Cette thèse étudie l'approche LPV pour la commande robuste des systèmes non linéaires. Son originalité est de proposer pour la première fois un cadre rigoureux permettant de résoudre efficacement des problèmes de synthèse non linéaire. L'approche LPV a été proposée comme une extension de l'approche H-infini dans le contexte des systèmes LPV (« Linéaires à Paramètres Variant dans le temps »), voire non linéaires. Quoique prometteuse, cette approche pour la commande des systèmes non linéaires restait peu utilisée. En effet, au-delà même de certaines limitations théoriques, la nature des solutions obtenues semblait inadéquate. Cette question ouverte est notre point de départ. Nous montrons tout d'abord que la faible variation des correcteurs constatée est due avant tout à la nature du schéma informationnel utilisé traditionnellement lors de la synthèse LPV, et que sous des hypothèses raisonnables, le cadre LPV peut permettre de recouvrir des stratégies de type « linéarisation par bouclage ». Ce point étant acquis, une deuxième difficulté réside dans l'obtention effective de correcteurs non linéaires donnant des garanties de performance. Nous proposons un cadre rigoureux permettant de résoudre efficacement un problème de synthèse incrémentale pondérée, par la résolution d'un problème LPV associé à un schéma informationnel spécifique compatible avec celui identifié dans la première partie. Cette étude et son aboutissement à la définition d'un cadre formel et d'une procédure complète d'obtention de correcteurs, incluant des méthodes de réduction de complexité, donnent des arguments puissants en faveur de l'approche LPV pour la commande robuste de systèmes non linéaires. / This thesis studies the LPV approach for the robust control of nonlinear systems. Its originality is to propose for the first time a rigorous framework allowing to solve efficiently nonlinear synthesis problems.The LPV approach was proposed as an extension of the H-infinity approach in the context of LPV (Linear Parameter-Varying) systems and nonlinear systems. Although this approach seemed promising, it was not much used in practise. Indeed, beyond certain theoretical limitations, the nature itself of the obtained solutions did not seem adequate. This open question constitutes the starting point of our work.We first prove that the observed weak variation of the controllers is in fact mostly due to the information structure traditionally used for LPV synthesis, and that under reasonable assumptions, the LPV framework can overlap feedback linearization strategies. This point having been resolved, a second difficulty lies in the actual achievement of nonlinear controllers yielding performance guarantees. We propose a rigorous framework allowing to solve efficiently an incremental synthesis problem, through the resolution of an LPV problem associated to a specific information structure compatible with the one identified in the first part.This study and its corollary description of a formal framework and of a complete controller synthesis procedure, including complexity reduction methods, provide powerful arguments in favor of the LPV approach for the robust control of nonlinear systems.

Orientador: José Manoel Balthazar / Banca: Júlio Cesar Ruiz Claeyssen / Banca: Bento Rodrigues de Pontes Junior / Resumo: O propósito deste trabalho foi estudar as não linearidades na dinâmica de sistemas mecânicos e eletromecânicos. Entre eles inclui-se um corpo em levitação. As não linearidades levam o movimento da estrutura para o Efeito Sommerfeld. Por este fato, o trabalho do motor fica próximo ou na frequência de ressonância. Quando a estrutura atinge a condição de ressonância, a melhor parte da energia é consumida para gerar vibrações de grande amplitude sem nenhuma mudança sensível na frequência do motor. Neste trabalho, foi verificado o fenômeno para alguns sistemas não ideais inclusive o sistema com levitação magnética, discutindo uma forma de conduzir o sistema à condição de ressonância e evitar o "absorvedor de energia" que ocorre com o efeito Sommerfeld / Abstract: This paper studies the nonlinearities in dynamics of mechanics and electro mechanics non ideal systems. One of them is a magnetically levitated body. These nonlinearities lead the motion of the structure to the Sommerfeld Effect. For this reason the motor's near or in resonance frequency. When the structure achieves resonance condition, the best part of the energy is consumed to generate large amplitude vibration, with no sensitive change in the motor frequency. In this paper, is checked whether the phenomenon in some non ideal systems and also, if occurs with magnetic levitation. Will be discussed how to drive the system to ressonance condition and to avoid the "energy sink" that occurs with the Sommerfeld effect / Mestre

Este trabalho aborda diversas técnicas de controle, com o intuito de comparação do desempenho e robustez ao aplicá-los a um conversor Buck. Iniciando pelo controlador PID (Proporcional, Integral e Derivativo), amplamente explorado e dominado no meio industrial, ele é adotado neste trabalho como referência de comparação para as demais técnicas desenvolvidas. Outra estratégia aqui apresentada é o GANLPID (Gaussian Adaptative Non Linear PID ou PID Adaptativo Não Linear Gaussiano), trata-se de uma técnica não linear, possui ganhos variantes em função do erro baseados em uma função gaussiana. O controle por alocação de polos é uma técnica de controle que em sua forma básica não possui parcela integral, sendo necessária a inclusão deste termo para minimizar o erro em regime permanente. As principais características de análise de desempenho são o tempo de acomodação e overshoot. Todas as técnicas são exploradas a fim de serem implementadas em dispositivos FPGA (Field Programmable Gate Array), possuindo algumas vantagens sobre microcontroladores e DSP’s (Digital Signal Processor), pois conseguem executar tarefas em paralelo deixando a execução do algoritmo mais rápida. As técnicas de controle escolhidas foram simuladas utilizando a ferramenta DSP Builder e compiladas diretamente em código HDL (linguagem de descrição de hardware). Os resultados de simulação e experimentais são apresentados e comentados para validar os projetos propostos. / This work discuss several techniques of control, with an intention of comparison of performance and robustness to apply them to Buck coverter. Starting with PID (Proportional, Integral, Derivative) controller, widely explored and dominated in an industrial environment, it’s used in this work as comparison reference for the others techniques developed. Another strategy presented here is the GANLPID (Gaussian Adaptative Non LinearPID), it’s a case of non linear technique, has won variants in function of the based on a Gaussian error function. variants have gains on function of error based on a Gaussian function. The pole placement control technique not having full part in their basic forms, being necessary to include this term to eliminate the steady-state error. The main performance analysis features are the settling time and overshoot. All the techniques are explored in order to be implemented in FPGA (Field Programmable Gate Array) devices, having some advantages over microcontrollers and DSP’s (Digital Signal Processor), because can execute tasks in parallel allowing the implementation of the algorithm more faster. The chosen control techniques were simulated using the DSP Builder tool and and compiled directly in HDL (hardware description language) code. The results of simulation and experimental are presented and discussed in order to validate the proposed projects.

Esta proposta de dissertação de mestrado trata da aplicação de Estimadores Algébricos em sistemas de controle como alternativa ao uso de observadores. Devido à dificuldade de obtenção de resultados teóricos, dificuldade essa oriunda da natureza complexa dos estimadores algébricos, o trabalho é desenvolvido através do estudo de casos. Considera-se que a topologia de controle é a união de uma técnica tradicional de controle (por exemplo, uma realimentação de estado ou o método do torque calculado) com a estimação algébrica. Os resultados obtidos defendem a idéia de que os Estimadores Algébricos, quando usados como estimadores de estado, permitem obter um desempenho e uma robustez que se aproxima muito do desempenho e a robustez da mesma lei de controle no caso em que o estado é perfeitamente conhecido. / The control topology that is considered in this work is the union of a traditional control technique (e.g. a state feedback or the computed torque method) with the Algebraic Estimator. The obtained results reinforce the common sense about this class of estimators, that the use of Algebraic Estimators may produce the performance, robustness and noise immunity that mimics the case where perfect information of the state is available.

Submitted by Maria Aparecida (cidazen@gmail.com) on 2017-04-17T12:44:32Z No. of bitstreams: 1 Hugo Alves Velozo.pdf: 5196080 bytes, checksum: 14e9edcc07c0256cf726b1d0f7eb9a02 (MD5) / Made available in DSpace on 2017-04-17T12:44:32Z (GMT). No. of bitstreams: 1 Hugo Alves Velozo.pdf: 5196080 bytes, checksum: 14e9edcc07c0256cf726b1d0f7eb9a02 (MD5) Previous issue date: 2017-02-20 / CAPES / Most methods of identifcation of closed-loop dynamic systems are developed for linear and deterministic systems. However, most closed loop systems are nonlinear dynamic systems. In addition, such systems are subject to stochastic perturbations. Considering this problem, this work presents a methodology for the identifcation of closed loop stochastic nonlinear systems. For this purpose, the proposed methodology uses a local approach to identify nonlinear dynamic systems, that is, a set of Box-Jenkins local models are used to identify the dynamics of the nonlinear system. In this work, the nonlinear system is modeled through a Takagi-Sugeno fuzzy inference system, where the parameters of the antecedent of the fuzzy rules are estimated with the fuzzy clustering algorithm GustafsonKessel and the consequent Box-Jenkins model parameters are estimated with the fuzzy fuzzy RIV (Refned Instrumental Variable) and fuzzy IVARMA (Instrumental Variable ARMA) algorithms. The proposed method is applied in the identifcation of a closed-loop nonlinear thermal plant. / A maioria dos métodos de identifcação de sistemas dinâmicos em malha fechada são desenvolvidos para sistemas lineares e determinísticos. Entretanto, a maioria dos sistemas operando em malha fechada são sistemas dinâmicos não lineares. Além disso, esses sistemas estão sujeitos a perturbações de natureza estocástica. Considerando essa problemática, este trabalho apresenta uma metodologia para identifcação de sistemas não lineares estocásticos em malha fechada. Para isso, a metodologia proposta utiliza uma abordagem local de identifcação de sistemas dinâmicos não lineares, ou seja, um conjunto de modelos locais Box-Jenkins são utilizados para identifcar a dinâmica do sistema não linear. Neste trabalho, o sistema não linear é modelado por meio de um sistema de inferência fuzzy Takagi-Sugeno, onde os parâmetros do antecedente das regras fuzzy são estimados com o algoritmo de agrupamento fuzzy Gustafson-Kessel e o parâmetros do modelo Box-Jenkins do consequente são estimados com os algoritmos RIV (Refned Instrumental Variable) fuzzy e IVARMA (Instrumental Variable ARMA) fuzzy. O método proposto é aplicado na identifcação de uma planta térmica não linear em malha fechada.

Submitted by Silvana Teresinha Dornelles Studzinski (sstudzinski) on 2016-12-23T10:42:58Z No. of bitstreams: 1 Cassio Binkowski_.pdf: 1965327 bytes, checksum: 87b7380f1bab367237fb868e0de20388 (MD5) / Made available in DSpace on 2016-12-23T10:42:59Z (GMT). No. of bitstreams: 1 Cassio Binkowski_.pdf: 1965327 bytes, checksum: 87b7380f1bab367237fb868e0de20388 (MD5) Previous issue date: 2016-09-14 / Nenhuma / A identificação de sistemas está longe de ser uma tarefa nova. Sendo inicialmente proposta na metade do século XX, foi extensamente desenvolvida para sistemas lineares, devido às exigências da época relacionadas à complexidade dos sistemas e também do poder computacional, atingindo excelente resultados. No entanto, com o aumento da complexidade dos sistemas e das exigências de controle, os modelos lineares não mais conseguiam representar os sistemas em toda a faixa de operação exigida, sendo assim requerendo uma aplicação dos modelos não-lineares. Visto que todos os sistemas presentes na natureza possuem certo grau de não linearidade, é correto afirmar que um modelo não-linear é capaz de representar as dinâmicas dos sistemas de forma mais compreensiva que um modelo linear. A identificação de sistemas não lineares foi então estudada e diversos modelos foram propostos, atingindo ótimos resultados. Nesse trabalho foi realizado um estudo de dois modelos não-lineares, NARMAX e Hammerstein-Wiener, aplicando esses modelos a dois processos simulados. Foram então derivados dois algoritmos para realizar a estimação dos parâmetros dos modelos NARMAX e Hammerstein-Wiener, utilizando um estimador ortogonal, e também um algoritmo para geração de sinais de entrada multinível. Os modelos foram então estimados para os sistemas simulados, e comparados utilizando os critérios AIC, FPE, Lipschitz e de correlação cruzada de alta ordem. Os melhores resultados foram obtidos com os modelos Hammerstein-Wiener-OLS e NARMAX-OLS, ao contrário do modelo NARMAX-RLS. No entanto, devido a resultados bastante divergentes entre os modelos, pode-se concluir que essa área ainda carece de desenvolvimento de técnicas precisas para comparação e avaliação de modelos, bem como quanto à quantificação do nível de não-linearidade do sistema em questão. / The task of system identification is far from being a new one. It was initially proposed in the mid of the 20th century, and had then been extensively developed for linear systems, due to the demands of that time concerning computational power, systems complexity and control requirements. It has achieved excellent results in this approach. However, due to the rise of systems complexity and control requirements, linear models were no longer able to meet the desired accuracy and larger operating range, and therefore the usage nonlinear models were pursued. As all systems in nature are nonlinear to some extent, it is correct to state that nonlinear models can represent a whole lot more of systems’ dynamics than linear models. Nonlinear models were then studied, and several techniques were presented, being able to achieve very good results. In this work, two of the available nonlinear models were studied, namely NARMAX and Hammerstein-Wiener, applying these models in two simulated systems. Two algorithms were then derived to estimate parameters for NARMAX and Hammerstein-Wiener models using an orthogonal estimator, and also an algorithm for generating multi-level input signals. The models were then estimated to the simulated systems, and compared using the AIC, FPE, Lipschitz and high-order cross-correlation criteria. The best results were obtained for the Hammerstein-Wiener-OLS and NARMAX-OLS models, as opposed to the NARMAX-RLS model. However, due to divergent observed results between models, it can be concluded that precise methods for model comparison and validation still needs to be developed, as well as a method for nonlinearity quantification for the system in hand.

In this study, accurate target tracking for bearings-only tracking problem is investigated. A new tracking filter for this nonlinear problem is designed where both range parameterization and Rao-Blackwellized (marginalized) particle filtering techniques are used in a Gaussian mixture formulation to track both constant velocity and maneuvering targets. The idea of using target turn rate in the state equation in such a way that marginalization is possible is elaborated. Addition to nonlinear nature, unobservability is a major problem of bearings-only tracking. Observer trajectory generation to increase the observability of the bearings-only tracking problem is studied. Novel formulation of observability measures based on mutual information between the state and the measurement sequences are derived for the problem. These measures are used as objective functions to improve observability. Based on the results obtained better understanding of the required observer trajectory for accurate bearings-only target tracking is developed.

Nonlinear systems occur in industrial processes, economical systems, biotechnology and in many other areas. The thesis treats methods for system identification and control of such nonlinear systems, and applies the proposed methods to a solar heating/cooling plant. Two applications, an anaerobic digestion process and a domestic solar heating system are first used to illustrate properties of an existing nonlinear recursive prediction error identification algorithm. In both cases, the accuracy of the obtained nonlinear black-box models are comparable to the results of application specific grey-box models. Next a convergence analysis is performed, where conditions for convergence are formulated. The results, together with the examples, indicate the need of a method for providing initial parameters for the nonlinear prediction error algorithm. Such a method is then suggested and shown to increase the usefulness of the prediction error algorithm, significantly decreasing the risk for convergence to suboptimal minimum points. Next, the thesis treats model based control of systems with input signal dependent time delays. The approach taken is to develop a controller for systems with constant time delays, and embed it by input signal dependent resampling; the resampling acting as an interface between the system and the controller. Finally a solar collector field for combined cooling and heating of office buildings is used to illustrate the system identification and control strategies discussed earlier in the thesis, the control objective being to control the solar collector output temperature. The system has nonlinear dynamic behavior and large flow dependent time delays. The simulated evaluation using measured disturbances confirm that the controller works as intended. A significant reduction of the impact of variations in solar radiation on the collector outlet temperature is achieved, though the limited control range of the system itself prevents full exploitation of the proposed feedforward control. The methods and results contribute to a better utilization of solar power.

In light of the complex and highly uncertain nature of dynamical systems requiring controls, it is not surprising that reliable system models for many high performance engineering and life science applications are unavailable. In the face of such high levels of system uncertainty, robust controllers may unnecessarily sacrifice system performance whereas adaptive controllers are clearly appropriate since they can tolerate far greater system uncertainty levels to improve system performance. In this dissertation, we develop a Lyapunov-based direct adaptive and neural adaptive control framework that addresses parametric uncertainty, unstructured uncertainty, disturbance rejection, amplitude and rate saturation constraints, and digital implementation issues. Specifically, we consider the following research topics: direct adaptive control for nonlinear uncertain systems with exogenous disturbances; robust adaptive control for nonlinear uncertain systems; adaptive control for nonlinear uncertain systems with actuator amplitude and rate saturation constraints; adaptive reduced-order dynamic compensation for nonlinear uncertain systems; direct adaptive control for nonlinear matrix second-order dynamical systems with state-dependent uncertainty; adaptive control for nonnegative and compartmental dynamical systems with applications to general anesthesia; direct adaptive control of nonnegative and compartmental dynamical systems with time delay; adaptive control for nonlinear nonnegative and compartmental dynamical systems with applications to clinical pharmacology; neural network adaptive control for nonlinear nonnegative dynamical systems; passivity-based neural network adaptive output feedback control for nonlinear nonnegative dynamical systems; neural network adaptive dynamic output feedback control for nonlinear nonnegative systems using tapped delay memory units; Lyapunov-based adaptive control framework for discrete-time nonlinear systems with exogenous disturbances; direct discrete-time adaptive control with guaranteed parameter error convergence; and hybrid adaptive control for nonlinear uncertain impulsive dynamical systems.

Despite recent advances in statistics, artificial neural network theory, and machine learning, nonlinear function estimation in high-dimensional space remains a nontrivial problem. As the response surface becomes more complicated and the dimensions of the input data increase, the dreaded "curse of dimensionality" takes hold, rendering the best of function approximation methods ineffective. This thesis takes a novel approach to solving the high-dimensional function estimation problem. In this work, we propose and develop two distinct parametric projection pursuit learning networks with wide-ranging applicability. Included in this work is a discussion of the choice of basis functions used as well as a description of the optimization schemes utilized to find the parameters that enable each network to best approximate a response surface. The essence of these new modeling methodologies is to approximate functions via the superposition of a series of piecewise one-dimensional models that are fit to specific directions, called projection directions. The key to the effectiveness of each model lies in its ability to find efficient projections for reducing the dimensionality of the input space to best fit an underlying response surface. Moreover, each method is capable of effectively selecting appropriate projections from the input data in the presence of relatively high levels of noise. This is accomplished by rigorously examining the theoretical conditions for approximating each solution space and taking full advantage of the principles of optimization to construct a pair of algorithms, each capable of effectively modeling high-dimensional nonlinear response surfaces to a higher degree of accuracy than previously possible.