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.

En aquesta Tesi es proposa una nova estructura de control amb l'objectiu de solucionar el conflicte entre rendiment i robustesa en l'esquema de realimentació tradicional. La teoria matemàtica de la factorització coprimera permet proposar un configuració de control basada en observador. És el que es denomina configuració Observador-Controlador i es fa servir de diferents maneres. La primera proposta enfoca la millorar les prestacions de robustesa com a una alternativa al disseny d'un controlador robust. Amb la intenció d'aconseguir un bon rendiment en presència de pertorbacions i d'incerteses procedim de la següent manera: en primer lloc, dissenyem un sistema de control per realimentació estàndard per tal de satisfer els requeriments de seguiment a referència; en segon lloc, millorem les propietats de robustesa sense alterar les propietats de seguiment del sistema de control inicial. Aquesta estratègia es basa en la generació d'un complement pel sistema de control nominal mitjançant una estructura fonamentada en la configuració Observador-Controlador. Els sistema de control resultant funciona de tal manera que la planta estarà controlada només pel controlador per realimentació nominal quan no hi hagi ni incerteses ni pertorbacions externes i el controlador per a la robustificació estarà actiu només en presencia de incerteses i/o pertorbacions externes.La segona proposta afronta l'objectiu d'aconseguir un bon rendiment en presència de pertorbacions i d'incerteses. En aquest cas, desenvolupen un controlador de dos graus de llibertat (2-DOF) i procedim de la següent manera: primer, dissenyem un sistema de control per realimentació basat en observador per tal de garantir un nivell mínim d'estabilitat robusta; segon, dissenyem un prefiltre per tal de garantir robustesa en les propietats de llaç obert. Malgrat les dues propostes no es basen en una reformulació en termes del factor de Youla, es possible fer una parametrització basada en Youla per tal de caracteritzar el conjunt de tots els observadors per una planta nominal. En essència, les dues propostes es poden veure com a estructures de dos graus de llibertat. Tot i que l'esquema de la primera proposta no s'adapta a una estructura de 2-DOF clàssica, amb un prefiltre i una part per realimentació, podem considerar-la com a tal pel fet que aconsegueix una complerta separació de propietats. En aquest cas, el controlador inicial s'ocupa de les especificacions de seguiment a referència per a la planta nominal i el controlador per a la robustificació s'encarrega de la millora, si cal, les prestacions de robustesa nominals. / In this Thesis, we shall propose a new controller architecture to try to completely overcome the conflict between performance and robustness in the traditional feedback framework. The proposed control configuration comes from the coprime factorization approach and, in such a context, a somewhat uncommon observer-based control configuration is derived. It is the Observer-Controller configuration and it is used in different arrangements.The first proposal deals with the robustness enhancement problem as an alternative to the design of a robust control system. With the lofty goal of achieving high performance in the face of disturbances and uncertainties we proceed as follows: first, an initial feedback control system is set for the nominal plant to satisfy tracking requirements and second, the resulting robustness properties are conveniently enhanced while leaving unaltered the tracking responses provided by the initial controller. The approach is based on the generation of a complement for the nominal control system by means of an structure based on the Observer-Controller configuration. The final control system works in such a way that the plant will be solely controlled by the initial nominal feedback controller when there is neither model uncertainties nor external disturbances and the robustification controller will only be active when there is model uncertainties and/or external disturbances. The second proposal also addresses the goal of high performance in the face of disturbances and uncertainties. In this case, a two degrees-of-freedom (2-DOF) control configuration is developed. We proceed as follows: first, an observer-based feedback control scheme is designed to guarantee some levels of stability robustness and second, a prefilter controller is computed to guarantee robust open-loop processing of the reference commands. Despite both proposals are not based on a reformulation in terms of the Youla parameter, it is possible to perform a Youla parametrization to characterize the set of all observers for the nominal plant. Essentially, both proposals can be considered as 2-DOF control configurations. The first presented proposal do not fit the standard 2-DOF control scheme made up with a feedback controller and a prefilter controller. Nevertheless, it can also be seen to lie in the 2-DOF control configuration in the sense that a complete separation of properties is achieved. In such case, the tracking properties of the nominal plant are attained by a controller and the robustness properties are considered and enhanced if necessary by the Observer-Controller configuration.

In the chemical or biochemical industry most processes are modeled by nonlinear equations. It is of a great significance to design high-performance nonlinear controllers for efficient control of these nonlinear processes to achieve closed-loop system's stability and high performance. However, there are many difficulties which hinder the design of such controllers due mainly to the process nonlinearity. In this work, comprehensive design procedures based on robust control have been proposed to efficiently deal with the design of gain-scheduled controllers for nonlinear systems. Since all the design procedures proposed in this work rely strongly on the process model, the first difficulty addressed in this thesis is the identification of a relatively simple model of the nonlinear processes under study. The nonlinearity of the processes makes it often difficult to obtain a first-principles model which can be used for analysis and design of the controller. As a result, relatively simple empirical models, Volterra series model and state-affine model, are chosen in this work to represent the nonlinear process for the design of controllers. The second major difficulty is that although the nonlinear models used in this thesis are easy to identify, the analysis of stability and performance for such models using nonlinear control theory is not straightforward. Instead, it is proposed in this study to investigate the stability and performance using a robust control approach. In this approach, the nonlinear model is approximated by a nominal linear model combined with a mathematical description of model error to be referred to, in this work, as model uncertainty. In the current work it was assumed that the main source of uncertainty with respect to the nominal linear model is due to the system nonlinearity. Then, in this study, robust control theoretical tools have been especially developed and applied for the design of gain-scheduled Proportional-Integral (PI) control and gain-scheduled Model Predictive Control (MPC). Gain-scheduled controllers are chosen because for nonlinear processes operated over a wide range of operation, gain-scheduling has proven to be a successful control design technique (Bequette, 1997) for nonlinear processes. To guarantee the closed-loop system's robust stability and performance with the designed controllers, a systematic approach has been proposed for the design of robust gain-scheduled controllers for nonlinear processes. The design procedure is based on robust stability and performance conditions proposed in this work. For time-varying uncertain parameters, robust stability and performance conditions using fixed Lyapunov functions and parameter-dependent Lyapunov functions, were used. Then, comprehensive procedures for the design and optimization of robust gain-scheduled PI and MPC controllers tuning parameters based on the robust stability and performance tests are then proposed. Since the closed-loop system represented by the combination of a state-affine process model and the gain-scheduled controller is found to have an affine dependence on the uncertain parameters, robust stability and performance conditions can be tested by a finite number of Linear Matrix Inequalities (LMIs). Thus, the final problems are numerically solvable. One of the inherent problems with robust control is that the design is conservative. Two approaches have been proposed in this work to reduce the conservatism. The first one is based on parameter-dependent Lyapunov functions, and it is applied when the rate of change of the time-varying uncertainty parameters is <i>a priori</i> available. The second one is based on the relaxation of an input-saturation factor defined in the thesis to deal with the issue of actuator saturation. Finally, to illustrate the techniques discussed in the thesis, robust gain-scheduled PI and MPC controllers are designed for a continuous stirred tank reactor (CSTR) process. A simple MIMO example with two inputs and two outputs controlled by a multivariable gain-scheduled MPC controller is also discussed to illustrate the applicability of the methods to multivariable situations. All the designed controllers are simulated and the simulations show that the proposed design procedures are efficient in designing and comparing robust gain-scheduled controllers for nonlinear processes.

This work focuses on the robustness issues related to distributed model predictive control (DMPC) strategies in the presence of model uncertainty. The robustness of DMPC with respect to model uncertainty has been identified by researchers as a key factor in the successful application of DMPC. A first task towards the formulation of robust DMPC strategy was to propose a new systematic methodology for the selection of a control structure in the context of DMPC. The methodology is based on the trade-off between performance and simplicity of structure (e.g., a centralized versus decentralized structure) and is formulated as a multi-objective mixed-integer nonlinear program (MINLP). The multi-objective function is composed of the contribution of two indices: 1) closed-loop performance index computed as an upper bound on the variability of the closed-loop system due to the effect on the output error of either set-point or disturbance input, and 2) a connectivity index used as a measure of the simplicity of the control structure. The parametric uncertainty in the models of the process is also considered in the methodology and it is described by a polytopic representation whereby the actual process’s states are assumed to evolve within a polytope whose vertices are defined by linear models that can be obtained from either linearizing a nonlinear model or from their identification in the neighborhood of different operating conditions. The system’s closed-loop performance and stability are formulated as Linear Matrix Inequalities (LMI) problems so that efficient interior-point methods can be exploited. To solve the MINLP a multi-start approach is adopted in which many starting points are generated in an attempt to obtain global optima. The efficiency of the proposed methodology is shown through its application to benchmark simulation examples. The simulation results are consistent with the conclusions obtained from the analysis. The proposed methodology can be applied at the design stage to select the best control configuration in the presence of model errors. A second goal accomplished in this research was the development of a novel online algorithm for robust DMPC that explicitly accounts for parametric uncertainty in the model. This algorithm requires the decomposition of the entire system’s model into N subsystems and the solution of N convex corresponding optimization problems in parallel. The objective of this parallel optimizations is to minimize an upper bound on a robust performance objective by using a time-varying state-feedback controller for each subsystem. Model uncertainty is explicitly considered through the use of polytopic description of the model. The algorithm employs an LMI approach, in which the solutions are convex and obtained in polynomial time. An observer is designed and embedded within each controller to perform state estimations and the stability of the observer integrated with the controller is tested online via LMI conditions. An iterative design method is also proposed for computing the observer gain. This algorithm has many practical advantages, the first of which is the fact that it can be implemented in real-time control applications and thus has the benefit of enabling the use of a decentralized structure while maintaining overall stability and improving the performance of the system. It has been shown that the proposed algorithm can achieve the theoretical performance of centralized control. Furthermore, the proposed algorithm can be formulated using a variety of objectives, such as Nash equilibrium, involving interacting processing units with local objective functions or fully decentralized control in the case of communication failure. Such cases are commonly encountered in the process industry. Simulations examples are considered to illustrate the application of the proposed method. Finally, a third goal was the formulation of a new algorithm to improve the online computational efficiency of DMPC algorithms. The closed-loop dual-mode paradigm was employed in order to perform most of the heavy computations offline using convex optimization to enlarge invariant sets thus rendering the iterative online solution more efficient. The solution requires the satisfaction of only relatively simple constraints and the solution of problems each involving a small number of decision variables. The algorithm requires solving N convex LMI problems in parallel when cooperative scheme is implemented. The option of using Nash scheme formulation is also available for this algorithm. A relaxation method was incorporated with the algorithm to satisfy initial feasibility by introducing slack variables that converge to zero quickly after a small number of early iterations. Simulation case studies have illustrated the applicability of this approach and have demonstrated that significant improvement can be achieved with respect to computation times. Extensions of the current work in the future should address issues of communication loss, delays and actuator failure and their impact on the robustness of DMPC algorithms. In addition, integration of the proposed DMPC algorithms with other layers in automation hierarchy can be an interesting topic for future work.