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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Power system stability studies using Liapunov methods

Metwally, Magda Mohsen January 1971 (has links)
The transient stability of power systems is investigated using Liapunov's direct method. Willems' method is applied to three-and four-machine power systems with the effect of damping included. The distribution of damping among the machines of a multi-machine system is studied, and optimum ratios are derived. An extension of Willems' method is used to include governor action in the system representation. Finally, the effect of flux decay on stability regions is studied using Chen's method. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate
2

Lyapunov spectrum and control sets

Grünvogel, Stefan Michael. January 2000 (has links)
Thesis (doctoral)--Universität Augsburg, 2000. / Includes bibliographical references (p. 177-179) and index.
3

Οι εκθέτες Lyapunov και ο αριθμητικός υπολογισμός τους

Τσαπικούνη, Αγγελική 26 August 2010 (has links)
Στην παρούσα διπλωματική εργασία, μελετάμε την έννοια και σημασία των εκθετών Lyapunov μέσω μεθόδων ανάλυσης πειραματικών δεδομένων που εφαρμόζονται στην φυσική, στην γεωλογία, στην αστρονομία, στην νευροβιολογία, στην οικολογία και στα οικονομικά. Οι εκθέτες Lyapunov παίζουν πολύ σημαντικό ρόλο στην ανίχνευση χάους, το οποίο εμφανίζεται σε πολλούς τομείς της επιστήμης και της τεχνολογίας. Άρα, το θέμα τους ανήκει στην θεωρία των χαοτικών δυναμικών συστημάτων αλλά και γενικότερα όλων των δυναμικών συστημάτων, τα οποία πρέπει να αναλυθούν σωστά και με ακρίβεια για να πάρουμε τα σωστά συμπεράσματα όσον αφορά τους εκθέτες Lyapunov. Σκοπός της μελέτης είναι η εύρεση των εκθετών Lyapunov για διάφορα δυναμικά συστήματα και η εξήγηση των αποτελεσμάτων όσον αφορά την δυναμική συμπεριφορά του κάθε συστήματος. Επίσης, παρουσιάζονται εφαρμογές στην επιστήμη όπου οι εκθέτες Lyapunov παίζουν σημαντικό ρόλο και εξηγούνται οι κυριότεροι αλγόριθμοι υπολογισμού αυτών των εκθετών υπό διαφορετική υλοποίηση και σε διαφορετικά υπολογιστικά πακέτα, όπως το Matlab, το Mathematica και ακόμα σε γλώσα προγραμματισμού C με σκοπό την εύρεση του καλύτερου και πιο ακριβή αλγόριθμου. Επιπρόσθετα, παρουσιάζονται τα συμπεράσματα μετά την ανάλυση όλων των αλγορίθμων και των αποτελεσμάτων και προτείνεται ο καλύτερος και αποτελεσματικότερος αλγόριθμος όσον αφορά την απόδοση, τον χρόνο εκτέλεσης, αλλά και το μέγεθος των σφαλμάτων. Στο τέλος, υπάρχει παράρτημα με επιμέρους κώδικες που χρησιμοποιούνται, όπως ακόμα και η βιβλιογραφία από την οποία αντλήθηκαν πολύ σημαντικές πληροφορίες. / In this paper, we study the meaning and importance of Lyapunov exponents through experimental data analysis methods applied in physics, geology, astronomy, neurobiology, ecology and economics. The Lyapunov exponents play an important role in the detection of chaos, which occurs in many areas of science and technology. So, their issue concerns the theory of chaotic dynamical systems and generally all dynamical systems, which must be analyzed properly and accurately to get the right conclusions for the Lyapunov exponents. The purpose of this paper is to find the Lyapunov exponents for various dynamical systems and the explanation of the results concerning the dynamic behavior of each system. Also, several applications in science are presented where Lyapunov exponents play an important role and the main algorithms, which calculate these exponents under different implementation and in different computer packages such as Matlab, Mathematica, and even in programming language C, are explained to find the best and most accurate algorithm. Additionally, conclusions are drawn after analyzing all the algorithms and the results and it is suggested the best and most efficient algorithm regarding the performance, the execution time and also the magnitude of errors. In the end, there is an appendix with individual codes which are used, as even the bibliography from which very important information are derived.
4

Analysis of chaotic multi-variate time-series from spatio-temporal dynamical systems

Orstavik, Odd-Halvdan Sakse January 1999 (has links)
No description available.
5

Products of random matrices and Lyapunov exponents.

January 2010 (has links)
Tsang, Chi Shing Sidney. / "October 2010." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 58-59). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- The main results --- p.6 / Chapter 1.2 --- Structure of the thesis --- p.8 / Chapter 2 --- The Upper Lyapunov Exponent --- p.10 / Chapter 2.1 --- Notation --- p.10 / Chapter 2.2 --- The upper Lyapunov exponent --- p.11 / Chapter 2.3 --- Cocycles --- p.12 / Chapter 2.4 --- The Theorem of Furstenberg and Kesten --- p.14 / Chapter 3 --- Contraction Properties --- p.19 / Chapter 3.1 --- Two basic lemmas --- p.20 / Chapter 3.2 --- Contracting sets --- p.25 / Chapter 3.3 --- Strong irreducibility --- p.29 / Chapter 3.4 --- A key property --- p.30 / Chapter 3.5 --- Contracting action on P(Rd) and converges in direction --- p.36 / Chapter 3.6 --- Lyapunov exponents --- p.39 / Chapter 3.7 --- Comparison of the top Lyapunov exponents and Fursten- berg's theorem --- p.43 / Chapter 4 --- Analytic Dependence of Lyapunov Exponents on The Probabilities --- p.48 / Chapter 4.1 --- Continuity and analyticity properties for i.i.d. products --- p.49 / Chapter 4.2 --- The proof of the main result --- p.50 / Chapter 5 --- The Expression of The Upper Lyapunov Exponent in Complex Functions --- p.54 / Chapter 5.1 --- The set-up --- p.54 / Chapter 5.2 --- The main result --- p.56 / Bibliography --- p.58
6

Funções de Lyapunov estendidas para análise de estabilidade transitória em sistemas elétricos de potência / Extended Lyapunov function for analysis and control of electrical power systems transient stability

Silva, Flávio Henrique Justiniano Ribeiro da 19 October 2004 (has links)
O método de Lyapunov, também conhecido como método direto, é eficiente para análise de estabilidade transitória em sistemas de potência. Tal método possibilita a análise de estabilidade sem requerer o conhecimento das soluções das equações diferenciais que modelam o problema. A maior desvantagem da utilização dos métodos diretos, é sem dúvida encontrar uma função (V) que satisfaça as condições do Teorema de Lyapunov, ou seja, V > 0 e V \'< ou =\' 0. Durante muitos anos a inclusão das condutâncias de transferência na modelagem do sistema de potência, com a rede reduzida aos nós dos geradores, foi um assunto que despertou interesse em vários pesquisadores. Em 1989, Chiang provou a não existência de uma Função de Lyapunov para sistemas de potência quando as condutâncias de transferência são consideradas. Essas condutâncias de transferência são responsáveis por gerar regiões no espaço de estados onde tem-se V > 0, não satisfazendo as condições do Teorema de Lyapunov. Recentemente, Rodrigues, Alberto e Bretas (2000) apresentaram a Extensão do Princípio de Invariância de LaSalle, onde é permitido que a Função de Lyapunov possua, em algumas regiões limitadas do espaço de estados, a derivada positiva. Neste caso, estas funções passam a ser denominadas Funções de Lyapunov Estendidas (FLE). Neste trabalho, são utilizadas a Extensão do Princípio de Invariância de LaSalle e as Funções de Lyapunov Estendidas para a análise de estabilidade transitória, considerando o efeito das condutâncias de transferência na modelagem do problema. Para isto, são propostas Funções de Lyapunov Estendidas para modelos de sistemas de potência que não apresentam uma Função de Lyapunov no sentido usual. Essas FLE\'s são propostas tanto para sistemas de 1-máquina versus barramento infinito quanto para sistemas multimáquinas. Para a obtenção de boas estimativas do tempo de abertura, nos estudos de estabilidade transitória, é proposto um algoritmo iterativo. Este algoritmo fornece uma boa estimativa local da área de atração do ponto de equilíbrio estável de interesse. / The method of Lyapunov, one of the direct method, is efficient for transient stability analysis of power systems. The direct methods are well-suited for stability analysis of power systems, since they do not require the solution of the set of differential equations of the system model. The great difficulty of the direct methods is to find an auxiliary function (V) which satisfies the conditions of Lyapunov\'s Theorem V > 0 and V \'< or =\' 0. For many years the inclusion of the transfer conductances in the power system model, with the reduced network, is a issue of interest for several researchers. In 1989, Chiang studied the existence of energy functions for power systems with losses and he proved the non existence of a Lyapunov Function for power systems when the transfer conductance is taken into account. The transfer conductances are responsible for generating regions in the state space where the derivative of V is positive. Therefore, the function V is nor a Lyapunov Function, because its derivative is not semi negative definite. Recently, an Extension of the LaSalle\'s Invariance Principle has been proposed by Rodrigues, Alberto and Bretas (2000). This extension relaxes some of the requirements on the auxiliary function which is commonly called Lyapunov Function. In this extension, the derivative of the auxiliary function can be positive in some bounded regions of the state space and, for distinction purposes, it is called, as Extended Lyapunov Function. Inthis work, the Extension of the LaSalle\'s Invariance Principle and the Extended Lyapunov Function are used for the transient stability analysis of power systems with the model taking transfer conductances in consideration. For at purpose in this research, Extended Lyapunov Functions for power system models which do not have Lyapunov Functions in the usual sense are proposed. Extended Lyapunov Functions are proposed for a single-machine-infinite- bus-system and multimachine systems. For obtaining good estimates of the critical clearing time in transient stability analysis, an iterative algorithm is proposed. This algorithm supplies a good local estimate of the attraction area for the post fault stable equilibrium point.
7

Spatial evaluation of Lyapunov exponents in Hamiltonian systems

Stanley, Paul Elliott 11 December 1995 (has links)
A new method for evaluating the Lyapunov exponent for a Hamiltonian system involves a spatial evaluation, rather than a numerical time integration. The introduction of a novel vector field to the phase space allows the Lyapunov exponent to be expressed in a form that does not involve time. The Lyapunov exponent is seen to be a property of the geometry and topology of ergodic regions of phase space. As a result it has a more regular behavior than previously thought. The Lyapunov exponent is found to be a differentiable function of the perturbation coupling in regions where it was previously thought to be discontinuous. Properties of the Lyapunov function once taken for granted are shown to be artifacts of the traditional computation methods. The technique is discussed with examples from a system of coupled quartic oscillators. / Graduation date: 1996
8

A Lyapunov Exponent Approach for Identifying Chaotic Behavior in a Finite Element Based Drillstring Vibration Model

Mongkolcheep, Kathira 2009 August 1900 (has links)
The purpose of this work is to present a methodology to predict vibrations of drilllstrings for oil recovery service. The work extends a previous model of the drill collar between two stabilizers in the literature to include drill collar flexibility utilizing a modal coordinate condensed, finite element approach. The stiffness due to the gravitational forces along the drillstring axis is included. The model also includes the nonlinear effects of drillstring-wellbore contact, friction and quadratic damping. Bifurcation diagrams are presented to illustrate the effects of speed, friction at wellbore, stabilizer clearance and drill collar length on chaotic vibration response. Their effects shifts resonance peaks away from the linear natural frequency values and influences the onset speed for chaos. A study is conducted on factors for improving the accuracy of Lyapunov Exponents to predict the presence of chaos. This study considers the length of time to steady state, the number and duration of linearization sub-intervals, the presence of rigid body modes and the number of finite elements and modal coordinates. The Poincare map and frequency spectrum are utilized to confirm the prediction of Lyapunov exponent analysis. The results may be helpful for computing Lyapunov exponents of other types of nonlinear vibrating systems with many degrees of freedom. Vibration response predictions may assist drilling rig operators in changing a variety of controlled parameters to improve operation procedures and/or equipment.
9

Modeling with Liapunov functions

Nordahl, Donald Marvin, 1942- January 1966 (has links)
No description available.
10

Design of sampled-data control systems using the second method of Liapunov

Ramirez-Guzman, Gustavo, 1940- January 1966 (has links)
No description available.

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