O projeto de estratégias de controle preditivo (MPC) com estabilidade garantida, que incorpora explicitamente a incerteza de modelo na formulação de controle, ainda permanece uma questão em aberto na literatura, embora uma ampla teoria já tenha sido desenvolvida para a síntese de algoritmos MPC robustamente estáveis. Em verdade, as soluções existentes para o problema de MPC robusto estão longe de uma etapa aceitável de implementação prática, principalmente se o sistema de processo é composto de modos integradores ou instáveis, e também apresenta atrasos de tempo (tempos mortos) entre suas variáveis de entrada e saída. Sob esta perspectiva, o objetivo principal desta tese é desenvolver uma estrutura de síntese de controladores MPC com estabilidade robusta garantida para sistemas de processo com as características integradoras ou instáveis, assim como tempos mortos entre as variáveis. Particularmente, três diferentes estratégias de MPC robusto são desenvolvidas neste trabalho. As duas primeiras referem-se a sistemas integradores com tempos mortos: o primeiro algoritmo é baseado em uma formulação de controle em dois passos, enquanto o segundo é posto como um problema de otimização de controle em um passo e a representação de modelo em variáveis de estado é mais geral do que aquela adotada na formulação do primeiro método. A terceira estratégia proposta focaliza os sistemas instáveis com tempos mortos através de uma formulação de controle em um passo. Ademais, visando o caso de implementação prática, os controladores desenvolvidos compreende os seguintes aspectos: (i) as leis de controle livre de erro permanente são obtidas sem a necessidade de incluir uma camada de otimização adicional de cálculo de estados estacionários, devido à formulação adequada de modelos em espaço de estados na forma incremental das entradas, os quais são derivados de expressões analíticas de resposta ao degrau do sistema de processo; (ii) a incerteza de todos os parâmetros do modelo, e.g. ganhos, constantes de tempo, atrasos de tempo, é considerada na formulação do problema; (iii) as provas de estabilidade robusta segundo Lyapunov são realizadas de uma forma intuitiva através da imposição de restrições terminais de igualdade e restrições de contração de custo; (iv) a inclusão adequada de variáveis de folga, que não comprometem as propriedades estabilizantes dos controladores, assegura que os problemas de otimização são sempre viáveis; (v) integração estável com camada de otimização em tempo real, visto que os controladores são projetados de tal forma a rastrear targets ótimos para algumas entradas e saídas do processo, mantendo as variáveis remanescentes dentro de faixas pré-definidas, ao invés de set-points xos. Exemplos de simulação típicos da indústria de processo são explorados para ilustrar as potenciais utilidades dos métodos propostos e demonstrar que eles podem ser aplicados em casos reais. / The design of stable model predictive control (MPC) strategies that explicitly incorporate the model uncertainty into the control formulation still remains an open issue, although a rich theory has been developed to the synthesis of robustly stabilizing MPC schemes. In fact, the existing solutions to the robust MPC problem seem far from an acceptable stage of practical imple mentations, chiey when the process system is composed of integrating and unstable poles, as well as time delays between its input and output variables. Within this perspective, the ultimate goal of this thesis is to develop a new framework for robust MPC synthesis which guarantees closed-loop stability of integrating and unstable time delay processes. On this subject, three different robust MPC strategies are developed. The two rst concerns on integrating time delay processes; the former is based on a two-step control formulation, whereas the latter is posed as a one-step control optimization problem and state-space model description is more general than that adopted in the former formulation. The third proposed strategy focuses on one-step control formulation-based unstable time delay processes. Aiming at practical implementation purposes, the controllers proposed herein comprise the following aspects: (i) the offset free control laws are obtained without the need to include an additional steady-state calculation op timization layer due to the enclosure of proper state-space models in the incremental form of the inputs, which are derived of analytical expressions of step response of the process system; (ii) the uncertainty of all model parameters, e.g. gains, time constants, time delays and so on, is considered in the problem formulation; (iii) the proofs of robust Lyapunov stability are easily carried out of an intuitive way by imposing terminal equality constraints and cost-contracting constraints; (iv) the suitable inclusion of slack variables, which does not commit the stabil ity properties of the controllers, ensure that the proposed optimization problems are always feasible; (v) stable integration with real-time optimization layer, seeing as the controllers are designed to work in the optimum target tracking scheme where they should drive the process to the optimum operating point, while maintaining the remaining inputs and outputs inside pre dened zones instead of xed set-points. Simulation examples typical of the process industry are exploited to illustrate the helpfulness of the proposed control methods and demonstrate that they can be implemented in real applications.

Este trabalho apresenta todos os passos para a implementação de técnicas de controle preditivo em uma coluna de destilação. Inicialmente a tese introduz basicamente o funcionamento e a meta do processo de destilação. Modelos linearizados em tempo contínuo da coluna de destilação são obtidos a partir de ensaios experimentais da coluna em diferentes pontos de operação. Com base nestes modelos, várias topologias de controladores preditivos baseados em modelo são implementadas. Um otimizador em tempo real é integrado aos controladores preditivos para a redução do custo operacional da planta. Resultados simulados e resultados experimentais de todas as topologias de controladores preditivos estudados são apresentados. / This work presents all the steps to the implementation of predictive control techniques in a distillation column. First the thesis basically introduces the working and the goal of the distillation process. Linearized models in continuous time of the distillation column are obtained from experimental tests of the column in different operating points. Based on this models, several model based predictive controllers topologies are implemented. A real time optimizer is integrated with the predictive controllers to the reduction of the plant operational cost. Simulated results and experimental results of all studied predictive controllers topologies are presented.

<p>Ova doktorska disertacija uvodi nov pristup ispitivanju stabilnosti dinamičkih<br />sistema, korišćenjem teorije pseudospektra. Na taj način se postojeći pojam<br />stabilnosti profinjuje pojmom robusne stabilnosti, koji mnogo adekvatnije<br />opisuje realnu ekološku stabilnost. Razvijen je nov matematički alat za<br />izračunavanje indikatora stabilnosti, koji je zatim ilustrovan na primeru dva<br />ekosistema tla, sa po četiri uzorka, u četiri različita stadijuma razvoja.</p> / <p>This doctoral dissertation establishes a novel approach to the stability analysis of<br />dynamical systems, in terms of matrix pseudospectrum. In that manner, the existing<br />concept of stability has undergone essential refinement so as to give birth to the<br />concept of robust stability, which has the ability to capture the ecological stability at a<br />more adequate level. Additionally, within the framework of the dissertation, a new<br />mathematical tool for the stability indicators computation has been developed, which<br />has then been used to illustrate theoretical results in form of two soil ecosystems,<br />each of them sampled four times, all of them observed in four distinct stages of<br />evolution.</p>

Negative-imaginary systems are broadly speaking stable and square (equal number of inputs and outputs) systems whose Nyquist plot lies underneath (never touches for strictly negative-imaginary systems) the real axis when the frequency varies in the open interval 0 to ∞. This class of systems appear quite often in engineering applications, for example, in lightly damped flexible structures with collocated position sensors and force actuators, multi-link robots, DC machines, active filters, etc. In this thesis, robustness analysis and controller synthesis methods for uncertain negative-imaginary systems are explored. Two new reformulation techniques are proposed that facilitate both the robustness analysis and controller synthesis for uncertain negative-imaginary systems. These reformulations are based on the transformation from negative-imaginary systems to a bounded-real framework via the positive-real property. In the presence of strictly negative-imaginary uncertainty, the robust stabilization problem is posed in an equivalent H∞ control framework; similarly, a negative-imaginary robust performance analysis problem is cast into an equivalent μ-framework. The latter framework also allows robust stability analysis when the perturbations are a mixture of bounded-real and negative-imaginary uncertainties. The proposed two techniques pave the way for existing H∞ control and μ theory to be applied to robustness analysis and controller synthesis for negative-imaginary systems. In addition, a static state-feedback synthesis method is proposed to achieve robust stability of a system in the presence of strictly negative-imaginary uncertainties. The method is developed in the LMI framework, which can be solved efficiently using convex optimization techniques. The controller synthesis method is based on the negative-imaginary stability theorem: a positive feedback interconnection of two negative-imaginary systems is internally stable if and only if the DC loop gain is contractive and at least one of the systems in the interconnected loop is strictly negative-imaginary. Also, in order to handle non-strict negative-imaginary uncertainties, a strongly strictly negative-imaginary lemma is proposed that helps to ensure the strictly negative-imaginary property of the nominal closed-loop system for robustness. To this end, a state-space characterization for strictly negative-imaginary property is given for non-minimal systems where the conditions are convex and hence numerically attractive. The results in this thesis hence facilitate both the robustness analysis and controller synthesis for negative-imaginary systems that quite often arise in practical scenarios. In addition, they can be applied to quantify the worse-case performance for this class of systems. Therefore, the proposed results have important implications in controller synthesis for uncertain negative-imaginary systems that achieve not only robust stabilization but also robust performance.

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Orientador: Edvaldo Assunção / Resumo: Neste trabalho é proposta a resolução do problema do regulador linear quadrático (Linear Quadratic Regulator - LQR) via desigualdades matriciais lineares (Linear Matrix Inequalities - LMIs) para sistemas lineares e invariantes no tempo sujeitos a incertezas politópicas, bem como para sistemas lineares sujeitos a parâmetros variantes no tempo (Linear Parameter Varying - LPV). O projeto dos controladores é baseado na realimentação derivativa. A escolha da realimentação derivativa se dá devido à sua fácil implementação em certas aplicações como, por exemplo, no controle de vibrações. Os sinais usados na realimentação são aceleração e velocidade, sendo obtidos por meio de acelerômetros. Por meio do método proposto é possível obter condições LMIs para a síntese de controladores que garantam a estabilização do sistema em malha fechada, sendo que os controladores possuem desempenho otimizado. Para a formulação das condições LMIs, uma função de Lyapunov do tipo quadrática é utilizada. Exemplos teóricos e simulações são utilizados como forma de validação dos métodos propostos, além de mostrar que os novos resultados apresentam condições menos conservadoras. Além disso, ao final é apresentada uma implementação prática em um sistema de suspensão ativa, produzida pela Quanser®. / Abstract: The resolution of linear quadratic regulator (LQR) problem via linear matrix inequalities (LMIs) for linear time-invariant systems subject to polytopic uncertainties, as linear systems subjects to linear parameter varying (LPV), is proposed in this work. The controllers' designs are based on the state derivative feedback. The aim to the choice of the state derivative feedback is your easy implementation in a class of mechanical systems, such as in vibration control, for example. The signals used for feedback are acceleration and velocity, it is obtained by means of accelerometers. Through the proposed method it is possible to obtain LMIs conditions for the synthesis of controllers that guarantee the stabilisation of the closed-loop system, being that the controllers have optimised performance. For the LMIs conditions formulations, a Lyapunov function of type quadratic is used. As a form of validation, theoretical examples and simulations are performed, besides to show that the new results are less conservative. Furthermore, a practical implementation in an active suspension system, produced by Quanser®, is performed. / Mestre

Cette recherche vise à résoudre un problème particulier du contrôle de vibration des structures intelligentes. Notre objectif est de réduire les vibrations dans une zone spécifique de la structure intelligente avec une perturbation qui couvre une large gamme de fréquences. De plus, dans cette zone spécifique, ni l'actionnement ni la détection ne sont possibles.Ici, nous faisons face à plusieurs défis principaux. Premièrement, nous devons contrôler les vibrations d’une zone spécifique de la structure, alors que nous n’avons accès aux mesures que dans d’autres zones. Deuxièmement, la large bande passante de la perturbation implique que nombreux modes doivent être contrôlés au même temps, ce qui nécessite l'utilisation de plusieurs actionneurs et capteurs. Cela conduit à un contrôleur MIMO difficile à obtenir avec les méthodes classiques de conception de contrôleur. Troisièmement, il faut éviter le problème de propagation, qui consiste à garantir la stabilité en boucle fermée lorsque le contrôleur basé sur un modèle est appliqué à la configuration réelle. Pour relever ces défis, nous étudions deux stratégies de contrôle: le contrôle centralisé et le contrôle distribué.Pour le contrôle centralisé, nous proposons une méthodologie qui nous permet d’obtenir un contrôleur MIMO simple permettant de relever ces défis. Tout d'abord, plusieurs techniques de modélisation et d’identification sont appliquées pour obtenir un modèle précis d'ordre faible de la structure intelligente. Ensuite, une méthode de synthèse basée sur le contrôle H_∞ avec un critère H_∞ particulièrement proposé est appliquée. Ce critère H_∞ intègre plusieurs objectifs de contrôle, y compris les défis principaux. En particulier, le problème de débordement se transforme en un problème de stabilité robuste et sera garanti en utilisant ce critère. Le contrôleur H_∞ obtenu est une solution standard du problème H_∞. Le contrôleur final est obtenu en simplifiant ce contrôleur H_∞ sans perdre la stabilité en boucle fermée ni dégrader les performances. Cette méthodologie est validée sur une structure de poutre avec des transducteurs piézoélectriques et la zone centrale est celle où les vibrations devraient être réduites. L'efficacité du contrôleur obtenu est validée par des simulations et des expériences.Pour le contrôle distribué, on considère la même structure de poutre et les mêmes objectifs de contrôle. Il existe des méthodes visant à concevoir des contrôleurs distribués pour les systèmes spatialement interconnectés. Cette recherche propose une méthode basée sur la FEM, associée à plusieurs techniques de réduction de modèle, permettant de discrétiser spatialement la structure de poutre et d'en déduire les modèles d’espace d'état des sous-systèmes interconnectés. La conception des contrôleurs distribués ne sera pas abordée dans cette recherche. / This research aims at solving a particular vibration control problem of smart structures. We aim at reducing the vibration in a specific zone of the smart structure under the disturbance that covers a wide frequency band. Moreover, at this specific zone, neither actuation nor sensing is possible.Here we face several main challenges. First, we need to control the vibration of a specific zone of the structure while we only have access to measurements at other zones. Second, the wide bandwidth of the disturbance implies that numerous modes should be controlled at the same time which requires the use of multiple actuators and sensors. This leads to a MIMO controller which is difficult to obtain using classical controller design methods. Third, the so-called spillover problem must be avoided which is to guarantee the closed-loop stability when the model-based controller is applied on the actual setup. To tackle these challenges, we investigate two control strategies: the centralized control and the distributed control.For centralized control, we propose a methodology that allows us to obtain a simple MIMO controller that accomplishes these challenges. First, several modeling and identification techniques are applied to obtain an accurate low-order model of the smart structure. Then, an H_∞ control based synthesis method with a particularly proposed H_∞ criterion is applied. This H_∞ criterion integrates multiple control objectives, including the main challenges. In particular, the spillover problem is transformed into a robust stability problem and will be guaranteed using this criterion. The obtained H_∞ controller is a standard solution of the H_∞ problem. The final controller is obtained by further simplifying this H_∞ controller without losing the closed-loop stability and degrading the performance. This methodology is validated on a beam structure with piezoelectric transducers and the central zone is where the vibration should be reduced. The effectiveness of the obtained controller is validated by simulations and experiments.For distributed control, we consider the same beam structure and the same control objectives. There exist methods aiming at designing distributed controllers of spatially interconnected system. This research proposes a FEM based method, combined with several model reduction techniques, that allows to spatially discretize the beam structure and deduce the state-space models of interconnected subsystems. The design of distributed controllers will not be tackled in this research.