Orientador: Edvaldo Assunção / Banca: Marcelo Carvalho Minhoto Teixeira / Banca: Ricardo Coração de Leão Fontoura de Oliveira / Resumo: Este trabalho trata do problema de estabilização robusta e de novas técnicas de otimização robusta de sistemas lineares contínuos no tempo sujeitos a incertezas politópicas no modelo. Todo trabalho é fundamentado em leis de controle por realimentação estática de saída. As técnicas de projetos apresentam condições suficientes na forma de desigualdades matriciais lineares (LMIs, acrônimo inglês para Linear Matrix Inequalities), formuladas com base na teoria de estabilidade segundo Lyapunov. Além do mais, índices de desempenho como a taxa de decaimento também são considerados no modelo, visto que, garantir apenas a estabilidade nem sempre é suficiente para fins de engenharia. As modelagens LMIs são realizadas através de lemas largamente utilizados em diversas áreas de sistema de controle, como, por exemplo, o lema de Finsler, que permite o uso tanto de uma função de Lyapunov dependente de parâmetros (PDLF, acrônimo inglês para Parameter-Dependent Lyapunov Function) quanto o uso de LMIs clássicas baseadas na existência de uma função de Lyapunov quadrática comum (CQLF, acrônimo inglês para Common Quadratic Lyapunov Function) para assegurar a estabilidade assintótica dos sistemas. Comparações entre ambos os métodos de projeto foram realizadas, e o presente trabalho apresenta resultados menos conservadores na maior parte das ocasiões, isto é, na maioria das vezes os problemas podem ser solucionados com PDLFs e não com CQLFs. Ainda, é proposta neste trabalho uma nova técnica para otimização da norma de controladores de saída e comparações são realizadas entre os métodos como forma de verificar a sua eficácia. O desafio deste trabalho consiste em realizar projetos de controladores robustos via LMIs através da realimentação estática de saída que fossem passíveis de implementação... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This thesis addresses the problem of robust stabilization and robust new optimization techniques for continuous-time linear systems subject to polytopic uncertainties in the model. All work is based on static output feedback control laws. The text presents sufficient conditions for control projects in the form of Linear Matrix Inequalities (LMIs), formulated in terms of the Lyapunov stability theory. Moreover, performance indices as decay rate are also considered in the model, since only ensure stability is not always sufficient for engineering purposes. The modeling is performed using LMIs widely used lemmas in several areas of control systems , such as, for example, the Lemma of Finsler, which allows the use of Parameters Dependent Lyapunov Functions (PDLFs) as the use of classic LMIs based on the existence of a Common Quadratic Lyapunov Functions (CQLFs) to ensure asymptotic stability of the systems. Comparisons between the two design methods were performed, and the present work shows less conservative results on most occasions, in other words, the problems can be solved with PDLFs and not with CQLFs in most cases. Still, this work proposes a new technique for optimizing the norm of output controllers and comparisons are made between the methods as a way to verify its effectiveness. The challenge of this work was to carry out robust controllers designs based on LMIs through static output feedback that could be implemented on a real physical system subject to failure. Thus, simulations were made and the designed output controllers were implemented in a 3-DOF (Degrees Of Freedom) helicopter bench of Quanserr trademark, always seeking alternative controllers with better performance and lower norm that... (Complete abstract click electronic access below) / Mestre

Orientador: Marcelo Carvalho Minhoto Teixeira / Banca: Edvaldo Assunção / Banca: Rodrigo Cardin / Banca: Ricardo Hiroshi Caldeira Takahashi / Banca: Grace Silva Deaecto / Resumo: Esta tese propõe novos métodos de projeto de controle chaveado para algumas classes de sistemas: lineares com incertezas politópicas e não lineares incertos descritos por modelos fuzzy Takagi-Sugeno. Inicialmente são propostos métodos que utilizam uma função quadrática de Lyapunov e a estabilidade quadrática é utilizada para projetar vários ganhos do controlador, baseado em desigualdades matriciais lineares (do inglês Linear Matrix Inequalities - LMIs). Os controladores propostos são compostos por um único ganho que é escolhido por uma lei de chaveamento que retorna o menor valor da derivada temporal da função quadrática de Lyapunov. Para o caso linear, os controladores concebidos apresentam um melhor desempenho quando comparados com o controlador que emprega um único ganho de realimentação do estado normalmente implementado, e as LMIs utilizadas para encontrar os ganhos são mais relaxadas. Para o caso não linear, os controladores propostos também apresentaram um bom desempenho e eliminam a necessidade de encontrar as expressões explícitas das funções de pertinência que muitas vezes podem ter expressões longas e/ou complexas, ou serem desconhecidas devido às incertezas na planta. Em seguida foram propostos novos métodos de projeto de controle chaveado e um novo critério de estabilidade para sistemas não lineares incertos descritos por modelos fuzzy Takagi-Sugeno. O projeto do controlador chaveado é baseado na função de Lyapunov quadrática por partes do tipo mínimo e na minimização da derivada temporal desta função de Lyapunov. As condições do novo critério de estabilidade são representadas por um tipo de desigualdades matriciais bilineares (do inglês Bilinear Matrix Inequalities - BMIs) que podem ser resolvidas de forma eficiente pelo método... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This thesis proposes new switched control design methods for some classes of linear systems with polytopic uncertainties and uncertain nonlinear systems described by Takagi-Sugeno fuzzy models. Initially, are proposed methods that use a quadratic Lyapunov function and quadratic stability to design, based on Linear Matrix Inequalities (LMIs), the feedback gains. The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the quadratic Lyapunov function. For the linear case, the proposed methodology presents a better performance when compared with the controller usually implemented which uses only one state feedback gain and the LMIs for finding the switched gains are more relaxed. For nonlinear plants described by Takagi-Sugeno fuzzy models, the proposed controller also presented good performance and eliminates the need to obtain the explicit expressions of the membership functions of the Takagi-Sugeno fuzzy controllers, which can often have long and/or complex expressions, or may not be known, for instance due to the plant uncertainties. The design of the switched controllers is based on a minimum-type piecewise quadratic Lyapunov function and the minimization of the time derivative of this Lyapunov function. The conditions of the new stability criterion are represented by a kind of Bilinear Matrix Inequalities (BMIs) that can be efficiently solved by the path-following method. Furthermore, the proposed switched controller can also operate even with an uncertain reference control signal. To verify the efficacy of the proposed methodology are presented numerical simulations, including robust nonlinear control designs of a ball-and-beam system and of a magnetic levitator, and finally a robust... (Complete abstract click electronic access below) / Doutor

Orientador: Marcelo Carvalho Minhoto Teixeira / Banca: Edvaldo Assunção / Banca: Márcio Roberto Covacic. / Resumo: Neste trabalho são propostas condições suficientes para o controle H∞ chaveado de sistemas lineares incertos contínuos no tempo. A técnica abordada para este estudo consiste na utilização de uma função quadrática de Lyapunov e em um caso mais específico, uma função quadrática de Lyapunov por partes. A análise de estabilidade é descrita por meio de Desigualdades Matriciais Lineares (em inglês: Linear Matrix Inequalities), LMIs, que, quando factíveis, são facilmente resolvidas por meio de ferramentas disponíveis na literatura de programação convexa. Assim é apresentada uma metodologia de chaveamento do ganho de realimentação do vetor de estado, que assegura também o critério de desempenho H∞, cuja estratégia busca a obtenção do mínimo valor da derivada de uma função de Lyapunov quadrática. O método foi estendido com o emprego de uma função de Lyapunov quadrática por partes, cujo projeto é baseado nas desigualdades de Lyapunov-Metzler. É demonstrado que esta nova estratégia de chaveamento, além de uma implementação simples, oferece uma flexibilização das LMIs em comparação com os métodos convencionais que também utilizam o controle H∞. A teoria é ilustrada através de exemplos, que permitem comprovar o bom desempenho dos métodos propostos, incluindo a implementação em laboratório do controle de um helicóptero 3-DOF de bancada da QUANSER, sujeito a falhas estruturais. / Abstract: Sufficient conditions for the switched H∞ control of continuous-time uncertain linear systems are proposed. The technique discussed in this study is based on quadratic Lyapunov functions and a piecewise quadratic Lyapunov functions. The stability analysis is described by LMIs that, when feasible, are easily solved by available tools in the convex programming literature. Thus, a methodology for designing the switching of state vector feedback gains, which also ensures H∞ performance criterion, is presented. This new procedure chooses the state feedback gain that returns the minimum value of the time derivative of the Lyapunov function. The method was extended to a piecewise quadratic Lyapunov function and is designed from the solution of Lyapunov-Metzler inequalities. It is shown that this switching strategy, beyond a simple implementation, offers a relaxation in the LMIs, when compared with the conventional methods used in H∞ control. The procedure are illustrated by means of examples, including an implementation in the control of a 3-DOF helicopter, subject to structural failures. / Mestre

Orientador: Edvaldo Assunção / Banca: Marcelo Carvalho Minhoto Teixeira / Banca: Rodrigo Cardim / Banca: Marcio Roberto Covacic / Banca: Eduardo Fontoura Costa / Resumo: Nesta tese apresentam-se resultados para a estabilidade robusta de sistemas lineares sujeitos a incertezas paramétricas do tipo politópicas, variantes no tempo (do inglês Linear Parameter Varying - LPV). De início, expõe-se um método aprimorado para o projeto com otimização da norma de controladores robustos via desigualdades matriciais lineares (do inglês Linear Matrix Inequalitites - LMIs), com base na teoria de estabilidade segundo Lyapunov. Esta nova formulação foi manipulada utilizando o lema de Finsler, e permitiu encontrar melhores resultados de factibilidade com o acréscimo de matrizes extras e redução do número de LMIs. Neste novo equacionamento houve a inclusão do índice de desempenho da taxa de decaimento, responsável por diminuir o tempo de duração do período transitório, e também da otimização da norma dos controladores, responsável por menores ganhos mantendo a mesma eficiência dos requisitos de projeto. Devido a importantes resultados da literatura para o projeto de controladores robustos com incertezas variantes no tempo, optou-se por explorar o projeto de controladores dinâmicos chaveados, inovando-se no tocante ao acréscimo da taxa de decaimento e à otimização da norma dos controladores chaveados, o que possibilitou encontrar melhores resultados de implementação. Por fim, foram propostos critérios menos conservadores para a análise de estabilidade e projeto de controladores chaveados, utilizando funções de Lyapunov quadráticas por partes do tipo mínimo. A vantagem desse procedimento está no aumento dos parâmetros de relaxação porém, concebido através de formulações baseadas em desigualdades matriciais bilineares (do inglês Bilinear Matrix Inequalitites - BMIs), nos quais os termos e se encontram no produto entre variáveis escalares de otimização e matrizes, que também são variáveis do procedimento de otimização. Apresentam-se, no corpo do texto, exemplos numéricos e ... / Abstract: This thesis presents results for robust stability of linear systems subject to polytopic timevarying parametric uncertainties (LPV). To start with, an improved method for the optimal gain design of robust controllers via Linear Matrix Inequalities (LMI), based on Lyapunov stability theory is presented. This new formulation was manipulated using the Finsler lemma, which enabled finding better feasibility results with the addition of extra matrices and reducing the number of LMIs. In this new equation it was included the decay rate performance index, responsible for reducing the transitional period time, as well as the controllers norm optimization, responsible for lower gains while maintaining the same project requirements efficiency. Then, due to important results in literature regarding the design of robust controllers with time-varying uncertainties, the design of switched dynamic controllers was explored by including the decay rate index and the optimization of the switched controllers norm in the equation, which allowed finding better implementation results. Finally, less conservative criteria were proposed for stability analysis and design of switched controllers using minimum-type piecewise quadratic Lyapunov functions. The advantage of this procedure lies in the increase of relaxation parameters, however, designed through formulations based on Bilinear Matrix Inequalities (BMIs), where the bilinear terms are in the product between optimization scalar variables and matrices, which are also variables on the optimization procedure. Numerical examples are presented and simulated to illustrate the efficiency of the proposed methodologies in relation to other existing throughout the text. The designed controllers were implemented using these new proposals in a Three Degrees Of Freedom (3-DOF) helicopter or in the Shake Table II (STII) + Active Mass Dumper - One Floor (AMD-1) system, in order to validate in practice the proposed theories / Doutor

Este trabalho apresenta os resultados da aplicação de três técnicas de controle utilizadas no projeto e implementação do controle de um manipulador subatuado planar de três juntas em série e de elos rígidos, projetado e construído pela Universidade Carnegie Mellon, EUA. Devido ao alto grau de não-linearidade deste sistema, seria muito difícil implementar um controlador H2, H&#8734 ou H2/H&#8734 que atuasse sozinho. Assim, propõe-se a utilização de um método de controle combinado: torque computado/H2, H&#8734 ou H2/H&#8734. No controle combinado, a porção correspondente ao torque computado lineariza e pré-compensa a dinâmica do modelo da planta nominal, enquanto a porção correspondente ao controle H2, H&#8734 ou H2/H&#8734 realiza uma pós-compensação dos erros residuais, que não foram completamente eliminados pelo método torque computado. Testes de acompanhamento de trajetória e testes de robustez são realizados aqui para comprovar a eficiência destes controladores, com resultados de implementação bastante satisfatórios. / This work presents the application results of three control techniques used for the control design and implementation of a serial planar underactuated manipulator with three joints and rigid links, designed and built by the Carnegie Mellon University, USA. Due to the high non-linearity degree of this system, it would be very difficult to implement an H2, H&#8734 or H2/ H&#8734 control which would actuate on the system by itself. Therefore, it is proposed a combined control method: computed torque/ H2, H&#8734 or H2/H&#8734. In the combined control, the portion corresponding to the computed torque linearizes and pre-compensates the dynamics of the nominal model, while the portion corresponding to the H2, H&#8734 or H2/H&#8734 control realizes a pos-compensation of the residual errors, not completely removed by the computed torque method. Trajetory tracking and robustness tests are performed here to demonstrate the efficiency of these controllers, with very satisfatory implementation results.

This thesis presents alternative methods for designing a speed controller for a hydrostatic power transmission system. Recognising that such a system, comprising a valve controlled motor supplied by the laboratory ring main and driving a hydraulic pump as a load, contains significant non-linearities, the thesis shows that robust 'modern control' approaches may be applied to produce viable controllers without recourse to the use of a detailed model of the system. In its introduction, it considers why similar approaches to the design of fluid power systems have not been applied hitherto. It then sets out the design and test, in simulation and on a physical rig, of two alternative linear controllers using H∞ based methods and a 'self organising fuzzy logic' controller (SOFLC). In the linear approaches, differences between the characteristics of the system and the simple models of it are accommodated in the controller design route as 'perturbations' or 'uncertainties'. The H∞ based optimisation methods allow these to be recognised in the design. “Mixed sensitivity” and “Loop shaping” methods are each applied to design controllers which are tested successfully on the laboratory rig. The SOFLC in operation does not rely on a model, but instead allows fuzzy control rules to evolve. In the practical tests, the system is subjected to a range of disturbances in the form of supply pressure fluctuations and load torque changes. Also presented are test results for proportional and proportional plus integral (PI) controllers, to provide a reference. It is demonstrated qualitatively that performance using the linear controllers is superior to that using proportional and PI controllers. An increased range of stable operation is achieved by the controller designed using “loop shaping” – performance is enhanced by the use of two controllers selected automatically according to the operating speed, using a “bumpless” transfer routine. The SOFLC proved difficult to tune. However, stable operation was achieved.

Liu Lu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 65-70). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Output Regulation Problem --- p.1 / Chapter 1.2 --- Control Design with Unknown High-frequency Gain Sign --- p.3 / Chapter 1.3 --- Contribution of the Thesis --- p.4 / Chapter 1.4 --- Thesis Outline --- p.5 / Chapter 2 --- Global Robust Stabilization of a Class of Nonlinear Systems --- p.6 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Problem Formulation and Preliminaries --- p.8 / Chapter 2.3 --- Main Result --- p.11 / Chapter 2.4 --- An Example --- p.20 / Chapter 2.5 --- Application of Theorem 2.1 --- p.26 / Chapter 2.5.1 --- Chua's Circuit and Control Problem --- p.26 / Chapter 2.5.2 --- Solvability of the Control Problem --- p.28 / Chapter 2.5.3 --- Simulation Results --- p.32 / Chapter 2.5.4 --- Conclusion --- p.33 / Chapter 2.6 --- Conclusion --- p.36 / Chapter 3 --- Global Robust Output Regulation of Nonlinear Systems in Output Feedback Form --- p.39 / Chapter 3.1 --- Introduction --- p.40 / Chapter 3.2 --- Output Regulation Converted to Stabilization --- p.42 / Chapter 3.3 --- Main Result --- p.49 / Chapter 3.4 --- An Example --- p.55 / Chapter 3.5 --- Conclusion --- p.58 / Chapter 4 --- Conclusions --- p.62 / List of Figures --- p.64 / Bibliography --- p.65 / Biography

Chen Zhiyong. / "April 2005." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 205-215) / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Zhong, Renxin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 107-114). / Abstracts in English and Chinese. / Abstract --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Non-Minimum Phase Nonlinear Systems --- p.1 / Chapter 1.2 --- Robust Output Regulation Problem --- p.4 / Chapter 1.3 --- Global Robust Output Regulation for Non-Minimum Phase Nonlinear Systems in Lower Triangular Form --- p.6 / Chapter 1.4 --- Rotational/Translational Actuator System --- p.8 / Chapter 1.5 --- Organization and Contributions --- p.8 / Chapter 2 --- Global Robust Output Regulation for Non-Minimum Phase Non-linear Systems in Lower Triangular Form --- p.10 / Chapter 2.1 --- Introduction --- p.10 / Chapter 2.2 --- Assumptions and Preliminaries --- p.12 / Chapter 2.3 --- Solvability Conditions --- p.17 / Chapter 2.4 --- Numerical Examples --- p.19 / Chapter 2.5 --- Concluding Remarks --- p.46 / Chapter 3 --- Global Robust Output Regulation for A Class of Non-Minimum Phase Nonlinear Systems by Output Feedback Control --- p.47 / Chapter 3.1 --- Introduction --- p.48 / Chapter 3.2 --- Assumptions and Preliminaries --- p.49 / Chapter 3.3 --- Reduced order observer design --- p.56 / Chapter 3.4 --- Stabilization of x system --- p.59 / Chapter 3.5 --- "Interconnection of the n,z,ζ,x subsystems and small gain condition" --- p.63 / Chapter 3.6 --- Numerical example --- p.67 / Chapter 3.7 --- Conclusion --- p.76 / Chapter 4 --- Robust output regulation for the nonlinear benchmark problem via output feedback --- p.77 / Chapter 4.1 --- Introduction --- p.78 / Chapter 4.2 --- Disturbance rejection problem of the RTAC system by output feedback control --- p.79 / Chapter 4.3 --- Robust Disturbance rejection problem of the RTAC system by output feedback --- p.88 / Chapter 4.4 --- Conclusion --- p.98 / Chapter 5 --- Conclusion --- p.103 / List of Figures --- p.105 / Bibliography --- p.107 / Biography --- p.115

Teleoperation systems have been used in the operating rooms for more than a decade. However, the lack of force feedback in commercially available systems still raises safety issues and forbids surgical gestures like palpation. Although force feedback has already been implemented in experimental setups, a systematic methodology is still lacking to design the control laws. The approach developed in this thesis is a contribution towards such a systematic methodology: it combines the use of disturbance observers with the use of a structured fixed-order controller. This approach is validated by experiments performed on a one degree of freedom teleoperation system. A physical model of this system is proposed and validated experimentally. Disturbance observers allow to compensate friction, which is responsible for performance degradation in teleoperation. Contrary to alternative approaches,they are based on a model of the frictionless mechanical system. This allows to compensate friction with a time varying behavior, which occurs in laparoscopy. Parametric uncertainties in this model may lead to an unstable closed-loop. A kind of "separation principle" is provided to decouple the design of the closed-loop system from the design of the observer. It relies on a modified problem statement and on the use of available robust design and analysis tools. A new metric is proposed to evaluate the performance of friction compensation systems experimentally. This metric evaluates the ability of a compensation system to linearize a motion system, irrespective of the task and as a function of frequency. The observer-based friction compensation is evaluated with respect to this new metric and to a task-based metric. It correctly attenuates the friction in the bandwidth of interest and significantly improves position and force tracking during a palpation task. Structured fixed-order controllers are optimized numerically to achieve robust closed-loop performance despite modeling uncertainty. The structure is chosen among classical teleoperation structures. An efficient algorithm is selected and implemented to design such a controller, which is evaluated for a palpation task. It is compared to a full-order unstructured controller, representative of the design approach that has been used in the teleoperation literature up to now. The comparison highlights the advantages of our new approach: order-reduction steps and counter-intuitive behaviors are avoided. A structured fixed-order controller combined with a disturbance observer is implemented during a needle insertion experiment and allowed to obtain excellent performance.