurs d’état peuvent être appliqués au cryptage des données pour les systèmes de télécommunication. Dans cette thèse, nous proposons quelques méthodes de synthèse d’observateurs d’état pour des systèmes commutés et des systèmes multi-modèles. En utilisant de nouvelles fonctions de Lyapunov, ces approches permettent de réduire le conservatisme des approches actuellement disponibles dans la littérature. Les résultats obtenus ont été vérifiés sur des exemples de la litteratureDue to the fact that many processes and systems in real world applications can be modeled as switched systems or multi-model systems, the synthesis of observers for these classes of systems has received a growing interest in the last decades. A second reason that justifies the interest for this research area comes from the fact that it can be applied to data encryption/decryption for telecommunication applications. In this thesis, we propose some methods for synthesizing state observers for switched systems and multi-model systems. By using new Lyapunov functions, these methods reduce the conservatism of the current approaches available in the literature. The results were verified on examples from literature
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Hua, Yunjie Boutayeb Mohamed. "State estimation for a class of non-linear systems." Strasbourg : Université de Strasbourg, 2009. http://eprints-scd-ulp.u-strasbg.fr:8080/1043/01/HUA_Yunjie_2008.pdf.
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Godasi, Satyam. "Identification and control of non-linear distributed parameter systems /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2002. http://uclibs.org/PID/11984.
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Xu, Jihan. "Synthesis of H{unendlich}⁻optimal robust regulator for linear systems /." Zürich, 1989. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=8791.
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