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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 stabilitySilva, 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 temse 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 1máquina 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 wellsuited 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 singlemachineinfinite bussystem 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.

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Estabilidade e oscilação de soluções de equações diferenciais com retardos e impulsos / Stability and oscillation for solutions of differential equations with delays and impulsesGimenes, Luciene Parron 07 March 2007 (has links)
O objetivo deste trabalho é investigar propriedades qualitativas de certas equações diferenciais funcionais retardadas de segunda ordem quando lhes são impostos controles de impulsos adequados. Os principais resultados dizem respeito a estabilidade e oscilação por impulsos. Mais especificamente, consideramos algumas equações e provamos que suas soluções triviais podem ser estabilizadas por impulsos. Em seguida, consideramos uma destas equações e provamos que suas soluções podem se tornar oscilatórias com a imposição apropriada de controles de impulsos. Apresentamos alguns exemplos que ilustram nossos resultados. Além do objetivo acima, procuramos produzir um texto que compreendesse a teoria fundamental das equações diferenciais funcionais retardadas impulsivas, teoria esta que, até então, não podia ser encontrada num único texto como este. Desenvolvemos e discutimos existência, unicidade, continuação de soluções, intervalo maximal de existência e dependência contínua de soluções dos valores iniciais para equações diferenciais retardadas impulsivas. / The purpose of this work is to investigate qualitative properties of certain second order delay differential equations when some proper impulse controls are added to them. The main results concern the stability and scillation by impulses. More specifically, we consider some equations and prove that their trivial solutions can be stabilized by impulses. We also consider one of these equations and prove that all solutions oscillate when proper impulse controls are imposed. We give some examples to illustrate our results. Because dealing with systems with both delays and impulses is a recent interest of some mathematicians we also considered producing a text that would encompass the fundamental theory of retarded functional differential equations with impulses. Up to now such theory could not be found in a single text as this one. Therefore we discuss and develop basic aspects of the theory as existence, uniqueness, continuability of solutions, maximal interval of existence and continuous dependence of solutions on initial values for impulsive retarded differential equations.

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Robustness of uncertain systems : globally optimal Lyapunov functionAhmadkhanlou, Fariborz 29 May 1992 (has links)
The Lyapunov direct method is utilized to determine the
robustness bounds for nonlinear, timevariant uncertainies
p[subscript i]. Determination of the robustness bounds consists of two
principal steps: (i) generation of a Lyapunov function and
(ii) determination of the bounds based on the generated
Lyapunov function. Presently in robustness investigations,
a Lyapunov function is generated by inserting the nominal
matrix to the Lyapunov equation and setting Q as identity
matrix. The objective of this study is to utilize structural
features of the uncertainties to develop a recursive
algorithm for the generation of the globally optimal quadratic
Lyapunov function. The proposed method is seemingly
an improvement with respect to those reported in recent
literature in three senses: i) ease of application, given
an interactive program which requires only system matrices
as inputs; ii) provision of improved estimates of the
robustness bounds; and iii) extendability of the procedure
to the design of robust controllers. The algorithm and the
program prepared (in MATLAB) are presented. Several examples
are considered for purposes of the comparison of
robustness bounds estimates. Examples are demonstrated to
show the superiority of the robustness bounds estimated by
the proposed method over those obtained by small gain
theorem. In a number of cases, the estimated robustness
bounds are proven to be the exact robustness bounds. / Graduation date: 1993

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A graphtheoretic approach to the construction of Lyapunov functions for coupled systems on networksShuai, Zhisheng 11 1900 (has links)
For coupled systems of differential equations on networks, a graphtheoretic approach to the construction of Lyapunov functions is systematically developed in this thesis. Kirchhoffs MatrixTree Theorem in graph theory plays
an essential role in the approachs development. The approach is successfully applied to several coupled systems wellknown in the literature to demonstrate its applicability and effectiveness. / Applied Mathematics

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Dynamics and control of collision of multilink humanoid robots with a rigid or elastic objectChen, Zengshi, January 2006 (has links)
Thesis (Ph. D.)Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 178191).

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Optimal data dissemination in stochastic and arbitrary wireless networksLi, Hongxing, 李宏兴 January 2012 (has links)
Data dissemination among wireless devices is an essential application in wireless networks. In contrast to its wired counterparts which have more stable network settings, wireless networks are subject to network dynamics, such as variable network topology, channel availability and capacity, which are due to user mobility, signal collision, random channel fading and scattering, etc. Network dynamics complicate the protocol design for optimal data disseminations. Although the topic has been intensively discussed for many years, existing solutions are still not completely satisfactory, especially for stochastic or arbitrary networks. In this thesis, we address optimal data dissemination in both stochastic and arbitrary wireless networks, using techniques of Lyapunov optimization, graph theory, network coding, multiresolution coding and successive interference cancellation.
We first discuss the maximization of timeaveraged throughput utility over a long run for unicast and multirate multicast, respectively, in stochastic wireless networks without probing into the future. For multisession unicast communications, a utilitymaximizing crosslayer design, composed of joint endtoend rate control, routing, and channel allocation, is proposed for cognitive radio networks with stochastic primary user occupations. Then, we study optimal multirate multicast to receivers with nonuniform receiving rates, also making dynamic crosslayer decisions, in a general wireless network with both a timevarying topology and random channel capacities, by utilizing random linear network coding and multiresolution coding. In both solutions, we assume users are selfish and prefer only to relay data for others with strong social ties. Such social selfishness of users is a new constraint in network protocol design. Its impact on efficient data dissemination in wireless networks is largely unstudied, especially under stochastic settings. Lyapunov optimization is applied in our protocol design achieving closetooptimal utilities.
Next, we turn to latencyminimizing data aggregation in wireless sensor networks having arbitrary network topologies under the physical interference model. Different from our effort for stochastic networks where we target at timeaveraged optimality over a long run, the objective here is to minimize the timespan to accomplish one round of aggregation scheduling for all sensors in an arbitrary topology. This problem is NPhard, involving both aggregation tree construction and collisionfree link scheduling. The current literature mostly considers the protocol interference model, which has been shown to be less practical than the physical interference model in characterizing the interference relations in the real world. A distributed solution under the physical interference model is challenging since cumulative interferences from all concurrently transmitting devices need to be well measured. In this thesis, we present a distributed aggregation protocol with an improved approximation ratio as compared with previous work. We then discuss the tradeoff between aggregation latency and energy consumption for arbitrary topologies when the successive interference cancellation technique is in force. Another distributed algorithm is introduced with asymptotic optimality in both aggregation latency and latencyenergy tradeoff.
Through theoretical analysis and empirical study, we rigorously examine the optimality of our protocols comparing with both the theoretical optima and existing solutions. / published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

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THE STABILITY OF COUPLEDCORE NUCLEAR REACTOR SYSTEMS BY THE SECOND METHOD OF LIAPUNOVMurray, Hugh Sutherland, 1939 January 1965 (has links)
No description available.

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Modeling and Control of VSCHVDC TransmissionsLatorre, Hector January 2011 (has links)
Presently power systems are being operated under high stress level conditions unforeseen at the moment they were designed. These operating conditions have negatively impacted reliability, controllability and security margins. FACTS devices and HVDC transmissions have emerged as solutions to help power systems to increase the stability margins. VSCHVDC transmissions are of particular interest since the principal characteristic of this type of transmission is its ability to independently control active power and reactive power. This thesis presents various control strategies to improve damping of electromechanical oscillations, and also enhance transient and voltage stability by using VSCHVDC transmissions. These control strategies are based of different theory frames, namely, modal analysis, nonlinear control (Lyapunov theory) and model predictive control. In the derivation of the control strategies two models of VSCHVDC transmissions were also derived. They are Injection Model and Simple Model. Simulations done in the HVDC Light Open Model showed the validity of the derived models of VSCHVDC transmissions and the effectiveness of the control strategies. Furthermore the thesis presents an analysis of local and remote information used as inputs signals in the control strategies. It also describes an approach to relate modal analysis and the SIME method. This approach allowed the application of SIME method with a reduced number of generators, which were selected based on modal analysis. As a general conclusion it was shown that VSCHVDC transmissions with an appropriate input signal and control strategy was an effective means to improve the system stability. / QC 20110412

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A graphtheoretic approach to the construction of Lyapunov functions for coupled systems on networksShuai, Zhisheng Unknown Date
No description available.

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Mathematical Analysis of Dynamics of Chlamydia trachomatisSharomi, Oluwaseun Yusuf 09 September 2010 (has links)
Chlamydia, caused by the bacterium Chlamydia trachomatis, is one of the most important sexuallytransmitted infections globally. In addition to accounting for millions of cases every year, the disease causes numerous irreversible complications such as chronic pelvic pain, infertility in females and pelvic inflammatory disease. This thesis presents a number of mathematical models, of the form of deterministic systems of nonlinear differential equations, for gaining qualitative insight into the transmission dynamics and control of Chlamydia within an infected host (in vivo) and in a population. The models designed address numerous important issues relating to the transmission dynamics of Chlamydia trachomatis, such as the roles of immune response, sex structure, time delay (in modelling the latency period) and risk structure (i.e., risk of acquiring or transmitting infection). The inhost model is shown to have a globallyasymptotically stable Chlamydiafree equilibrium whenever a certain biological threshold is less than unity. It has a unique Chlamydiapresent equilibrium when the threshold exceeds unity. Unlike the inhost model, the twogroup (males and females) populationlevel model undergoes a backward bifurcation, where a stable diseasefree equilibrium coexists with one or more stable endemic equilibria when the associated reproduction number is less than unity. This phenomenon, which is shown to be caused by the reinfection of recovered individuals, makes the effort to eliminate the disease from the population more difficult. Extending the twogroup model to incorporate risk structure shows that the backward bifurcation phenomenon persists even when recovered individuals do not acquire reinfection. In other words, it is shown that stratifying the sexuallyactive population in terms of risk of acquiring or transmitting infection guarantees the presence of backward bifurcation in the transmission dynamics of Chlamydia in a population. Finally, it is shown (via numerical simulations) that a future Chlamydia vaccine that boosts cellmediated immune response will be more effective in curtailing Chlamydia burden in vivo than a vaccine that enhances humoral immune response. The populationlevel impact of various targeted treatment strategies, in controlling the spread of Chlamydia in a population, are compared. In particular, it is shown that the use of treatment could have positive or negative populationlevel impact (depending on the sign of a certain epidemiological threshold).

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