Dissertations / Theses on the topic 'Switched linear/nonlinear systems'
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Lim, Hong Sun. "Design and Control of A Ropeless Elevator with Linear Switched Reluctance Motor Drive Actuation Systems." Diss., Virginia Tech, 2007. http://hdl.handle.net/10919/26541.
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Linear switched reluctance motor (LSRM) drives are investigated and proved as an alternative actuator for vertical linear transportation applications such as a linear elevator. A one-tenth scaled prototype elevator focused on a home elevator with LSRMs is designed and extensive experimental correlation is presented for the first time.
The proposed LSRM has twin stators and a set of translator poles without back-iron. The translators are placed between the two stators. The design procedures and features of the LSRM and the prototype elevator are described. The designed LSRM is validated through a finite element analysis (FEA) and experimental measurements. Furthermore, a control strategy for the prototype elevator is introduced consisting of four control loops, viz., current, force, velocity, and position feedback control loops. For force control, a novel force distribution function (FDF) is proposed and compared with conventional FDFs. A trapezoidal velocity profile is introduced to control vertical travel position smoothly during the elevator's ascent, descent, and halt operations. Conventional proportional plus integral (PI) controller is used for the current and velocity control loops and their designs are described. The proposed control strategy is dynamically simulated and experimentally correlated. Analytical and experimental results of this research prove that LSRMs are one of the strong candidates for ropeless linear elevator applications.
However, the proposed FDF is assuming that the feedback current signals are ideal currents indicating actual phase currents without any measurement disturbances mainly arising from sensor noise, DC-link voltage ripple, measurement offset, and variations in the plant model. Meanwhile, real control systems in industry have measurement disturbance problems. Phase current corrupted by measurement disturbances increases torque or force ripple, acoustic noise and EMI. Therefore, this dissertation also presents a novel current control method to suppress measurement disturbances without extra hardware.
The controller is based on an extended state observer (ESO) and a nonlinear P controller (NLP). The proposed method does not require an accurate mathematical model of system and can be implemented on a low-cost DSP controller. The proposed ESO is exploited to estimate the measurement disturbances on measured phase currents, and the proposed NLP compensates for the measurement disturbances estimated by the ESO. The performance of the proposed current control is validated through extensive dynamic simulations and experiments. Moreover, this rejection of measurement disturbances results in a reduction of force ripple and acoustic noise. Due to superior and robust current control performance, it is believed that the proposed method can be successfully applied into other motor drive systems to suppress measurement disturbances with the same promising results without extra hardware.Ph. D.
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Suto, Alan Pereira 1989. "Análise de estabilidade e desempenho H2 de sistemas do tipo Lur'e com comutação." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/265797.
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Orientador: Grace Silva DeaectoDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica
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Resumo: Esta dissertação trata do controle H2 de sistemas com comutação do tipo Lur¿e baseado no critério generalizado de Popov. Mais especificamente, uma nova regra de comutação dependente do estado e da entrada externa é proposta de tal forma a assegurar estabilidade assintótica global e um custo garantido H2 de desempenho. Esta nova estratégia de comutação é o ponto chave para a generalização do célebre critério de Popov. Como no caso de sistemas invariantes no tempo, propomos um teste de estabilidade baseado no domínio da frequência expresso em termos de uma certa combinação convexa das matrizes de espaço de estado dos subsistemas. Ademais, este teste leva em conta a inclusão de um índice de desempenho H2 cujo estudo, no presente contexto, é inédito na literatura. Os resultados teóricos obtidos são aplicados no controle de uma suspensão semi-ativa automotiva evidenciando a validade e a eficiência da função de comutação proposta
Abstract: This Master¿s dissertation deals with H2 control design of Lur¿e-type switched systems based on the generalized Popov criterion. More specifically, a novel state-input dependent switching rule is proposed in order to assure global asymptotic stability and an H2 guaranteed cost. This new switching strategy is the key issue to generalize the celebrated Popov criterion. Likewise the case of time invariant systems, we propose a frequency domain stability test that is expressed in terms of a certain convex combination of the subsystems state space matrices. Moreover, this test takes into account an H2 performance index whose study, in the present context, is new in the literature. The theoretical results are used to the control design of a car semiactive suspension and to put in evidence the validity and the efficiency of the proposed switching function
Mestrado
Mecanica dos Sólidos e Projeto Mecanico
Mestre em Engenharia Mecânica
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Ramos, Igor Thiago Minari. "Projetos de controladores robustos chaveados para sistemas não lineares baseados na decomposição em soma de quadrados /." Ilha Solteira, 2018. http://hdl.handle.net/11449/154369.
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Orientador: Marcelo Carvalho Minhoto TeixeiraResumo: Neste trabalho são propostos novos métodos de controle chaveado para uma classe de sistemas não lineares incertos utilizando a decomposição em soma de quadrados. Inicialmente é apresentada uma revisão dos conceitos e projetos de controladores baseados em desigualdades matriciais lineares (do inglês Linear Matrix Inequalities - LMIs) e a decomposição em soma de quadrados (do inglês Sum of Squares - SOS), buscando evidenciar as diferenças e vantagens das metodologias para a área de controle. Comumente são utilizados modelos fuzzy para realizar a análise da estabilidade e projeto de controladores para sistemas não lineares, e estes modelos podem ser classificados de acordo com a parte consequente linear ou polinomial. Busca-se neste trabalho evidenciar as diferenças entre os dois modelos fuzzy e a metodologia para projeto de controladores. Para o caso de sistemas cujas dinâmicas podem ser descritas apenas por funções polinomiais, serão consideradas incertezas politópicas. Então, visando flexibilizar o projeto utilizando um controlador composto por um único ganho polinomial e aumentar a região de factibilidade, são propostos controladores com ganhos polinomiais chaveados. O objetivo desta lei de chaveamento é minimizar a derivada da função de Lyapunov empregada no projeto. Considerando uma classe de sistemas não lineares mais geral, são propostos controladores com ganhos chaveados para modelos fuzzy polinomiais. A metodologia proposta não necessita do conhecimento das funções de ... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: In this manuscript new control methods are proposed for a class of uncertain nonlinear systems using a sum of squares decomposition. Initially is presented a revision of concepts and control design procedures based on Linear Matrix Inequalities (LMIs) and on sum of squares (SOS) evidencing the differences and advantages of these methodologies in the control system design. Fuzzy models are commonly used to perform stability analysis and controller design for nonlinear systems, and can be classified by a linear or polynomial consequent model. A goal of this dissertation is to compare these two methodologies in the control system design of a class of uncertain nonlinear systems. For the case of systems whose dynamics can be described only by polynomial functions will be also considered polytopic uncertainty. Therefore, in order to make the design more flexible than that obtained with only one controller with polynomial gain and increase the feasibility region, a new procedure for designing controllers with switched polynomial gains is proposed. The purpose of this switching law is to minimize the time derivative of the Lyapunov function employed in the design. For a more general class of nonlinear systems, controllers with switched gains for polynomial fuzzy models are proposed. The proposed methodology does not require the knowledge of the membership functions for an implementation of the control law. This fact is an important advantage over the many methods that consider avail... (Complete abstract click electronic access below)
Mestre
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Mayo, Maldonado Jonathan. "Switched linear differential systems." Thesis, University of Southampton, 2015. https://eprints.soton.ac.uk/383678/.
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In this thesis we study systems with switching dynamics and we propose new mathematical tools to analyse them. We show that the postulation of a global state space structure in current frameworks is restrictive and lead to potential difficulties that limit its use for the analysis of new emerging applications. In order to overcome such shortcomings, we reformulate the foundations in the study of switched systems by developing a trajectory-based approach, where we allow the use of models that are most suitable for the analysis of a each system. These models can involve sets of higher-order differential equations whose state space does not necessarily coincide. Based on this new approach, we first study closed switched systems, and we provide sufficient conditions for stability based on LMIs using the concept of multiple higher order Lyapunov function. We also study the role of positive-realness in stability of bimodal systems and we introduce the concept of positive-real completion. Furthermore, we study open switched systems by developing a dissipativity theory. We give necessary and sufficient conditions for dissipativity in terms of LMIs constructed from the coefficient matrices of the differential equations describing the modes. The relationship between dissipativity and stability is also discussed. Finally, we study the dynamics of energy distribution networks. We develop parsimonious models that deal effectively with the variant complexity of the network and the inherent switching phenomena induced by power converters. We also present the solution to instability problems caused by devices with negative impedance characteristics such as constant power loads, using tools developed in our framework.
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Babaali, Mohamed. "Switched Linear Systems: Observability and Observers." Diss., Available online, Georgia Institute of Technology, 2004:, 2004. http://etd.gatech.edu/theses/available/etd-04122004-073020/unrestricted/babaali%5Fmohamed%5F200405%5Fphd.pdf.
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Thesis (Ph. D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2004.Verriest, Erik, Committee Member ; Wardi, Yorai, Committee Member ; Yezzi, Anthony, Committee Member ; Wang, Yang, Committee Member ; Egerstedt, Magnus, Committee Chair. Vita. Includes bibliographical references (leaves 80-85).
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Alves, Uiliam Nelson Lendzion Tomaz. "Controle chaveado e chaveado suave de sistemas não lineares incertos via modelos fuzzy T-S." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/152448.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
O controle chaveado pode ser eficientemente utilizado no controle de sistemas fuzzy TakagiSugeno (T-S) incertos, que possuam funções de pertinência incertas e modelos locais conhecidos. Como estes sistemas fuzzy podem representar exatamente uma classe de sistemas não lineares incertos em uma região do espaço de estados, é interessante utilizá-los para descrever sistemas não lineares, usando no projeto do controlador o modelo fuzzy que descreve exatamente o sistema não linear. Porém, como a representação através de combinação convexa obtida é válida apenas em uma região do espaço de estados, garantias de que o estado do sistema permaneça nessa região devem ser obtidas. Neste trabalho são propostas condições que garantem a estabilização local, com a especificação da taxa decaimento, de uma classe de sistemas não lineares contínuos no tempo, incertos e com saturação no atuador, utilizando o controle chaveado. Os projetos dos controladores são realizados com base no modelo fuzzy T-S que representa exatamente o sistema não linear e os procedimentos de projeto fornecem uma região na qual as condições iniciais devam estar, tal que, o sistema não linear seja exatamente descrito pelo modelo fuzzy T-S incerto durante toda a trajetória de estado do sistema e ainda que esta trajetória permaneça dentro de uma região de operação previamente especificada. Em geral, o controle chaveado não possui restrição na frequência de chaveamento dos ganhos, o que pode levar ao chattering, que se manifesta pelo chaveamento em frequência infinitamente rápida dos ganhos de realimentação. Visando a eliminação do chattering no controle chaveado, propõe-se uma nova técnica de suavização do controle chaveado, o controle chaveado suave. Esta nova lei de controle pode ser utilizada nas mesmas condições do controle chaveado e é baseada no conceito do mínimo suave, definido neste trabalho. Além disso, são propostos procedimentos de projeto que consideram distúrbios para ambas as leis de controle chaveada e chaveada suave. Ademais, neste trabalho também se apresenta uma implementação da lei de controle chaveada em um sistema Ball Balancer fabricado pela Quanser.
The switched control can be efficiently used for controlling uncertain Takagi-Sugeno (T-S) fuzzy systems, which have uncertain membership functions and known local models. Because these fuzzy systems can exactly represent a class of uncertain nonlinear systems in a given operation region in the state space, it is interesting to use them to describe nonlinear systems, performing the controller design based on a T-S fuzzy model that exactly describes the nonlinear system. However, the perfect representation of the uncertain nonlinear system by the T-S fuzzy model as a convex combination is only valid in the operation region. Therefore, it is necessary to assure conditions such that the state of the system remains in that region. This work proposes conditions to ensure the local stabilization, with decay rate, of a class of uncertain continuoustime nonlinear systems with saturation on the actuator, using a switched control. The designs of the controllers are performed based on the T-S fuzzy model which exactly describes the nonlinear system and the design procedures provide a region in which the initial conditions must be such that the nonlinear system is exactly described by the uncertain T-S fuzzy model along the whole state trajectory of the system and this trajectory remains in a specified operation region. Usually, the switched control has no bound on the frequency of the feedback gains switching, and this can lead to chattering, which is manifested by infinitely fast frequency of the feedback gains switching. In order to avoid the chattering in the switched control, this work proposes a new technique to smooth the switched control, the smooth switched control. This new control law can be used under the same conditions as the switched control and it is based on the concept of smooth minimum, which is defined in this work. In addition, design procedures considering disturbances for both switched and smooth switched control laws are proposed. Furthermore, in this work it is also presented an implementation of the proposed switched control law in a Ball Balancer system manufactured by Quanser.
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Tse, Wilfred See Foon. "Linear equivalents of nonlinear systems." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/26652.
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Consider the following nonlinear system
[Formula Omitted]
where ϰ ∈ Rⁿ, f, ℊ₁,…,ℊｍ are C∞ function in Rⁿ and ℎ is a C∞ function in R⍴, all defined on a neighborhood of 0. The problem of finding a necessary and sufficient condition such that system (1) can be transformed to a linear controllable system by a state coordinate change and feedback has been studied
quite well. In this thesis, we first discuss a few different approaches to this problem and eventually we will show that the slightly different versions of the necessary and sufficient condition discovered are equivalent. Next we consider
system (1) with all սi,= 0 together with system (2), and study the dual problem of transforming it to a linear observable system by a state and output coordinate change. Finally, we consider briefly system (l) and (2) with nonzero սi and study the problem of transforming it to a linear system that is both completely controllable and observable. Examples are given and applications to local stabilization and estimation are discussed.Science, Faculty of
Mathematics, Department of
Graduate
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Enqvist, Martin. "Linear Models of Nonlinear Systems." Doctoral thesis, Linköping : Linköpings universitet, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-5330.
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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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Samavat, Mohmoud. "Robust control of nonlinear systems." Thesis, University of Sheffield, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327647.
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Carniato, Leonardo Ataide. "Robust H∞ switched static output feedback control design for linear switched systems subject to actuator saturation /." Ilha Solteira, 2019. http://hdl.handle.net/11449/183007.
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Orientador: Marcelo Carvalho Minhoto TeixeiraResumo: Este trabalho dedica-se ao estudo do problema de controle robusto envolvendo custo H∞ para sistemas lineares chaveados no tempo contínuo, sujeitos à saturação no atuador e com incertezas politópicas, considerando leis de chaveamento e controladores chaveados dependentes da saída da planta. Os métodos propostos oferecem novas condições baseadas em Desigualdades Matriciais Lineares (LMIs - do inglês, Linear Matrix Inequalities) para o projeto de controladores chaveados utilizando funções de Lyapunov dependentes de parâmetros. O método é baseado em um resultado recentemente introduzido na literatura para o projeto de controle H∞ de saída o qual evita igualdades matriciais lineares (LMEs - do inglês, Linear Matrix Equalities) e a necessidade de impor restrições nas matrizes de saída do sistema, isto é, as matrizes de saída do sistema podem ser de posto linha incompleto. Com o objetivo de estender estes resultados, a restrição de saturação no atuador é estudada. Análises teóricas e resultados de simulações mostram que os novos procedimentos são menos conservativos quando comparados a métodos publicados recentemente na literatura. No método proposto, as condições são uma classe particular de desigualdades matriciais bilineares (BMIs - do inglês, Bilinear Matrix Inequalities), as quais contêm alguns termos bilineares devido à multiplicação de matrizes por escalares. Estes termos estão relacionados à combinação convexa das matrizes de chaveamento bem como a outros parâmetros escalare... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: This thesis is devoted to the study of the robust H∞ control problem of continuous-time switched linear systems subject to actuator saturation with polytopic uncertainties, considering an output-dependent switching law and a switched static output feedback controller. The proposed method offers new sufficient conditions based on linear matrix inequalities (LMIs) for designing the switched controllers using parameter-dependent Lyapunov functions. The method is based on a static output feedback H∞ control design recently presented in the literature that avoids linear matrices equalities (LMEs) and the need to impose any constraints on output system matrices, that is, the output matrices of the system are allowed to be of non-full row rank. In order to extend those results, the actuator saturation constraint is also studied. Theoretical analyses and simulation results show that these new procedures are less conservative than recent methods available in the literature. The conditions of the proposed methods are a particular class of Bilinear Matrix Inequalities (BMIs), which contain some bilinear terms as the product of a matrix and a scalar, related to a suitable convex combination and scalars parameters to provide extra free dimensions in the solution space. The hybrid algorithm Differential Evolution-Linear Matrix Inequality (DE-LMI), is proposed for obtaining feasible solutions of this particular NP-hard problem. Examples show that the proposed methodologies reduce the design ... (Complete abstract click electronic access below)
Doutor
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Duan, Chang. "Analysis and Control of Switched Linear Systems Using Different Switching Strategies." Thesis, North Carolina State University, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3586263.
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As a subclass of hybrid systems that exhibiting both continuous and discrete dynamics, switched systems typically consists of a family of differential/difference equations and a rule that orchestrates the switching among them. Switched systems provide a useful mechanism to model complex dynamics that are subject to abrupt parameter variations and sudden changes of system configurations. Moreover, as an additional degree of freedom besides control laws, switching strategies can be utilized to improve system performance as seen in many engineering systems such as electronics, communication network, power systems, automobile and traffic control. Nevertheless, analysis and control design of switched systems are difficult and pose significant challenges for control researchers and engineers. This dissertation is dedicated to analysis and control design of switched linear systems using different switching strategies.
We first study the analysis and control problem of switched linear systems subject to actuator saturation under controlled switching. With a state-dependent switching strategy and linear differential inclusion (LDI) description of the saturated switched systems, both stabilization and output feedback control design problem are addressed. Initially, we proposed an approach based on polytopic differential inclusion (PDI) description of the saturated system. We then found two major drawbacks of this approach: 1) Computational cost grows drastically when the number of control inputs increases. 2) A conservative set mapping results in conservativeness in the synthesis conditions. Thus we proposed another approach based norm-bounded differential inclusion (NDI) characterization of the saturated system that performs better than the previous approach in these two aspects mentioned above.
We then investigate the inherent chattering behavior of the well-known state-dependent minimum switching strategy since chattering is undesirable in practice. To mitigate chattering, we developed a relaxed min-switching strategy based on the idea that switching is not forced whenever a different subsystem obtains the minimum of the Lyapunov function but held until the minimum of the Lyapunov function falls below the Lyapunov function of the active subsystem by certain margin. Based on this idea, a tunable parameter, which is related to how large the margin will be, is introduced into the switching rule. Consequently, stability analysis and control synthesis conditions are derived in terms of modified Lyapunov-Metzler inequalities.
The above mentioned relaxed min-switching strategy can effectively reduce the frequency of the switching. However, as a state-dependent switching strategy, it cannot guarantee how slow the switching can be in terms of the activation time of each subsystem. This motivates us to consider time-driven switching strategies. The so-called ”dwell-time” and ”average dwell-time” based switching strategies are the most popular time-driven switching strategies. Nevertheless, they are restricted to the class of switched systems with some or all stable subsystems. In view of this, a novel mixed state-dependent and time-driven switching strategy is developed for switched systems with all unstable subsystems. It guarantees the stability of the switched system with a sufficiently small dwell time by enforcing a decrement of the Lyapunov function at each switch. Moreover, it provides a more general framework of analyzing switched linear systems as it contains the min-switching and the relaxed min-switching as special cases when dwell-time is not concerned. When dwell-time is concerned, it eliminates the chattering behavior commonly observed in min-switching based designs.
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Lee, Byeong-Seok. "Linear Switched Reluctance Machine Drives with Electromagnetic Levitation and Guidance Systems." Diss., Virginia Tech, 2000. http://hdl.handle.net/10919/29751.
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Many electrically propelled, and magnetically levitated and guided actuation systems (maglev) use either linear induction or synchronous machine topologies. From the cost, reliability, fault tolerance, and phase independence points of view, linear switched reluctance topologies are attractive for transportation application. This thesis investigates a novel topology in which a linear switched reluctance machine (LSRM) propulsion drive is incorporated in the magnetically levitated and guided vehicle. Designs of the LSRM and dc electromagnet, analytical aspects of modeling and dynamics of the vehicle, and closed loop control of propulsion, levitation, and guidance systems are discussed with comprehensive simulations and experimental results.
Due to the lack of standard design procedure for LSRM, a novel design procedure is proposed using the current knowledge and design procedure of rotating switched reluctance machines. Analysis procedures for the phase winding inductance, propulsion and normal forces with translator position are developed with a lumped-parameter magnetic circuit model and the results from it are verified with two-dimensional finite element analysis. Extensive experimental correlation of inductance, propulsion and normal forces to validate the analysis and design procedure is presented.
For the stable operation of the electromagnetic levitation and guidance systems, which have inherent unstable characteristics, the air gap position and force/current control loops are designed using PID (or PD) and PI controllers, respectively, and implemented and tested. The step-by-step design procedures for each controller are systematically derived. A feedforward compensation strategy for the levitation air gap control is proposed to reject the external force disturbance mainly caused by the normal force component generated in the LSRM propulsion drive system. The reduction of mechanical vibration and hence the enhancement of ride quality is achieved. Extensive dynamic simulations and experimental results for the integrated maglev system are presented with a 6 m long prototype system. Experimental correlation proves the validity of the controller design procedure based on the single-input and single-output model, and shows the feasibility of the LSRM-propelled electromagnetic levitation and guidance systems.
A novel maglev topology in which only two sets of LSRMs are utilized to control individually propulsion, levitation, and guidance forces is proposed. One set of the linear switched reluctance actuator produces the levitation and propulsion forces and the other set generates the propulsion and guidance forces. The proposed architecture, thereby, obviates the need for design, development, and implementation of separate actuation systems for individual control of propulsion, levitation, and guidance forces and in contrast to most of the present practice. Further, the proposed system utilizes each of the linear switched reluctance actuation system for producing the propulsion force, thereby giving an overall high force density package for the entire system. The feasibility of the proposed system by finite element analysis is demonstrated.Ph. D.
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Huang, Jungang. "Spontaneous optical fractals in linear & nonlinear systems." Thesis, University of Salford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491053.
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This thesis concerns the generation and characterisation of optical fractals. Chapter 1 presents a brief introduction to fractals and fractal dimensions, and then a review of contexts where fractal concepts have arisen in optics. These contexts are classified in terms of whether the fractal-generating mechanisms at work are linear or nonlinear.
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Walker, Jimmie Dale 1977. "Analysis of primitive linear and nonlinear stochastic systems." Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/86841.
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Thesis (M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2001."September 29, 2000."
Includes bibliographical references (p. 91-92).
by Jimmie Dale Walker, III.
M.Eng.
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Toenger, Shanti. "Linear and Nonlinear Rogue Waves in Optical Systems." Thesis, Besançon, 2016. http://www.theses.fr/2016BESA2029/document.
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Ces travaux de thèse présentent l’étude des différentes classes d’effets linéaires et non-linéaires en optiquequi génèrent des événements extrêmes dont les propriétés sont analogues à celles des « vagues scélérates » destructrices qui apparaissent à la surface des océans. La thèse commence avec un bref aperçu de l’analogie physique entre la localisation d’onde dans les systèmes hydrodynamique et les systèmes optique, pour lesquels nous décrivons les mécanismes de génération de vagues scélérates linéaire et non-linéaire. Nous présentons ensuite quelques résultats numérique et expérimentaux de la génération de vagues scélérates dans un système optique linéaire dans le cas d’une propagation spatiale d’un champ optique qui présenteune phase aléatoire, où nous interprétons les résultats obtenus en terme de caustiques optiques localisées.Nous considérons ensuite les vagues scélérates obtenues dans des systèmes non-linéaires qui présentent une instabilité de modulation décrite par l’équation de Schrödinger non-linéaire (ESNL). Nous présentons une étude numérique détaillée comparant les caractéristiques spatio-temporelles des structures localisées obtenues dans les simulation numérique avec les différentes solutions analytiques obtenues à partir de l’ESNL.Deux études expérimentales d’instabilités de modulation sont ensuite effectuées. Dans la première, nous présentons des résultats expérimentaux qui étudient les propriétés d’instabilité de modulation en utilisant un système d’agrandissement temporel par lentille temporelle; dans la deuxième, nous rapportons des résultats expérimentaux sur les propriétés des instabilités de modulation dans le domaine fréquentiel en utilisant une technique de mesure spectrale en temps-réel. Cette dernière étude examine l’effet sur la bande spectrale et surla stabilité d’un faible champ perturbateur. Tous les résultats expérimentaux sont comparés avec la simulation d’ESNL et abordés en termes des propriétés qualitatives d’instabilité de modulation. Dans toutes ces études,différentes propriétés statistiques sont analysées en rapport avec l’apparition des vagues scélératesThis thesis describes the study of several different classes of linear and nonlinear effects in optics that generatelarge amplitude extreme events with properties analogous to the destructive “rogue waves” on the surface of theocean. The thesis begins with a brief overview of the analogous physics of wave localisation in hydrodynamicand optical systems, where we describe linear and nonlinear rogue wave generating mechanisms in bothcases. We then present numerical and experimental results for rogue wave generation in a linear opticalsystem consisting of free space propagation of a spatial optical field with random phase. Computed statisticsbetween experiment and modelling are in good agreement, and we interpret the results obtained in termsof the properties of localised optical caustics. We then consider rogue waves in the nonlinear system ofmodulation instability described by the Nonlinear Schrodinger Equation (NLSE), and a detailed numericalstudy is presented comparing the spatio-temporal characteristics of localised structures seen from numericalsimulations with different known analytic solutions to the NLSE. Two experimental studies of modulationinstability are then reported. In the first, we present experimental results studying the properties of modulationinstability using a time-lens magnifier system; in the second, we report experimental results studying thefrequency-domain properties of modulation instability using real-time spectral measurements. The latter studyexamines the effect of a weak seed field on spectral bandwidth and stability. All experimental results arecompared with the NLSE simulations and discussed in terms of the qualitative properties of modulationinstability, in order to gain new insights into the complex dynamics associated with nonlinear pulse propagation.In all of these studies, different statistical properties are analised in relation to the emergence of rogue waves
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Anand, Mantrala. "Transition through resonance in linear and nonlinear systems /." Online version of thesis, 1991. http://hdl.handle.net/1850/10995.
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Tucher, Christopher A. "Steady-state oscillations of linear and nonlinear systems /." Online version of thesis, 1992. http://hdl.handle.net/1850/10990.
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Schweickhardt, Tobias. "Nonlinearity assessment and linear control of nonlinear systems." [S.l. : s.n.], 2006. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-29806.
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Cardwell, E. A. "Stability of linear and nonlinear delay-differential systems." Thesis, University of Bath, 1995. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.295447.
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Kloiber, Tobias [Verfasser]. "Constructive Passivity-Based Control of Smooth and Switched Nonlinear Systems / Tobias Kloiber." Aachen : Shaker, 2015. http://d-nb.info/1070152137/34.
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Ohlsson, Henrik, and Lennart Ljung. "Identification of switched linear regression models using sum-of-norms regularization." Linköpings universitet, Reglerteknik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-92612.
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This paper proposes a general convex framework for the identification of switched linear systems. The proposed framework uses over-parameterization to avoid solving the otherwise combinatorially forbidding identification problem, and takes the form of a least-squares problem with a sum-of-norms regularization, a generalization of the ℓ1-regularization. The regularization constant regulates the complexity and is used to trade off the fit and the number of submodels.Funding Agencies|Swedish foundation for strategic research in the center MOVIII||Swedish Research Council in the Linnaeus center CADICS||European Research Council|267381|Sweden-America Foundation||Swedish Science Foundation||
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Wang, Ying-tsai 1955. "Frequency response of nonlinear pneumatic systems /." The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487266362339231.
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Mazanti, Guilherme. "Stability and stabilization of linear switched systems in finite and infinite dimensions." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX045/document.
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Motivée par les travaux précédents sur la stabilisation de systèmes à excitation persistante, cette thèse s'intéresse à la stabilité et à la stabilisation de systèmes linéaires à commutation en dimensions finie et infinie. Après une introduction générale présentant les principales motivations et les résultats importants de la littérature, on aborde quatre sujets.On commence par l'étude d'un système linéaire en dimension finie à commutation aléatoire. Le temps passé en chaque sous-système $i$ est choisi selon une loi de probabilité ne dépendant que de $i$, les commutations entre sous-systèmes étant déterminées par une chaine de Markov discrète. On caractérise les exposants de Lyapunov en appliquant le Théorème Ergodique Multiplicatif d'Oseledets à un système associé en temps discret, et on donne une expression pour l'exposant de Lyapunov maximal. Ces résultats sont appliqués à un système de contrôle à commutation. Sous une hypothèse de contrôlabilité, on montre que ce système peut être stabilisé presque surement avec taux de convergence arbitraire, ce qui est en contraste avec les systèmes déterministes à excitation persistante.On considère ensuite un système de $N$ équations de transport avec amortissement interne à excitation persistante, couplées linéairement par le bord à travers une matrice $M$, ce qui peut être vu comme un système d'EDPs sur un réseau étoilé. On montre que, si l'activité de l'amortissement intermittent est déterminée par des signaux à excitation persistante, alors, sous des bonnes hypothèses sur $M$ et sur la rationalité des rapports entre les longueurs des arêtes du réseau, ce système est exponentiellement stable, uniformément par rapport aux signaux à excitation persistante. Ce résultat est montré grâce à une formule explicite pour les solutions du système, qui permet de bien suivre les effets de l'amortissement intermittent.Le sujet suivant que l'on considère est le comportement asymptotique d'équations aux différences non-autonomes. On obtient une formule explicite pour les solutions en termes des conditions initiales et de certains coefficients matriciels dépendants du temps, qui généralise la formule obtenue pour le système de $N$ équations de transport. Le comportement asymptotique des solutions est caractérisé à travers les coefficients matriciels. Dans le cas d'équations aux différences à commutation arbitraire, on obtient un résultat de stabilité qui généralise le critère de Hale--Silkowski pour les systèmes autonomes. Grâce à des transformations classiques d'EDPs hyperboliques en équations aux différences, on applique ces résultats au transport et à la propagation d'ondes sur des réseaux.Finalement, la formule explicite précédente est généralisée à une équation aux différences contrôlée, dont la contrôlabilité est alors analysée. La contrôlabilité relative est caractérisée à travers un critère algébrique sur les coefficients matriciels de la formule explicite, ce qui généralise le critère de Kalman. On compare également la contrôlabilité relative pour des retards différents en termes de leur structure de dépendance rationnelle, et on donne une borne sur le temps minimal de contrôlabilité. Pour des systèmes avec retards commensurables, on montre que la contrôlabilité exacte est équivalente à l'approchée et on donne un critère qui les caractérise. On analyse également la contrôlabilité exacte et approchée de systèmes en dimension $2$ avec deux retards sans l'hypothèse de commensurabilitéMotivated by previous work on the stabilization of persistently excited systems, this thesis addresses stability and stabilization issues for linear switched systems in finite and infinite dimensions. After a general introduction presenting the main motivations and important results from the literature, we analyze four problems.The first system we study is a linear finite-dimensional random switched system. The time spend on each subsystem $i$ is chosen according to a probability law depending only on $i$, and the switches between subsystems are determined by a discrete Markov chain. We characterize the Lyapunov exponents by applying Oseledets' Multiplicative Ergodic Theorem to an associated discrete-time system, and provide an expression for the maximal Lyapunov exponent. These results are applied to a switched control system, showing that, under a controllability hypothesis, almost sure stabilization can be achieved with arbitrarily large decay rates, a situation in contrast to deterministic persistently excited systems.We next consider a system of $N$ transport equations with intermittent internal damping, linearly coupled by their boundary conditions through a matrix $M$, which can be seen as a system of PDEs on a star-shaped network. We prove that, if the activity of the intermittent damping terms is determined by persistently exciting signals, then, under suitable hypotheses on $M$ and on the rationality of the ratios between the lengths of the network edges, such system is exponentially stable, uniformly with respect to the persistently exciting signals. The proof of this result is based on an explicit representation formula for the solutions of the system, which allows one to efficiently track down the effects of the intermittent damping.The following topic we address is the asymptotic behavior of non-autonomous difference equations. We obtain an explicit representation formula for their solutions in terms of their initial conditions and some time-dependent matrix coefficients, which generalizes the one for the system of $N$ transport equations. The asymptotic behavior of solutions is characterized in terms of the matrix coefficients. In the case of difference equations with arbitrary switching, we obtain a stability result which generalizes Hale--Silkowski criterion for autonomous systems. Using classical transformations of hyperbolic PDEs into difference equations, we apply our results to transport and wave propagation on networks.Finally, we generalize the previous representation formula to a controlled difference equation, whose controllability is then analyzed. Relative controllability is characterized in terms of an algebraic property on the matrix coefficients from the explicit formula, generalizing Kalman criterion. We also compare the relative controllability for different delays in terms of their rational dependence structure, and provide a bound on the minimal controllability time. Exact and approximate controllability for systems with commensurable delays are characterized and proved to be equivalent. We also describe exact and approximate controllability for two-dimensional systems with two delays not necessarily commensurable
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Ait, Ladel Ayyoub. "Commande tolérante aux défauts des systèmes à multimodèles : application à des systèmes à multi-source d'énergie." Electronic Thesis or Diss., Aix-Marseille, 2022. http://theses.univ-amu.fr.lama.univ-amu.fr/220330_AITLADEL_882kmyqu655hkbca383zrkcz402ihwf_TH.pdf.
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Cette thèse traite des problématiques de détection/estimation des défauts et de commande tolérante aux défauts par conception intégrée. L’objectif est de concevoir des stratégies de contrôle capables de maintenir une performance robuste et acceptable même en présence de défauts. Les systèmes considérés sont de nature dynamique et sont à multi-modèles. Les approches proposées, dans le cadre de la thèse, consistent à formaliser la conception intégrée des unités de détection/estimation et de contrôle tolérant aux défauts sous la forme d’inégalités matricielles linéaires afin de surmonter la difficulté posée par le couplage observateur/contrôleur. Ces approches offrent la possibilité de considérer les différentes interactions entre le système, l’unité de détection/estimation et l’unité de contrôle. Cela permet d’assurer une analyse de stabilité globale du système en boucle fermée, et des performances robustes en termes de détection/estimation, de contrôle et de compensation des défauts. La thèse est composée principalement de trois parties. Dans la première partie, les résultats sur le contrôle, en présence de défauts capteurs ou actionneurs, sont établis pour les systèmes linéaires à commutation. Dans la deuxième partie, des extensions aux systèmes non-linéaires à commutation avec des défauts de capteurs et d’actionneurs sont proposées. Finalement, la troisième partie est constituée d’une étude complète d’un système à base d’énergies renouvelables. Il s’agit d’un système de nature multi-sources et multi-charges conçu pour répondre à plusieurs demandes et est assujetti à l’intermittence des énergies renouvelablesThis thesis deals with the fault detection/estimation and fault-tolerant control challenges through integrated design. The aim is to design control strategies able to maintain robust and acceptable performance even in the presence of faults. The considered systems are dynamic in nature and are multi-model. The approaches proposed in this thesis consist in formalizing the integrated design of the detection/estimation and fault-tolerant control units in the form of linear matrix inequalities to overcome the difficulty posed by the observer/controller coupling. These approaches provide the ability to consider the different interactions between the system, the detection/estimation unit, and the control unit. Therefore, ensuring a global stability analysis of the closed-loop system and robust performances in terms of detection/estimation, control, and fault compensation. The thesis is mainly composed of three parts. In the first part, results on the control in the presence of sensor or actuator faults are established for switched linear systems. In the second part, extensions to switched nonlinear systems with sensor and actuator faults are proposed. Finally, the third part consists of a complete study of a renewable energy system. It is a multi-source/multi-load system designed to meet multiple demands and is subject to the intermittency of renewable energies
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Kartal, Elcin. "Metamodeling Complex Systems Using Linear And Nonlinear Regression Methods." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/2/12608930/index.pdf.
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Metamodeling is a very popular approach for the approximation of complex systems. Metamodeling techniques can be categorized according to the type of regression method employed as linear and nonlinear models. The Response Surface Methodology (RSM) is an example of linear regression. In classical RSM metamodels, parameters are estimated using the Least Squares (LS) Method. Robust regression techniques, such as Least Absolute Deviation (LAD) and M-regression, are also considered in this study due to the outliers existing in data sets. Artificial Neural Networks (ANN) and Multivariate Adaptive Regression Splines (MARS) are examples for non-linear regression technique. In this thesis these two nonlinear metamodeling techniques are constructed and their performances are compared with the performances of linear models.
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Paruchuri, Sai Tej. "Modeling and Estimation of Linear and Nonlinear Piezoelectric Systems." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/100484.
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A bulk of the research on piezoelectric systems in recent years can be classified into two categories, 1) studies of linear piezoelectric oscillator arrays, 2) studies of nonlinear piezoelectric oscillators. This dissertation derives novel linear and nonlinear modeling and estimation methods for such piezoelectric systems. In the first part, this work develops modeling and design methods for Piezoelectric Subordinate Oscillator Arrays (PSOAs) for the wideband vibration attenuation problem. PSOAs offer a straightforward and low mass ratio solution to cancel out the resonant peaks in a host structure's frequency domain. Further, they provide adaptability through shunt tuning, which gives them the ability to recover performance losses because of structural parameter errors. This dissertation studies the derivation of governing equations that result in a closed-form expression for the frequency response function. It also analyzes systematic approaches to assign distributions to the nondimensional parameters in the frequency response function to achieve the desired flat-band frequency response. Finally, the effectiveness of PSOAs under ideal and nonideal conditions are demonstrated in this dissertation through extensive numerical and experimental studies. The concept of performance recovery, introduced in empirical studies, gives a measure of the PSOA's effectiveness in the presence of disorder before and after capacitive tuning. The second part of this dissertation introduces novel modeling and estimation methods for nonlinear piezoelectric oscillators. Traditional modeling techniques require knowledge of the structure as well as the source of nonlinearity. Data-driven modeling techniques used extensively in recent times build approximations. An adaptive estimation method, that uses reproducing kernel Hilbert space (RKHS) embedding methods, can estimate the underlying nonlinear function that governs the system's dynamics. A model built by such a method can overcome some of the limitations of the modeling approaches mentioned above. This dissertation discusses (i) how to construct the RKHS based estimator for the piezoelectric oscillator problem, (ii) how to choose kernel centers for approximating the RKHS, and (iii) derives sufficient conditions for convergence of the function estimate to the actual function. In each of these discussions, numerical studies are used to show the RKHS based adaptive estimator's effectiveness for identifying linearities in piezoelectric oscillators.Doctor of Philosophy
Piezoelectric materials are materials that generate an electric charge when mechanical stress is applied, and vice versa, in a lossless transformation. Engineers have used piezoelectric materials for a variety of applications, including vibration control and energy harvesting. This dissertation introduces (1) novel methods for vibration attenuation using an array of piezoelectric oscillators, and (2) methods to model and estimate the nonlinear behavior exhibited by piezoelectric materials at very high mechanical forces or electric charges. Arrays of piezoelectric oscillators attached to a host structure are termed piezoelectric subordinate oscillator arrays (PSOAs). With the careful design of PSOAs, we show that we can reduce the vibration of the host structure. This dissertation analyzes methodologies for designing PSOAs and illustrates their vibration attenuation capabilities numerically and experimentally. The numerical and experimental studies also illustrate the robustness of PSOAs. In the second part of this dissertation, we analyze reproducing kernel Hilbert space embedding methods for adaptive estimation of nonlinearities in piezoelectric systems. Kernel methods are extensively used in machine learning, and control theorists have studied adaptive estimation of functions in finite-dimensional spaces. In this work, we adapt kernel methods for adaptive estimation of functions in infinite-dimensional spaces that appear while modeling piezoelectric systems. We derive theorems that ensure convergence of function estimates to the actual function and develop algorithms for careful selection of the kernel basis functions.
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Fuster, Criado Laura. "Linear and nonlinear room compensation of audio rendering systems." Doctoral thesis, Universitat Politècnica de València, 2016. http://hdl.handle.net/10251/59459.
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[EN] Common audio systems are designed with the intent of creating real and immersive scenarios that allow the user to experience a particular acoustic sensation that does not depend on the room he is perceiving the sound. However, acoustic devices and multichannel rendering systems working inside a room, can impair the global audio effect and thus the 3D spatial sound.
In order to preserve the spatial sound characteristics of multichannel rendering techniques, adaptive filtering schemes are presented in this dissertation to compensate these electroacoustic effects and to achieve the immersive sensation of the desired acoustic system. Adaptive filtering offers a solution to the room equalization problem that is doubly interesting. First of all, it iteratively solves the room inversion problem, which can become computationally complex to obtain when direct methods are used. Secondly, the use of adaptive filters allows to follow the time-varying room conditions.
In this regard, adaptive equalization (AE) filters try to cancel the echoes due to the room effects. In this work, we consider this problem and propose effective and robust linear schemes to solve this equalization problem by using adaptive filters. To do this, different adaptive filtering schemes are introduced in the AE context. These filtering schemes are based on three strategies previously introduced in the literature: the convex combination of filters, the biasing of the filter weights and the block-based filtering. More specifically, and motivated by the sparse nature of the acoustic impulse response and its corresponding optimal inverse filter, we introduce different adaptive equalization algorithms.
In addition, since audio immersive systems usually require the use of multiple transducers, the multichannel adaptive equalization problem should be also taken into account when new single-channel approaches are presented, in the sense that they can be straightforwardly extended to the multichannel case.
On the other hand, when dealing with audio devices, consideration must be given to the nonlinearities of the system in order to properly equalize the electroacoustic system. For that purpose, we propose a novel nonlinear filtered-x approach to compensate both room reverberation and nonlinear distortion with memory caused by the amplifier and loudspeaker devices.
Finally, it is important to validate the algorithms proposed in a real-time implementation. Thus, some initial research results demonstrate that an adaptive equalizer can be used to compensate room distortions.[ES] Los sistemas de audio actuales están diseñados con la idea de crear escenarios reales e inmersivos que permitan al usuario experimentar determinadas sensaciones acústicas que no dependan de la sala o situación donde se esté percibiendo el sonido. Sin embargo, los dispositivos acústicos y los sistemas multicanal funcionando dentro de salas, pueden perjudicar el efecto global sonoro y de esta forma, el sonido espacial 3D. Para poder preservar las características espaciales sonoras de los sistemas de reproducción multicanal, en esta tesis se presentan los esquemas de filtrado adaptativo para compensar dichos efectos electroacústicos y conseguir la sensación inmersiva del sistema sonoro deseado. El filtrado adaptativo ofrece una solución al problema de salas que es interesante por dos motivos. Por un lado, resuelve de forma iterativa el problema de inversión de salas, que puede llegar a ser computacionalmente costoso para los métodos de inversión directos existentes. Por otro lado, el uso de filtros adaptativos permite seguir las variaciones cambiantes de los efectos de la sala de escucha. A este respecto, los filtros de ecualización adaptativa (AE) intentan cancelar los ecos introducidos por la sala de escucha. En esta tesis se considera este problema y se proponen esquemas lineales efectivos y robustos para resolver el problema de ecualización mediante filtros adaptativos. Para conseguirlo, se introducen diferentes esquemas de filtrado adaptativo para AE. Estos esquemas de filtrado se basan en tres estrategias ya usadas en la literatura: la combinación convexa de filtros, el sesgado de los coeficientes del filtro y el filtrado basado en bloques. Más especificamente y motivado por la naturaleza dispersiva de las respuestas al impulso acústicas y de sus correspondientes filtros inversos óptimos, se presentan diversos algoritmos adaptativos de ecualización específicos. Además, ya que los sistemas de audio inmersivos requieren usar normalmente múltiples trasductores, se debe considerar también el problema de ecualización multicanal adaptativa cuando se diseñan nuevas estrategias de filtrado adaptativo para sistemas monocanal, ya que éstas deben ser fácilmente extrapolables al caso multicanal. Por otro lado, cuando se utilizan dispositivos acústicos, se debe considerar la existencia de no linearidades en el sistema elactroacústico, para poder ecualizarlo correctamente. Por este motivo, se propone un nuevo modelo no lineal de filtrado-x que compense a la vez la reverberación introducida por la sala y la distorsión no lineal con memoria provocada por el amplificador y el altavoz. Por último, es importante validar los algoritmos propuestos mediante implementaciones en tiempo real, para asegurarnos que pueden realizarse. Para ello, se presentan algunos resultados experimentales iniciales que muestran la idoneidad de la ecualización adaptativa en problemas de compensación de salas.
[CAT] Els sistemes d'àudio actuals es dissenyen amb l'objectiu de crear ambients reals i immersius que permeten a l'usuari experimentar una sensació acústica particular que no depèn de la sala on està percebent el so. No obstant això, els dispositius acústics i els sistemes de renderització multicanal treballant dins d'una sala poden arribar a modificar l'efecte global de l'àudio i per tant, l'efecte 3D del so a l'espai. Amb l'objectiu de conservar les característiques espacials del so obtingut amb tècniques de renderització multicanal, aquesta tesi doctoral presenta esquemes de filtrat adaptatiu per a compensar aquests efectes electroacústics i aconseguir una sensació immersiva del sistema acústic desitjat. El filtrat adaptatiu presenta una solució al problema d'equalització de sales que es interessant baix dos punts de vista. Per una banda, el filtrat adaptatiu resol de forma iterativa el problema inversió de sales, que pot arribar a ser molt complexe computacionalment quan s'utilitzen mètodes directes. Per altra banda, l'ús de filtres adaptatius permet fer un seguiment de les condicions canviants de la sala amb el temps. Més concretament, els filtres d'equalització adaptatius (EA) intenten cancel·lar els ecos produïts per la sala. A aquesta tesi, considerem aquest problema i proposem esquemes lineals efectius i robustos per a resoldre aquest problema d'equalització mitjançant filtres adaptatius. Per aconseguir-ho, diferent esquemes de filtrat adaptatiu es presenten dins del context del problema d'EA. Aquests esquemes de filtrat es basen en tres estratègies ja presentades a l'estat de l'art: la combinació convexa de filtres, el sesgat dels pesos del filtre i el filtrat basat en blocs. Més concretament, i motivat per la naturalesa dispersa de la resposta a l'impuls acústica i el corresponent filtre òptim invers, presentem diferents algorismes d'equalització adaptativa. A més a més, com que els sistemes d'àudio immersiu normalment requereixen l'ús de múltiples transductors, cal considerar també el problema d'equalització adaptativa multicanal quan es presenten noves solucions de canal simple, ja que aquestes s'han de poder estendre fàcilment al cas multicanal. Un altre aspecte a considerar quan es treballa amb dispositius d'àudio és el de les no linealitats del sistema a l'hora d'equalitzar correctament el sistema electroacústic. Amb aquest objectiu, a aquesta tesi es proposa una nova tècnica basada en filtrat-x no lineal, per a compensar tant la reverberació de la sala com la distorsió no lineal amb memòria introduïda per l'amplificador i els altaveus. Per últim, és important validar la implementació en temps real dels algorismes proposats. Amb aquest objectiu, alguns resultats inicials demostren la idoneïtat de l'equalització adaptativa en problemes de compensació de sales.
Fuster Criado, L. (2015). Linear and nonlinear room compensation of audio rendering systems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/59459
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Meair, Jonathan Isaac. "Aspects of Linear and Nonlinear Transport in Mesoscopic Systems." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/301737.
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We begin this thesis with a general introduction to mesoscopic physics and the scattering approach to transport. The subsequent chapters are broken up into two related topics in mesoscopic physics. The first of these topics, in Chapters 2 and 3, focuses on developing a scattering approach to treat weakly nonlinear transport of charge and heat through mesoscopic systems. In Chapter 2 we develop a weakly nonlinear theory for thermoelectric transport in purely metallic systems while emphasizing its importance in the study of thermoelectric efficiencies. In Chapter 3 we extend the theory to treat electric current rectification in metallic systems contacted to superconducting islands. The next topic we discuss is on how electric current noise can be used to make measurements in mesoscopic systems. In Chapter 4 we demonstrate that electric current noise in a temperature probe can provide a measure of an "effective" local temperature in a non-equilibrium system. We show that this electrical measurement is consistent with a thermal measurement of the temperature probe, within the limit of the validity of a Sommerfeld expansion. Finally, in Chapter 5 we describe how current noise can be used to measure spin accumulation in reservoirs connected to a scatterer with strong spin-orbit coupling. Throughout this thesis we emphasize conservation relations and provide general multi-terminal expressions whenever possible.
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Cocetti, Matteo. "Nonlinear and Hybrid Feedbacks with Continuous-Time Linear Systems." Thesis, Toulouse, INSA, 2019. http://www.theses.fr/2019ISAT0014/document.
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Dans cette thèse, nous étudions la rétroaction de systèmes linéaires invariants dans le temps reliés entre eux par trois blocs non linéaires spécifiques : un opérateur de lecture/arrêt, un mécanisme de réinitialisation de commutation et une zone morte adaptative. Cette configuration ressemble au problème de Lure étudié dans le cadre de stabilité absolue, mais les types de non-linéarités considérés ici ne satisfont pas (en général) une condition sectorielle. Ces blocs non linéaires donnent lieu à toute une série de phénomènes intéressants, tels que des ensembles compacts d’équilibres, des ensembles hybrides oméga-limites et des contraintes d’état. Tout au long de la thèse, nous utilisons le formalisme des systèmes hybrides pour décrire ces phénomènes et analyser ces boucles. Nous obtenons des conditions de stabilité très précises qui peuvent être formulées sous forme d’inégalités matricielles linéaires, donc vérifiables avec des solveurs numériques efficaces. Enfin, nous appliquons les résultats théoriques à deux applications automobilesIn this thesis we study linear time-invariant systems feedback interconnected with three specific nonlinear blocks; a play/stop operator, a switching-reset mechanism, and an adaptive dead-zone. This setup resembles the Lure problem studied in the absolute stability framework, but the types of nonlinearities considered here do not satisfy (in general) a sector condition. These nonlinear blocks give rise to a whole range of interesting phenomena, such as compact sets of equilibria, hybrid omega-limit sets, and state constraints. Throughout the thesis, we use the hybrid systems formalism to describe these phenomena and to analyze these loops. We obtain sharp stability conditions that can be formulated as linear matrix inequalities, thus verifiable with numerically efficient solvers. Finally, we apply the theoretical findings to two automotive applications
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Cocetti, Matteo. "Nonlinear and Hybrid Feedbacks with Continuous-Time Linear Systems." Doctoral thesis, Università degli studi di Trento, 2019. https://hdl.handle.net/11572/368312.
Full textAbstract:
In this thesis we study linear time-invariant systems feedback interconnected with three specific nonlinear blocks; a play/stop operator, a switching-reset mechanism, and an adaptive dead-zone. This setup resembles the Lure problem studied in the absolute stability framework, but the types of nonlinearities considered here do not satisfy
(in general) a sector condition. These nonlinear blocks give rise to a whole range of interesting phenomena, such as compact sets of equilibria, hybrid omega-limit sets, and state constraints. Throughout the thesis, we use the hybrid systems formalism to describe these
phenomena and to analyze these loops. We obtain sharp stability conditions that can be formulated as linear matrix inequalities, thus verifiable with numerically efficient solvers.
Finally, we apply the theoretical findings to two automotive applications.
32
Cocetti, Matteo. "Nonlinear and Hybrid Feedbacks with Continuous-Time Linear Systems." Doctoral thesis, University of Trento, 2019. http://eprints-phd.biblio.unitn.it/3675/1/phdthesis-matteococetti.pdf.
Full textAbstract:
In this thesis we study linear time-invariant systems feedback interconnected with three specific nonlinear blocks; a play/stop operator, a switching-reset mechanism, and an adaptive dead-zone. This setup resembles the Lure problem studied in the absolute stability framework, but the types of nonlinearities considered here do not satisfy
(in general) a sector condition. These nonlinear blocks give rise to a whole range of interesting phenomena, such as compact sets of equilibria, hybrid omega-limit sets, and state constraints. Throughout the thesis, we use the hybrid systems formalism to describe these
phenomena and to analyze these loops. We obtain sharp stability conditions that can be formulated as linear matrix inequalities, thus verifiable with numerically efficient solvers.
Finally, we apply the theoretical findings to two automotive applications.
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Feng, Ming. "Local modelling and control of nonlinear systems." Thesis, University of Southampton, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.326788.
Full text
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Benouarets, Mourad. "Some design methods for linear and nonlinear controllers." Thesis, University of Sussex, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.333454.
Full text
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Santarelli, Keith R. (Keith Robert) 1977. "On the synthesis of switched output feedback controllers for linear, time-invariant systems." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/38690.
Full textAbstract:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 189-193).
The theory of switching systems has seen many advances in the past decade. Its beginnings were founded primarily due to the physical limitations in devices to implement control such as relays, but today there exists a strong interest in the development of switching systems where switching is introduced as a means of increasing performance. With the newer set of problems that arise from this viewpoint comes the need for many new tools for analysis and design. Analysis tools which include, for instance, the celebrated work on multiple Lyapunov functions are extensive. Tools for the design of switched systems also exist, but, in many cases, the method of designing stabilizing switching laws is often a separate process from the method which is used to determine the set of vector fields between which switching takes place. For instance, one typical method of designing switching controllers for linear, time-invariant (LTI) systems is to first design a set of stabilizing LTI controllers using standard LTI methods, and then design a switching law to increase performance. While such design algorithms can lead to increases in performance, they often impose restrictions that do not allow the designer to take full advantage of the switching architecture being considered.
(cont.) For instance, if one switches between controllers that are individually stabilizing (without any switching), then, effectively, one is forced to switch only between stable systems and, hence, cannot take advantage of the potential benefits of switching between unstable systems in a stable way. It is, therefore, natural to wonder whether design algorithms can be developed which simultaneously design both the set of controllers to be switched and a stabilizing switching law. The work investigated here attempts to take a small step in the above direction. We consider a simple switching architecture that implements switched proportional gain control for second order LTI systems. Examination of this particular structure is motivated by its mathematical simplicity for ease of analysis (and, hence, as a means of gaining insight into the problem-at-large), but, as we will see, the design techniques investigated here can be extended to a larger class of (higher order, potentially non-linear and/or time-varying) systems using standard tools from robust control. The overall problem we investigate is the ability to create algorithms to simultaneously determine a set of switching gains and an associated switching law for a particular plant and performance objective.
(cont.) After determining a set of necessary and sufficient conditions for a given second order plant to be stabilizable via the given switching architecture, we synthesize an algorithm for constructing controllers for which the corresponding closed-loop system dynamics are finite L, gain stable. Also, in an effort to demonstrate that the the given structure can, in fact. he used to increase performance. we consider a step-tracking design problem for a class of plants, where we use overshoot and settling time of the output step response to measure performance. We compare the results obtained using our switching architecture to the performance that can be obtained via two other LTI controller architectures to illustrate some of the performance benefits.
by Keith Robert Santarelli.
Ph.D.
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Reichelt, Matthias. "Linear and nonlinear optical excitations in spatially-inhomogeneous semiconductor systems." [S.l. : s.n.], 2005. http://archiv.ub.uni-marburg.de/diss/z2005/0123/.
Full text
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Farag, Emile. "Modeling of nonlinear systems using linear time-varying ARMAX models." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape4/PQDD_0017/MQ54107.pdf.
Full text
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Wei, Xiaojun. "Active vibration control in linear time-invariant and nonlinear systems." Thesis, University of Liverpool, 2015. http://livrepository.liverpool.ac.uk/2012679/.
Full textAbstract:
Active vibration control techniques are widely used in linear time-invariant and nonlinear systems. However, there still exist many difficulties in the application of conventional active vibration control techniques, including the following: (1) In application, some of the degrees of freedom may not be physically accessible to actuation and sensing simultaneously; (2) large flexible structures are difficult in terms of isolating one substructure from the vibration of another; (3) the incomplete understanding of the effects of softening nonlinearity may put conventional active controllers at risk; and (4) global stability of under-actuated nonlinear aeroelastic systems, resulting from actuator failure or motivated by weight and cost constraints imposed on next-generation flight vehicles, is extremely challenging, especially in the case of uncertainty and external disturbances. These intellectual challenges are addressed in this research by linear and nonlinear active control techniques. A new theory for partial pole placement by the method of receptances in the presence of inaccessible degrees of freedom is proposed. By the application of a new double input control and orthogonality conditions on the input and feedback gain vectors, partial pole placement is achieved in a linear fashion while some chosen degrees of freedom are free from both actuation and sensing. A lower bound on the maximum number of degrees of freedom inaccessible to both actuation and sensing is established. A theoretical study is presented on the feasibility of applying active control for the purpose of simultaneous vibration isolation and suppression in large flexible structures by block diagonalisation of the system matrices and at the same time assigning eigenvalues to the chosen substructures separately. The methodology, based on eigenstructure assignment using the method of receptances, is found to work successfully when the open-loop system, with lumped or banded mass matrix, is controllable. A comprehensive study of the effects of softening structural nonlinearity in aeroelastic systems is carried out using the simple example of a pitch-flap wing, with softening cubic nonlinearity in the pitch stiffness. Complex dynamical behaviour, including stable and unstable limit cycles and chaos, is revealed using sinusoidal-input describing functions and numerical integration in the time domain. Bifurcation analysis is undertaken using numerical continuation methods to reveal Hopf, symmetry breaking, fold and period doubling bifurcations. The effects of initial conditions on the system stability and the destabilising effects of softening nonlinearity on aerodynamic responses are considered. The global stability of an under-actuated wing section with torsional nonlinearity, softening or hardening, is addressed using a robust passivity-based continuous sliding-mode control approach. The controller is shown to be capable of stabilising the system in the presence of large matched and mismatched uncertainties and large input disturbance. With known bounds on the input disturbance and nonlinearity uncertainty, the continuous control input is able to globally stabilise the overall system if the zero dynamics of the system are globally exponentially stable. The merits and performance of the proposed methods are exemplified in a series of numerical case studies.
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Ahmadi, Amir Ali. "Non-monotonic Lyapunov functions for stability of nonlinear and switched systems : theory and computation." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44206.
Full textAbstract:
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 87-90).
Lyapunov's direct method, which is based on the existence of a scalar function of the state that decreases monotonically along trajectories, still serves as the primary tool for establishing stability of nonlinear systems. Since the main challenge in stability analysis based on Lyapunov theory is always to nd a suitable Lyapunov function, weakening the requirements of the Lyapunov function is of great interest. In this thesis, we relax the monotonicity requirement of Lyapunov's theorem to enlarge the class of functions that can provide certicates of stability. Both the discrete time case and the continuous time case are covered. Throughout the thesis, special attention is given to techniques from convex optimization that allow for computationally tractable ways of searching for Lyapunov functions. Our theoretical contributions are therefore amenable to convex programming formulations. In the discrete time case, we propose two new sucient conditions for global asymptotic stability that allow the Lyapunov functions to increase locally, but guarantee an average decrease every few steps. Our first condition is nonconvex, but allows an intuitive interpretation. The second condition, which includes the first one as a special case, is convex and can be cast as a semidenite program. We show that when non-monotonic Lyapunov functions exist, one can construct a more complicated function that decreases monotonically. We demonstrate the strength of our methodology over standard Lyapunov theory through examples from three different classes of dynamical systems. First, we consider polynomial dynamics where we utilize techniques from sum-of-squares programming. Second, analysis of piecewise ane systems is performed. Here, connections to the method of piecewise quadratic Lyapunov functions are made.
(cont.) Finally, we examine systems with arbitrary switching between a finite set of matrices. It will be shown that tighter bounds on the joint spectral radius can be obtained using our technique. In continuous time, we present conditions invoking higher derivatives of Lyapunov functions that allow the Lyapunov function to increase but bound the rate at which the increase can happen. Here, we build on previous work by Butz that provides a nonconvex sucient condition for asymptotic stability using the first three derivatives of Lyapunov functions. We give a convex condition for asymptotic stability that includes the condition by Butz as a special case. Once again, we draw the connection to standard Lyapunov functions. An example of a polynomial vector field is given to show the potential advantages of using higher order derivatives over standard Lyapunov theory. We also discuss a theorem by Yorke that imposes minor conditions on the first and second derivatives to reject existence of periodic orbits, limit cycles, or chaotic attractors. We give some simple convex conditions that imply the requirement by Yorke and we compare them with those given in another earlier work. Before presenting our main contributions, we review some aspects of convex programming with more emphasis on semidenite programming. We explain in detail how the method of sum of squares decomposition can be used to efficiently search for polynomial Lyapunov functions.
by Amir Ali Ahmadi.
S.M.
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VITAIOLI, Giorgio. "Control of nonlinear systems with limited information." Doctoral thesis, Università Politecnica delle Marche, 2011. http://hdl.handle.net/11566/242009.
Full textAbstract:
Nei sistemi di controllo tradizionali si presume che l’informazione sia disponibile ai fini del controllo in tempo reale e continuo, cioè senza ritardo e per ogni istante temporale. Nelle applicazioni queste
condizioni sono molto raramente soddisfatte. In molti sistemi, il ritardo è talmente minore delle costanti di tempo, che può essere ignorato. Inoltre, spesso, la frequenza di campionamento è talmente
elevata che il segnale di feedback può essere considerato a tempo continuo. Tuttavia, quando sono presenti limitazioni sulla frequenza di trasmissione e sull’occupazione di banda, come nei sistemi
di controllo Networked, i ritardi non possono essere trascurati e il flusso di informazioni non può essere considerato continuo.
Il contributo originale di questa tesi riguarda le proprietà di stabilità
di un sistema di controllo con le seguenti caratteristiche: i segnali possono essere trasferiti dal livello del controllore al livello del processo a tempo continuo, mentre dal livello del processo a
quello del controllore l’informazione è campionata. Come spesso accade nelle applicazioni, non è possibile conoscere esattamente la dinamica del processo da controllare, ma soltanto un modello di
tale processo è disponibile a fini di controllo. In tale situazione,
l’informazione campionata proveniente dal plant e i dati provenienti
dal modello possono essere utilizzati contemporaneamente per effettuare la sintesi del segnale di controllo, in un sistema di controllo che di fatto è model-based. Dato un sistema di questo tipo, l’obiettivo è di determinare il massimo intervallo di campionamento tale che le caratteristiche di stabilità siano garantite. Il problema è stato approfondito, sotto analoghe considerazioni, da L. Montestruque e P. J. Antsaklis, che hanno sviluppato lo schema di controllo Model-Based per sistemi Networked (Model-Based Networked Control o MB-NC Scheme) per sistemi con dinamica
lineare e per una particolare classe di sistemi nonlineari,nel caso in cui l’errore di modellazione è nullo in corrispondenza
dell’origine dello spazio di stato.
Nello schema MB-NC il modello viene utilizzato per simulare il comportamento del processo tra due successivi istanti di campionamento, quando non sono disponibili informazioni dirette dal processo
stesso. L’obiettivo di questa tesi è di presentare l’approccio MB-NC e di estenderlo a tipologie più generali di sistemi nonlineari. In particolare è stata effettualta l’analisi di stabilità di sistemi
nonlineari con dinamica generale, controllati mediante lo schema
Model-Based Networked, nei casi di perturbazioni vanishing e nonvanishing
ed in presenza di disturbi. Sotto opportune ipotesi sulla dinamica del processo, sull’entità dell’errore di modellazione, sulle prestazioni del controllore e sul periodo di campionamento, si sono
ottenute condizioni sufficienti per la stabilità asintotica semiglobale
dei sistemi retroazionati presi in esame.In traditional control, system’s sensory information is assumed to be available for control purposes in real time and continuously, for any t, although, in practice, these conditions are not usually satisfied. Actually, in many situations, delays may be so small, compared with the time constants of the systems at issue, that they can be safely ignored and sampling frequencies may be so high that continuous signals can be accurately reconstructed from sampled data. However, when there are limitations on the information’s transmission rate and on the band occupancy, like in networked systems, delays cannot be neglected and the information flow cannot be assumed to be continuous. This dissertation investigates the stability properties of a controlled plant in which signals can be transferred from the controller’s level to the plant’s level continuously, while information can be fed back from the plant’s level to the controller’s level only at sampling times. As frequently happens in application, one cannot assume a complete knowledge of the plant’s dynamics, but only that a model of it is available for control purposes. In such situations, sampled information coming from the plant and information coming from the model can be used to synthesize the control signal in a suitable model-based feedback control scheme. The results one would like to obtain concern the maximum length of the sampling interval for which the stabilizing performances of a given control scheme can be assured. The problem was previously considered, under analogous assumptions, by L.Montestruque and P.J.Antsaklis, who developed the Model-Based control scheme for Networked Systems (Model-Based Networked Control System or MB-NCS) for linear dynamics and for particular nonlinear dynamics with vanishing perturbation. In MB-NCS a model is used to simulate the plant evolution between transmission instants when no information about the plant is available. The aim of this dissertation is to present the MBNCS approach and to extend it to more general type of nonlinear plants and problems. The stability analysis of particular and general nonlinear MB-NC systems is carried out, for various types of perturbations and in the presence of disturbances. Under suitable hypotheses on the plant’s dynamics, the perturbation entity, the control performances and the length of the sampling period, sufficient conditions for semiglobal uniform boundedness or semiglobal asymptotical stability have been found.
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Loxton, Ryan Christopher. "Optimal control problems involving constrained, switched, and delay systems." Thesis, Curtin University, 2010. http://hdl.handle.net/20.500.11937/1479.
Full textAbstract:
In this thesis, we develop numerical methods for solving five nonstandard optimal control problems. The main idea of each method is to reformulate the optimal control problem as, or approximate it by, a nonlinear programming problem. The decision variables in this nonlinear programming problem influence its cost function (and constraints, if it has any) implicitly through the dynamic system. Hence, deriving the gradient of the cost and the constraint functions is a difficult task. A major focus of this thesis is on developing methods for computing these gradients. These methods can then be used in conjunction with a gradient-based optimization technique to solve the optimal control problem efficiently.The first optimal control problem that we consider has nonlinear inequality constraints that depend on the state at two or more discrete time points. These time points are decision variables that, together with a control function, should be chosen in an optimal manner. To tackle this problem, we first approximate the control by a piecewise constant function whose values and switching times (the times at which it changes value) are decision variables. We then apply a novel time-scaling transformation that maps the switching times to fixed points in a new time horizon. This yields an approximate dynamic optimization problem with a finite number of decision variables. We develop a new algorithm, which involves integrating an auxiliary dynamic system forward in time, for computing the gradient of the cost and constraints in this approximate problem.The second optimal control problem that we consider has nonlinear continuous inequality constraints. These constraints restrict both the state and the control at every point in the time horizon. As with the first problem, we approximate the control by a piecewise constant function and then transform the time variable. This yields an approximate semi-infinite programming problem, which can be solved using a penalty function algorithm. A solution of this problem immediately furnishes a suboptimal control for the original optimal control problem. By repeatedly increasing the number of parameters used in the approximation, we can generate a sequence of suboptimal controls. Our main result shows that the cost of these suboptimal controls converges to the minimum cost.The third optimal control problem that we consider is an applied problem from electrical engineering. Its aim is to determine an optimal operating scheme for a switchedcapacitor DC-DC power converter—an electronic device that transforms one DC voltage into another by periodically switching between several circuit topologies. Specifically, the optimal control problem is to choose the times at which the topology switches occur so that the output voltage ripple is minimized and the load regulation is maximized. This problem is governed by a switched system with linear subsystems (each subsystem models one of the power converter’s topologies). Moreover, its cost function is non-smooth. By introducing an auxiliary dynamic system and transforming the time variable (so that the topology switching times become fixed), we derive an equivalent semi-infinite programming problem. This semi-infinite programming problem, like the one that approximates the continuously-constrained optimal control problem, can be solved using a penalty function algorithm.The fourth optimal control problem that we consider involves a general switched system, which includes the model of a switched-capacitor DC-DC power converter as a special case. This switched system evolves by switching between several subsystems of nonlinear ordinary differential equations. Furthermore, each subsystem switch is accompanied by an instantaneous change in the state. These instantaneous changes—so-called state jumps—are influenced by control variables that, together with the subsystem switching times, should be selected in an optimal manner. As with the previous optimal control problems, we tackle this problem by transforming the time variable to obtain an equivalent problem in which the switching times are fixed. However, the functions governing the state jumps in this new problem are discontinuous. To overcome this difficulty, we introduce an approximate problem whose state jumps are governed by smooth functions. This approximate problem can be solved using a nonlinear programming algorithm. We prove an important convergence result that links the approximate problem’s solution with the original problem’s solution.The final optimal control problem that we consider is a parameter identification problem. The aim of this problem is to use given experimental data to identify unknown state-delays in a nonlinear delay-differential system. More precisely, the optimal control problem involves choosing the state-delays to minimize a cost function measuring the discrepancy between predicted and observed system output. We show that the gradient of this cost function can be computed by solving an auxiliary delay-differential system. On the basis of this result, the optimal control problem can be formulated—and hence solved—as a standard nonlinear programming problem.
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Xi, Zhiyu Electrical Engineering & Telecommunications Faculty of Engineering UNSW. "Identification and control of nonlinear laboratory processes." Awarded by:University of New South Wales. Electrical Engineering & Telecommunications, 2007. http://handle.unsw.edu.au/1959.4/40461.
Full textAbstract:
In this thesis, a class of control and identification methods on a typical laboratory process - a ball and beam system - are discussed. The ball and beam is a common laboratory process which contains nonlinearity, a double integrator and time-delay. In our project, the hardware made by Wincon (Quanser SRV02 +BB01) is used. The main contribution of this work is the development of a variety of controller design methods, which together with suitable parameter identification techniques provide tools for rapid prototyping for real time control of processes within the laboratory, in preparation for industrial implementation of more complex schemes. The novelty of this work lies in the use of model predictive control (MPC) methods based on a non-minimal state space formulation, which permits the inclusion of process measurements and actuations in the state vector, leading to controller designs which are immediately ready for on-line implementation. A linear MPC controller based on a non-minimal state space model is based on an approximate linear model. The results from simulation and online experiment show that the linear MPC controller realizes a satisfying reference tracking in the face of nonlinearity and time-delay. In the following chapter, a nonlinear Hammerstein model is identified, which is a type of reliable structure for describing nonlinear plants. A nonlinear MPC scheme is developed based on the Hammerstein model. An inversion block is created to cancel the effect of the nonlinearity. The performance IS also tested in both simulation and experiment. Finally, MPC is combined with sliding mode control. The non-minimal state space model is also used here. In the first part of this chapter, the idea underlying sliding mode control contributes a method of modifying the definition of the cost function in MPC. In the second half, MPC is used to design the switching surface in sliding mode control. The performance of tests on the example (ball and beam system) illustrates that these are both valid methods for dealing with complex processes.
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PETTINARI, SILVIA. "Fault Diagnosis Techniques for Linear Sampled Data Systems and a Class of Nonlinear Systems." Doctoral thesis, Università degli Studi di Camerino, 2012. http://hdl.handle.net/11581/401797.
Full textAbstract:
This thesis deals with the fault diagnosis design problem both for dynamical continuous time systems whose output signal are affected by fixed point quantization, referred as sampled-data systems, and for two different applications whose dynamics are inherent high nonlinear: a remotely operated underwater vehicle and a scramjet-powered hypersonic vehicle. Robustness is a crucial issue. In sampled-data systems, full decoupling of disturbance terms from faulty signals becomes more difficult after discretization. In nonlinear processes, due to hard nonlinearity or the inefficiency of linearization, the ''classical'' linear fault detection and isolation and fault tolerant control methods may not be applied. Some observer-based fault detection and fault tolerant control techniques are studied throughout the thesis, and the effectiveness of such methods are validated with simulations. The most challenging trade-off is to increase sensitivity to faults and robustness to other unknown inputs, like disturbances. Broadly speaking, fault detection filters are designed in order to generate analytical diagnosis functions, called residuals, which should be independent with respect to the system operating state and should be decoupled from disturbances. Decisions on the occurrence of a possible fault are therefore taken on the basis such residual signals.
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Tan, Kay Chen. "Evolutionary methods for modelling and control of linear and nonlinear systems." Thesis, University of Glasgow, 1997. http://theses.gla.ac.uk/8473/.
Full textAbstract:
The aim of this work is to explore the potential and enhance the capability of evolutionary computation for the development of novel and advanced methodologies for engineering system modelling and controller design automation. The key to these modelling and design problems is optimisation. Conventional calculus-based methods currently adopted in engineering optimisation are in essence local search techniques, which require derivative information and lack of robustness in solving practical engineering problems. One objective of this research is thus to develop an effective and reliable evolutionary algorithm for engineering applications. For this, a hybrid evolutionary algorithm is developed, which combines the global search power of a "generational" EA with the interactive local fine-tuning of Boltzmann learning. It overcomes the weakness in local exploration and chromosome stagnation usually encountered in pure EAs. A novel one-integer-one-parameter coding scheme is also developed to significantly reduce the quantisation error, chromosome length and processing overhead time. An "Elitist Direct Inheritance" technique is developed to incorporate with Bolzmann learning for reducing the control parameters and convergence time of EAs. Parallelism of the hybrid EA is also realised in this thesis with nearly linear pipelinability. Generic model reduction and linearisation techniques in L2 and L∞ norms are developed based on the hybrid EA technique. They are applicable to both discrete and continuous-time systems in both the time and the frequency domains. Superior to conventional model reduction methods, the EA based techniques are capable of simultaneously recommending both an optimal order number and optimal parameters by a control gene used as a structural switch. This approach is extended to MIMO system linearisation from both a non-linear model and I/O data of the plant. It also allows linearisation for an entire operating region with the linear approximate-model network technique studied in this thesis. To build an original model, evolutionary black-box and clear-box system identification techniques are developed based on the L2 norm. These techniques can identify both the system parameters and transport delay in the same evolution process. These open-loop identification methods are further extended to closed-loop system identification. For robust control, evolutionary L∞ identification techniques are developed. Since most practical systems are nonlinear in nature and it is difficult to model the dominant dynamics of such a system while retaining neglected dynamics for accuracy, evolutionary grey-box modelling techniques are proposed. These techniques can utilise physical law dominated global clearbox structure, with local black-boxes to include unmeasurable nonlinearities as the coefficient models of the clear-box. This unveils a new way of engineering system modelling. With an accurately identified model, controller design problems still need to be overcome. Design difficulties by conventional analytical and numerical means are discussed and a design automation technique is then developed. This is again enabled by the hybrid evolutionary algorithm in this thesis. More importantly, this technique enables the unification of linear control system designs in both the time and the frequency domains under performance satisfaction. It is also extended to control along a trajectory of operating points for nonlinear systems. In addition, a multi-objective evolutionary algorithm is developed to make the design more transparent and visible. To achieve a step towards autonomy in building control systems, a technique for direct designs from plant step response data is developed, which bypasses the system identification phase. These computer-automated intelligent design methodologies are expected to offer added productivity and quality of control systems.
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Alqasas, Neveen. "Membrane Characterization for Linear and Nonlinear Systems: Upstream and Downstream Methods." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/34979.
Full textAbstract:
Gas separation with polymer membranes are becoming one of the mainstream separation techniques for a myriad of industrial applications. Membrane technologies are recognized as a viable and economical unit operation compared to more conventional separation processes. The design and material selection of membrane separation processes depends highly on the transport properties of separated gas molecules within the membrane material. Therefore, to use efficient methods for gas membrane characterization is paramount for the proper design of membrane separation processes. A membrane can be typically characterized by three main properties: permeability, solubility and diffusivity. The permeability of a membrane is the product of its diffusivity and solubility, therefore obtaining two of the three parameters is sufficient to fully characterize a membrane. The time-lag method is one of the oldest and most used gas membrane characterization methods. However, it suffers from various limitations that make the method not applicable for many types of membranes.
The focus in this study was to develop new gas membrane characterization techniques that are based on extracting the membrane properties from the upstream gas pressure measurements rather than only from the downstream pressure measurements. It is believed that characterizing the membrane based on the upstream pressure measurements would be highly useful in characterizing barrier materials which are usually difficult to characterize using the conventional time-lag method. Moreover, glassy polymers which are widely used in industry exhibit behavior associated with nonlinear sorption isotherms and, therefore, the conventional time-lag method is incapable of obtaining an accurate estimation of glassy polymer properties. As a result, sorption experiments to generate a sorption isotherm are usually required in addition to permeation experiments to fully characterize glassy polymer membranes.
To quantify the errors associated with the conventional time-lag assumptions and to fundamentally comprehend the impact of nonlinearities on the time-lag method, a comprehensive numerical investigation has been undertaken using the finite difference method. The investigation has clearly put in evidence the effect of the various Langmuir parameters on the accuracy of the time lag and on the time required to achieve steady state. This investigation also allowed assessing the errors associated with the usual assumptions made on the boundary conditions in determining the time lag.
In this study, three novel gas membrane characterization methods were developed and proposed. Two of the proposed methods are concerned with the characterization of membranes that can be represented with a linear sorption isotherm. These two methods are entirely based on the upstream pressure measurements. The third membrane characterization method that is proposed is based on the dynamic monitoring of both upstream and downstream pressure measurements and is applicable to systems that exhibit a nonlinear isotherm sorption behavior. The three proposed methods are promising and further experimental validation is recommended to determine their full range of applicability.
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Franz, David, and University of Lethbridge Faculty of Arts and Science. "Turing patterns in linear chemical reaction systems with nonlinear cross diffusion." Thesis, Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2007, 2007. http://hdl.handle.net/10133/659.
Full textAbstract:
Turing patterns have been studied for over 50 years as a pattern forming mechanism.
To date the current focus has been on the reaction mechanism, with little to no
emphasis on the diffusion terms.
This work focuses on combining the simplest reaction mechanism possible and
the use of nonlinear cross diffusion to form Turing patterns. We start by using two
methods of bifurcation analysis to show that our model can form a Turing instability.
A diffusion model (along with some variants) is then presented along with the results
of numerical simulations. Various tests on both the numerical methods and the model
are done to ensure the accuracy of the results. Finally an additional model that is
closed to mass flow is introduced along with preliminary results.vi, 55 leaves : ill. ; 29 cm.
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Phadnis, Akash. "Uncertainty quantification and prediction for non-autonomous linear and nonlinear systems." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/85476.
Full textAbstract:
Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2013.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 189-197).
The science of uncertainty quantification has gained a lot of attention over recent years. This is because models of real processes always contain some elements of uncertainty, and also because real systems can be better described using stochastic components. Stochastic models can therefore be utilized to provide a most informative prediction of possible future states of the system. In light of the multiple scales, nonlinearities and uncertainties in ocean dynamics, stochastic models can be most useful to describe ocean systems. Uncertainty quantification schemes developed in recent years include order reduction methods (e.g. proper orthogonal decomposition (POD)), error subspace statistical estimation (ESSE), polynomial chaos (PC) schemes and dynamically orthogonal (DO) field equations. In this thesis, we focus our attention on DO and various PC schemes for quantifying and predicting uncertainty in systems with external stochastic forcing. We develop and implement these schemes in a generic stochastic solver for a class of non-autonomous linear and nonlinear dynamical systems. This class of systems encapsulates most systems encountered in classic nonlinear dynamics and ocean modeling, including flows modeled by Navier-Stokes equations. We first study systems with uncertainty in input parameters (e.g. stochastic decay models and Kraichnan-Orszag system) and then with external stochastic forcing (autonomous and non-autonomous self-engineered nonlinear systems). For time-integration of system dynamics, stochastic numerical schemes of varied order are employed and compared. Using our generic stochastic solver, the Monte Carlo, DO and polynomial chaos schemes are inter-compared in terms of accuracy of solution and computational cost. To allow accurate time-integration of uncertainty due to external stochastic forcing, we also derive two novel PC schemes, namely, the reduced space KLgPC scheme and the modified TDgPC (MTDgPC) scheme. We utilize a set of numerical examples to show that the two new PC schemes and the DO scheme can integrate both additive and multiplicative stochastic forcing over significant time intervals. For the final example, we consider shallow water ocean surface waves and the modeling of these waves by deterministic dynamics and stochastic forcing components. Specifically, we time-integrate the Korteweg-de Vries (KdV) equation with external stochastic forcing, comparing the performance of the DO and Monte Carlo schemes. We find that the DO scheme is computationally efficient to integrate uncertainty in such systems with external stochastic forcing.
by Akash Phadnis.
S.M.
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Mason, Richard. "A chordal sparsity approach to scalable linear and nonlinear systems analysis." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:c4a978aa-185e-4029-a887-6aa2ab9efb37.
Full textAbstract:
In this thesis we investigate how the properties of chordal graphs can be used to exploit sparsity in several optimisation problems that arise in control theory. In particular, we focus on analysis and synthesis problems that involve semidefinite constraints and can be formulated as semidefinite programming (SDP) problems. Using a relationship between chordal graphs and sparse semidefinite matrices, we decompose the semidefinite constraints in the associated SDP problems into multiple, smaller semidefinite constraints along with some additional equality constraints. The benefit of this approach is that for sparse dynamical systems we can solve significantly larger analysis and synthesis problems than is possible using traditional dense methods. We begin by considering the properties of chordal graphs and their connection to sparse positive semidefinite matrices. We then turn our attention to the problem of constructing Lyapunov functions for linear time-invariant (LTI) systems. From this starting point, we derive methods of exploiting chordal sparsity in other analysis problems found in control theory. In particular, this approach is applied to the problem of bounding the input-output properties of systems via the KYP lemma for both continuous and discrete-time systems. We then consider how the properties of chordal graphs can be exploited in the SDPs that arise in static state feedback controller synthesis problems for LTI systems. We show that the sparse inverse property of the maximum determinant completion of a partial positive matrix can be used to design controllers with a pre-specified sparsity pattern. We then consider how to exploit chordal sparsity when designing a static state feedback controller to minimise the H-infinity norm of an LTI system. Next we shift from linear systems to nonlinear systems and develop a chordal sparsity approach to scalable stability analysis of systems with polynomial dynamics using the Sums of Squares (SOS) technique. We develop a method of exploiting chordal sparsity that avoids the computationally costly step of forming the coefficient matrix in the SOS problem. We then apply this method to the problem of constructing Lyapunov functions for systems with correlatively sparse polynomial vector fields. Finally, we conclude by discussing some directions for future research.
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Tien, Meng-Hsuan. "Analyzing and Exploiting the Dynamics of Complex Piecewise-Linear Nonlinear Systems." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1586039513469825.
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Tan, Hendra. "Linear and nonlinear rheological properties of diblock and triblock copolymer systems." 京都大学 (Kyoto University), 2004. http://hdl.handle.net/2433/145340.
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