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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.
51

Parameter-Dependent Lyapunov Functions and Stability Analysis of Linear Parameter-Dependent Dynamical Systems

Zhang, Xiping 27 October 2003 (has links)
The purpose of this thesis is to develop new stability conditions for several linear dynamic systems, including linear parameter-varying (LPV), time-delay systems (LPVTD), slow LPV systems, and parameter-dependent linear time invariant (LTI) systems. These stability conditions are less conservative and/or computationally easier to apply than existing ones. This dissertation is composed of four parts. In the first part of this thesis, the complete stability domain for LTI parameter-dependent (LTIPD) systems is synthesized by extending existing results in the literature. This domain is calculated through a guardian map which involves the determinant of the Kronecker sum of a matrix with itself. The stability domain is synthesized for both single- and multi-parameter dependent LTI systems. The single-parameter case is easily computable, whereas the multi-parameter case is more involved. The determinant of the bialternate sum of a matrix with itself is also exploited to reduce the computational complexity. In the second part of the thesis, a class of parameter-dependent Lyapunov functions is proposed, which can be used to assess the stability properties of single-parameter LTIPD systems in a non-conservative manner. It is shown that stability of LTIPD systems is equivalent to the existence of a Lyapunov function of a polynomial type (in terms of the parameter) of known, bounded degree satisfying two matrix inequalities. The bound of polynomial degree of the Lyapunov functions is then reduced by taking advantage of the fact that the Lyapunov matrices are symmetric. If the matrix multiplying the parameter is not full rank, the polynomial order can be reduced even further. It is also shown that checking the feasibility of these matrix inequalities over a compact set can be cast as a convex optimization problem. Such Lyapunov functions and stability conditions for affine single-parameter LTIPD systems are then generalized to single-parameter polynomially-dependent LTIPD systems and affine multi-parameter LTIPD systems. The third part of the thesis provides one of the first attempts to derive computationally tractable criteria for analyzing the stability of LPV time-delayed systems. It presents both delay-independent and delay-dependent stability conditions, which are derived using appropriately selected Lyapunov-Krasovskii functionals. According to the system parameter dependence, these functionals can be selected to obtain increasingly non-conservative results. Gridding techniques may be used to cast these tests as Linear Matrix Inequalities (LMI's). In cases when the system matrices depend affinely or quadratically on the parameter, gridding may be avoided. These LMI's can be solved efficiently using available software. A numerical example of a time-delayed system motivated by a metal removal process is used to demonstrate the theoretical results. In the last part of the thesis, topics for future investigation are proposed. Among the most interesting avenues for research in this context, it is proposed to extend the existing stability analysis results to controller synthesis, which will be based on the same Lyapunov functions used to derive the nonconservative stability conditions. While designing the dynamic ontroller for linear and parameter-dependent systems, it is desired to take the advantage of the rank deficiency of the system matrix multiplying the parameter such that the controller is of lower dimension, or rank deficient without sacrificing the performance of closed-loop systems.
52

Switched observers and input-delay compensation for anti-lock brake systems

Hoang, Trong bien 04 April 2014 (has links) (PDF)
Many control algorithms for ABS systems have been proposed in the literature since the introduction of this equipment by Bosch in 1978. In general, one can divide these control algorithms into two different types: those based on a regulation logic with wheel acceleration thresholds that are used by most commercial ABS systems; and those based on wheel slip control that are preferred in the large majority of academic algorithms. Each approach has its pros and cons [Shida 2010]. Oversimplifying, one can say that the strength of the first ones is their robustness; while that of the latter ones their short braking distances (on dry grounds) and their absence of limit cycles. At the midpoint of this industry/academy dichotomy, based on the concept of extended braking stiffness (XBS), a quite different class of ABS control strategies has been proposed by several researchers (see, e.g., [Sugai 1999] and [Ono 2003]). This concept combines the advantages from both the industrial and academic approaches. Nevertheless, since the slope of the tyre characteristic is not directly measurable, it introduces the question of real-time XBS estimation. The first part of this thesis is devoted to the study of this estimation problem and to a generalization of the proposed technique to a larger class of systems. From the technological point of view, the design of ABS control systems is highly dependent on the ABS system characteristics and actuator performance. Current ABS control algorithms on passenger cars, for instance the Bosch ABS algorithm, are based on heuristics that are deeply associated to the hydraulic nature of the actuator. An interesting observation is that they seem to work properly only in the presence of a specific delay coming from the hydraulic actuation [Gerard 2012]. For brake systems that have different delays compared to those of hydraulic actuators, like electric in-wheel motors (with a smaller delay) or pneumatic trailer brakes (with a bigger delay), they might be no longer suitable [Miller 2013]. Therefore, adapting standard ABS algorithms to other advanced actuators becomes an imperative goal in the automobile industry. This goal can be reached by the compensation of the delays induced by actuators. The second part of this thesis is focused on this issue, and to the generalization of the proposed technique to a particular class of nonlinear systems. Throughout this thesis, we employ two different linearization techniques: the linearization of the error dynamics in the construction of model-based observers [Krener 1983] and the linearization based on restricted state feedback [Brockett 1979]. The former is one of the simplest ways to build an observer for dynamical systems with output and to analyze its convergence. The main idea is to transform the original nonlinear system via a coordinate change to a special form that admits an observer with a linear error dynamics and thus the observer gains can be easily computed to ensure the observer convergence. The latter is a classical method to control nonlinear systems by converting them into a controllable linear state equation via the cancellation of their nonlinearities. It is worth mentioning that existing results for observer design by error linearization in the literature are only applied to the case of regular time scalings ([Guay 2002] and [Respondek 2004]). The thesis shows how to extend them to the case of singular time scalings. Besides, the thesis combines the classical state feedback linearization with a new method for the input delay compensation to resolve the output tracking problem for restricted feedback linearizable systems with input delays.
53

Qualitative Properties of Stochastic Hybrid Systems and Applications

Alwan, Mohamad January 2011 (has links)
Hybrid systems with or without stochastic noise and with or without time delay are addressed and the qualitative properties of these systems are investigated. The main contribution of this thesis is distributed in three parts. In Part I, nonlinear stochastic impulsive systems with time delay (SISD) with variable impulses are formulated and some of the fundamental properties of the systems, such as existence of local and global solution, uniqueness, and forward continuation of the solution are established. After that, stability and input-to-state stability (ISS) properties of SISD with fixed impulses are developed, where Razumikhin methodology is used. These results are then carried over to discussed the same qualitative properties of large scale SISD. Applications to automated control systems and control systems with faulty actuators are used to justify the proposed approaches. Part II is devoted to address ISS of stochastic ordinary and delay switched systems. To achieve a variety stability-like results, multiple Lyapunov technique as a tool is applied. Moreover, to organize the switching among the system modes, a newly developed initial-state-dependent dwell-time switching law and Markovian switching are separately employed. Part III deals with systems of differential equations with piecewise constant arguments with and without random noise. These systems are viewed as a special type of hybrid systems. Existence and uniqueness results are first obtained. Then, comparison principles are established which are later applied to develop some stability results of the systems.
54

Nonlinear dynamical systems and control for large-scale, hybrid, and network systems

Hui, Qing 08 July 2008 (has links)
In this dissertation, we present several main research thrusts involving thermodynamic stabilization via energy dissipating hybrid controllers and nonlinear control of network systems. Specifically, a novel class of fixed-order, energy-based hybrid controllers is presented as a means for achieving enhanced energy dissipation in Euler-Lagrange, lossless, and dissipative dynamical systems. These dynamic controllers combine a logical switching architecture with continuous dynamics to guarantee that the system plant energy is strictly decreasing across switching. In addition, we construct hybrid dynamic controllers that guarantee that the closed-loop system is consistent with basic thermodynamic principles. In particular, the existence of an entropy function for the closed-loop system is established that satisfies a hybrid Clausius-type inequality. Special cases of energy-based hybrid controllers involving state-dependent switching are described, and the framework is applied to aerospace system models. The overall framework demonstrates that energy-based hybrid resetting controllers provide an extremely efficient mechanism for dissipating energy in nonlinear dynamical systems. Next, we present finite-time coordination controllers for multiagent network systems. Recent technological advances in communications and computation have spurred a broad interest in autonomous, adaptable vehicle formations. Distributed decision-making for coordination of networks of dynamic agents addresses a broad area of applications including cooperative control of unmanned air vehicles, microsatellite clusters, mobile robotics, and congestion control in communication networks. In this part of the dissertation we focus on finite-time consensus protocols for networks of dynamic agents with undirected information flow. The proposed controller architectures are predicated on the recently developed notion of system thermodynamics resulting in thermodynamically consistent continuous controller architectures involving the exchange of information between agents that guarantee that the closed-loop dynamical network is consistent with basic thermodynamic principles.
55

Análise de estabilidade de sistemas dinâmicos híbridos e descontínuos modelados por semigrupos:

Pena, Ismael da Silva [UNESP] 26 February 2008 (has links) (PDF)
Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-02-26Bitstream added on 2014-06-13T18:30:53Z : No. of bitstreams: 1 pena_is_me_sjrp.pdf: 488383 bytes, checksum: 40a97f3540caa6b8f6f2691c3a402579 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Sistemas dinâmicos híbridos se diferenciam por exibir simultaneamente variados tipos de comportamento dinâmico (contínuo, discreto, eventos discretos) em diferentes partes do sistema. Neste trabalho foram estudados resultados de estabilidade no sentido de Lyapunov para sistemas dinâmicos híbridos gerais, que utilizam uma noção de tempo generalizado, definido em um espaço métrico totalmente ordenado. Mostrou-se que estes sistemas podem ser imersos em sistemas dinâmicos descontínuos definidos em R+, de forma que sejam preservadas suas propriedades qualitativas. Como foco principal, estudou-se resultados de estabilidade para sistemas dinâmicos descontínuos modelados por semigrupos de operadores, em que os estados do sistema pertencem à espaços de Banach. Neste caso, de forma alternativa à teoria clássica de estabilidade, os resultados não utilizam as usuais funções de Lyapunov, sendo portanto mais fáceis de se aplicar, tendo em vista a dificuldade em se encontrar tais funções para muitos sistemas. Além disso, os resultados foram aplicados à uma classe de equações diferenciais com retardo. / Hybrid dynamical systems are characterized for showing simultaneously a variety of dynamic behaviors (continuous, discrete, discrete events) in different parts of the System. This work discusses stability results in the Lyapunov sense for general hybrid dynamical systems that use a generalized notion of time, defined in a completely ordered metric space. It has been shown that these systems may be immersed in discontinuous dynamical systems defined in R+, so that their quality properties are preserved. As the main focus, it is studied stability results for discontinuous dynamical systems modeled by semigroup operators, in which the states belong to Banach spaces. In this case, an alternative to the classical theory of stability, the results do not make use of the usual Lyapunov functions, and therefore are easier to apply, in view of the difficulty in finding such functions for many systems. Furthermore, the results were applied to a class of time-delay discontinuous differential equations.
56

Optimal control and stability of four-wheeled vehicles

Masouleh, Mehdi Imani January 2017 (has links)
Two vehicular optimal control problems are visited. The first relates to the minimum lap time problem, which is of interest in racing and the second the minimum fuel problem, which is of great importance in commercial road vehicles. Historically, minimum lap time problems were considered impractical due to their slow solution times compared with the quasi-steady static (QSS) simulations. However, with increasing computational power and advancement of numerical algorithms, such problems have become an invaluable tool for the racing teams. To keep the solution times reasonable, much attention still has to be paid to the problem formulation. The suspension of a Formula One car is modelled using classical mechanics and a meta-model is proposed to enable its incorporation in the optimal control problem. The interactions between the aerodynamics and the suspension are thereby studied and various related parameters are optimised. Aerodynamics plays a crucial role in the performance of Formula One cars. The influence of a locally applied perturbation to the aerodynamic balance is investigated to determine if a compromise made in design can actually lead to lap time improvements. Various issues related to minimum lap time calculations are then discussed. With the danger of climate change and the pressing need to reduce emissions, improvements in fuel consumption are presently needed more than ever. A methodology is developed for fuel performance optimisation of a hybrid vehicle equipped with an undersized engine, battery and a flywheel. Rather than using the widely used driving cycles, a three-dimensional route is chosen and the optimal driving and power management strategy is found with respect to a time of arrival constraint. The benefits of a multi-storage configuration are thereby demonstrated. Finally, the nonlinear stability of a vehicle model described by rational vector fields is investigated using region of attraction (RoA) analysis. With the aid of sum-of-squares programming techniques, Lyapunov functions are found whose level sets act as an under-approximation to the RoA. The influence of different vehicle parameters and driving conditions on the RoA is studied.
57

Aplicações de controle vetorial e análise da robustez em motores de indução trifásicos com atraso no controle /

Garcia, Saulo Crnkowise. January 2018 (has links)
Orientador: Falcondes José Mendes de Seixas / Resumo: O foco principal deste trabalho é a investigação de métodos de controle capazes de rejeitar perturbações, incertezas e influências degenerativas do atraso no problema referente ao controle vetorial por campo orientado do Motor de Indução Trifásico (MIT), através de um modelo matemático não linear deste. Dá-se ênfase à utilização do método de controle Proporcional-Integral em conjunto com o Controle com Estrutura Variável e Modos Deslizantes, sendo que este tem como principal característica a rejeição de perturbações e incertezas. São realizadas análises da robustez da estabilidade e também das influências que as incertezas e atrasos exercem sobre o comportamento dinâmico deste sistema. Para corroborar com as análises, são feitas simulações utilizando exemplos numéricos num sistema linear de ordem dois e aplicações no MIT através de um modelo matemático não linear. / Abstract: This work deals the investigation of control methods capable of rejecting perturbations, uncertainties and degenerative influence of input time-delay in the Three-phase Induction Motor (TIM) vector control problem, through a nonlinear mathematical model. The main focus is the use of the Proportional-Integral control method in conjunction with the Variable Structure Control with Sliding Mode, which has as main characteristic the rejection of perturbations and uncertainties. Analyzes are performed on the stability robustness and also on the influence that the uncertainties and input time-delay on the dynamic behavior of this system. In order to corroborate with the analyzes simulations are made using numerical examples of two-order linear system and applications in a non-linear mathematical model of a Three-phase Induction Motor. / Doutor
58

Otimização de controladores robustos de sistemas dinâmicos sujeitos a falhas estruturais

Buzachero, Luiz Francisco Sanches [UNESP] 25 March 2010 (has links) (PDF)
Made available in DSpace on 2014-06-11T19:22:31Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-03-25Bitstream added on 2014-06-13T19:26:16Z : No. of bitstreams: 1 buzachero_lfs_me_ilha.pdf: 810037 bytes, checksum: 87b0daa8f9193eb11af167f798712fc5 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho propõem-se novas técnicas para otimização da norma de controladores robustos de sistemas dinâmicos lineares sujeitos a falhas estruturais, utilizando realimentação dos estados. As técnicas de projeto utilizadas baseiam-se em LMIs (do inglês Linear Matrix Inequalities) formuladas com base na teoria de estabilidade segundo Lyapunov, utilizando o lema de Finsler e o lema projetivo recíproco. As LMIs utilizadas tiveram o acréscimo da restrição da taxa de decaimento, incluindo o parâmetro g nas LMIs, responsável por diminuir o tempo de duração do transitório dos sistemas realimentados. Foram realizadas comparações qualitativas e quantitativas entre os métodos de projeto com otimização da norma dos controladores, visando alternativas de controladores com menor norma e melhor desempenho que atendam às restrições do projeto. O trabalho se encerra com uma seção de conclusões e perspectivas futuras / This work proposes new techniques to optimize robust controllers norm of linear systems subject to structural failures, with states feedback. The design techniques used are based on LMIs (Linear Matrix Inequalities) formulated on the basis of Lyapunov’s stability theory, using Finsler’s lemma and reciprocal projection lemma. The LMIs have used the addition of the decay rate restriction, including a parameter g in the LMIs, responsible for decreasing the settling time of the feedback system. Qualitative and quantitative comparisons were made between methods of design and optimization of the robust controllers norm, seeking alternatives with small norm and better performance that meet the design constraints. The work ends with a section of conclusions and future prospects
59

Otimização de controladores robustos de sistemas dinâmicos sujeitos a falhas estruturais /

Buzachero, Luiz Francisco Sanches. January 2010 (has links)
Orientador: Edvaldo Assunção / Banca: Marcelo Carvalho Minhoto Teixeira / Banca: Celso Correia de Souza / Resumo: Neste trabalho propõem-se novas técnicas para otimização da norma de controladores robustos de sistemas dinâmicos lineares sujeitos a falhas estruturais, utilizando realimentação dos estados. As técnicas de projeto utilizadas baseiam-se em LMIs (do inglês Linear Matrix Inequalities) formuladas com base na teoria de estabilidade segundo Lyapunov, utilizando o lema de Finsler e o lema projetivo recíproco. As LMIs utilizadas tiveram o acréscimo da restrição da taxa de decaimento, incluindo o parâmetro g nas LMIs, responsável por diminuir o tempo de duração do transitório dos sistemas realimentados. Foram realizadas comparações qualitativas e quantitativas entre os métodos de projeto com otimização da norma dos controladores, visando alternativas de controladores com menor norma e melhor desempenho que atendam às restrições do projeto. O trabalho se encerra com uma seção de conclusões e perspectivas futuras / Abstract: This work proposes new techniques to optimize robust controllers norm of linear systems subject to structural failures, with states feedback. The design techniques used are based on LMIs (Linear Matrix Inequalities) formulated on the basis of Lyapunov's stability theory, using Finsler's lemma and reciprocal projection lemma. The LMIs have used the addition of the decay rate restriction, including a parameter g in the LMIs, responsible for decreasing the settling time of the feedback system. Qualitative and quantitative comparisons were made between methods of design and optimization of the robust controllers norm, seeking alternatives with small norm and better performance that meet the design constraints. The work ends with a section of conclusions and future prospects / Mestre
60

Análise de estabilidade de sistemas dinâmicos híbridos e descontínuos modelados por semigrupos /

Pena, Ismael da Silva. January 2008 (has links)
Resumo: Sistemas dinâmicos híbridos se diferenciam por exibir simultaneamente variados tipos de comportamento dinâmico (contínuo, discreto, eventos discretos) em diferentes partes do sistema. Neste trabalho foram estudados resultados de estabilidade no sentido de Lyapunov para sistemas dinâmicos híbridos gerais, que utilizam uma noção de tempo generalizado, definido em um espaço métrico totalmente ordenado. Mostrou-se que estes sistemas podem ser imersos em sistemas dinâmicos descontínuos definidos em R+, de forma que sejam preservadas suas propriedades qualitativas. Como foco principal, estudou-se resultados de estabilidade para sistemas dinâmicos descontínuos modelados por semigrupos de operadores, em que os estados do sistema pertencem à espaços de Banach. Neste caso, de forma alternativa à teoria clássica de estabilidade, os resultados não utilizam as usuais funções de Lyapunov, sendo portanto mais fáceis de se aplicar, tendo em vista a dificuldade em se encontrar tais funções para muitos sistemas. Além disso, os resultados foram aplicados à uma classe de equações diferenciais com retardo. / Abstract: Hybrid dynamical systems are characterized for showing simultaneously a variety of dynamic behaviors (continuous, discrete, discrete events) in different parts of the System. This work discusses stability results in the Lyapunov sense for general hybrid dynamical systems that use a generalized notion of time, defined in a completely ordered metric space. It has been shown that these systems may be immersed in discontinuous dynamical systems defined in R+, so that their quality properties are preserved. As the main focus, it is studied stability results for discontinuous dynamical systems modeled by semigroup operators, in which the states belong to Banach spaces. In this case, an alternative to the classical theory of stability, the results do not make use of the usual Lyapunov functions, and therefore are easier to apply, in view of the difficulty in finding such functions for many systems. Furthermore, the results were applied to a class of time-delay discontinuous differential equations. / Orientador: Geraldo Nunes Silva / Coorientador: Luís Antônio Fernandes de Oliveira / Banca: Carlos Alberto Raposo da Cunha / Banca: Waldemar Donizete Bastos / Mestre

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