Orientador: Grace Silva Deaecto / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-27T00:51:44Z (GMT). No. of bitstreams: 1 Santos_GuilhermeCavalari_M.pdf: 16424850 bytes, checksum: 7f2f16f9c4c4f920f928c8d19273978a (MD5) Previous issue date: 2015 / Resumo: Esta dissertação trata do projeto de controle H2 e Hoo via realimentação de estado para sistemas afins com comutação a tempo contínuo. Nosso objetivo principal é projetar um conjunto de ganhos de realimentação de estado e uma função de comutação assegurando estabilidade assintótica global do ponto de equilíbrio desejado. Este ponto deve pertencer a um conjunto de pontos de equilíbrio atingíveis a ser determinado. Além disso, o projeto deve levar em conta índices de desempenho H2 e Hoo que são adequadamente definidos. Para o projeto de controle Hoo, duas funções de comutação são propostas e discutidas. A primeira delas depende somente do estado, enquanto a segunda representa uma nova proposta que é mais geral e depende também da entrada externa. As condições obtidas são menos conservadoras do que as técnicas recentes disponíveis na literatura, por exemplo, os métodos baseados na função de Lyapunov do tipo máximo e os utilizados normalmente para assegurar estabilidade prática. Exemplos numéricos ilustram os resultados teóricos obtidos e são usados para comparações / Abstract: This Master's thesis deals with state feedback H2 and Hoo control design of continuous-time switched affine systems. Our main goal is to design a set of state feedback gains and a switching function assuring global asymptotical stability of a desired equilibrium point. This point must belong to a set of attainable equilibrium points to be determined. Moreover, the design must consider H2 and Hoo performance indexes to be defined. For the Hoo control design, two different switching functions are proposed and discussed. The first one depends only on the state and the other depends on the state and on the external input. The conditions are less conservative than the techniques available in the literature to date, as for instance, those based on a max-type Lyapunov function and those commonly used to assure practical stability. Numerical examples illustrate the theoretical results and are used for comparisons / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

abstract: For the last 50 years, oscillator modeling in ranging systems has received considerable attention. Many components in a navigation system, such as the master oscillator driving the receiver system, as well the master oscillator in the transmitting system contribute significantly to timing errors. Algorithms in the navigation processor must be able to predict and compensate such errors to achieve a specified accuracy. While much work has been done on the fundamentals of these problems, the thinking on said problems has not progressed. On the hardware end, the designers of local oscillators focus on synthesized frequency and loop noise bandwidth. This does nothing to mitigate, or reduce frequency stability degradation in band. Similarly, there are not systematic methods to accommodate phase and frequency anomalies such as clock jumps. Phase locked loops are fundamentally control systems, and while control theory has had significant advancement over the last 30 years, the design of timekeeping sources has not advanced beyond classical control. On the software end, single or two state oscillator models are typically embedded in a Kalman Filter to alleviate time errors between the transmitter and receiver clock. Such models are appropriate for short term time accuracy, but insufficient for long term time accuracy. Additionally, flicker frequency noise may be present in oscillators, and it presents mathematical modeling complications. This work proposes novel H∞ control methods to address the shortcomings in the standard design of time-keeping phase locked loops. Such methods allow the designer to address frequency stability degradation as well as high phase/frequency dynamics. Additionally, finite-dimensional approximants of flicker frequency noise that are more representative of the truth system than the tradition Gauss Markov approach are derived. Last, to maintain timing accuracy in a wide variety of operating environments, novel Banks of Adaptive Extended Kalman Filters are used to address both stochastic and dynamic uncertainty. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2020

No description available.

Neste trabalho, o equacionamento dinâmico de um manipulador espacial de base livre flutuante é descrito a partir do conceito do manipulador dinamicamente equivalente para que as técnicas de controle desenvolvidas sejam experimentalmente validadas em um manipulador convencional de base fixa. Dois tipos de controle de movimento são considerados. O primeiro foi desenvolvido no espaço das juntas e realiza o comando direto de posicionamento das juntas do manipulador; o segundo foi desenvolvido no espaço inercial e o controle é direcionado para o posicionamento do efetuador no espaço Cartesiano. Nos dois casos, o problema de acompanhamento de trajetória de um manipulador espacial com base livre flutuante sujeito a incertezas na planta e perturbações externas é proposto e solucionado sob o ponto de vista do critério de desempenho H \'INFINITO\'. Considerando métodos de controle para sistemas subatuados, três técnicas adaptativas foram desenvolvidas a partir de um controlador H \'INFINITO\' não-linear baseado na teoria dos jogos. A primeira técnica foi proposta considerando a estrutura do modelo bem definida, porém calculada com base em parâmetros incertos. Uma lei adaptativa foi aplicada para estimar esses parâmetros utilizando parametrização linear. Redes neurais artificiais são aplicadas nas outras duas abordagens adaptativas. A primeira utiliza uma rede neural para aprender o comportamento dinâmico do sistema robótico, considerado totalmente desconhecido. Nenhum dado cinemático ou dinâmico da base é utilizado neste caso. A segunda abordagem considera a estrutura do modelo nominal do manipulador bem definida e a rede neural é aplicada para estimar o comportamento das incertezas paramétricas e da dinâmica não-modelada da base. O critério H \'INFINITO\' é aplicado nas três técnicas para atenuar o efeito dos erros de estimativa. Resultados experimentais foram obtidos com um robô manipulador de base fixa subatuado (UArmII) e apresentaram melhor desempenho no acompanhamento da trajetória e no consumo de energia para as abordagens baseadas em redes neurais. / In the present work, the dynamics of a free-floating space manipulator is described through the dynamically equivalent manipulator approach in order to obtain experimental results in a planar fixed base manipulator. Control in joint and Cartesian spaces are considered. The first acts directly on joints positioning; the second control scheme acts on positioning the end-effector in some inertially fixed position. In both cases, the problem of tracking control with a guaranteed H-infinity performance for free-floating manipulator systems with plant uncertainties and external disturbances is proposed and solved. Considering control methods for underactuated systems, three adaptive techniques were developed from a nonlinear H-infinity controller based on game theory. The first approach was proposed considering a well defined structure for the plant, however it was computed based on uncertain parameters. An adaptive law was applied to estimate these parameters using linear parametrization. Artificial neural networks were applied in the two other approaches. The first one uses a neural network to learn the dynamic behavior from the robotic system, which is considered totally unknown. No kinematics or dynamics data from the spacecraft are necessary in this case. The second approach considers the nominal model structure well defined and the neural network is applied to estimate the behavior of the parametric uncertainties and of the spacecraft non-modeled dynamics. The H-infinity criterion was applied to attenuate the effect of estimation errors in the three techniques. Experimental results were obtained with an underactuated fixed-base planar manipulator (UArmII) and presented better performance in tracking and energy consumption for the neural based approaches.

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.

No description available.

No description available.

Dans ce travail, nous abordons les problèmes de l'analyse de la stabilité et de la synthèse de contrôleur pour une Equation aux Dérivées Partielles (EDP) parabolique linéaire de dimension 1. Ces problèmes sont résolus avec des méthodologies analogues au cadre des inégalités matricielles linéaires (LMI) pour les équations différentielles ordinaires (EDO). Nous développons une méthode pour EDP paraboliques dans laquelle nous testons la faisabilité de certaines LMIs utilisant la programmation semi-définie (SDP) pour construire des fonctions de Lyapunov quadratiques et des contrôleurs. Le cœur de notre démarche est la construction de fonctions de Lyapunov quadratiques paramétrées par les opérateurs définis positifs sur les espaces de Hilbert de dimension infinie. Contrairement aux matrices positives, il n'y a pas de méthode unique paramétrisant l'ensemble des opérateurs positifs sur un espace de Hilbert. Bien sûr, nous pouvons toujours paramétrer un sous-ensemble des opérateurs positifs en utilisant, par exemple, des scalaires positifs. Cependant, nous devons nous assurer que le paramétrage des opérateurs positifs ne doit pas être conservatif. Notre contribution est de construire une paramétrisation qui a seulement une petite quantité de conservatisme comme indiqué par nos résultats numériques. Nous utilisons des polynômes en somme des carrés (SOS) pour paramétrer l'ensemble des opérateurs positifs, linéaire et bornés sur les espaces de Hilbert. Comme son nom l'indique, un polynôme SOS est celui qui peut être représenté comme une somme de polynômes carrés. La propriété la plus importante d'un polynôme SOS est qu'il peut être représenté au moyen d'une matrice (semi-)définie positive. Cela implique que, même si le problème de polynôme (semi-)positif est NP-difficile, le problème de vérifier si polynôme est SOS (et donc (semi-)positif) peut être résolu en utilisant la SDP. Par conséquent, nous nous efforçons de construire des fonctions de Lyapunov quadratiques paramétrées par les opérateurs positifs. Ces opérateurs positifs sont à leur tour paramétrés par des polynômes SOS. Cette paramétrisation SOS nous permet de formuler le problème de faisabilité pour l'existence d'une fonction de Lyapunov quadratique comme un problème de faisabilité LMI. Le problème de la faisabilité LMI peut alors être adressé à l'aide de SDP. Dans la première partie de la thèse nous considérons analyse de stabilité et la synthèse de contrôleur aux frontières pour une large classe d'EDP paraboliques. Les EDP ont des coefficients de transport distribués spatialement. Ces EDP sont utilisés pour modéliser les processus de diffusion, de convection et de réaction de quantités physiques dans les milieux anisotropes. Nous considérons la synthèse de contrôleurs limite à la fois pour le cas de retour d'état et le cas de retour de sortie (à l'aide d'un observateur). Dans la deuxième partie de la thèse, nous concevons un contrôleur distribué pour la régulation du flux magnétique poloïdal dans un tokamak (procédé de fusion thermonucléaire par confinement magnétique). Tout d'abord, nous concevons un contrôleur régulant la pente des lignes de champ magnétique (le facteur de sécurité). La régulation du profil du facteur de sécurité est importante pour supprimer les instabilités MHD dans un tokamak. Ensuite, nous concevons un contrôleur maximisant la densité de courant bootstrap généré en interne. Une proportion accrue du courant bootstrap conduirait à une réduction des besoins énergétiques exogènes pour l'exploitation d'un tokamak. / In this work we address the problems of stability analysis and controller synthesis for one dimensional linear parabolic Partial Differential Equations (PDEs). To achieve the tasks of stability analysis and controller synthesis we develop methodologies akin to the Linear Matrix Inequality (LMI) framework for Ordinary Differential Equations (ODEs). We develop a method for parabolic PDEs wherein we test the feasibility of certain LMIs using SDP to construct quadratic Lyapunov functions and controllers. The core of our approach is the construction of quadratic Lyapunov functions parametrized by positive definite operators on infinite dimensional Hilbert spaces. Unlike positive matrices, there is no single method of parametrizing the set of all positive operators on a Hilbert space. Of course, we can always parametrize a subset of positive operators, using, for example, positive scalars. However, we must ensure that the parametrization of positive operators should not be conservative. Our contribution is constructing a parametrization which has only a small amount of conservatism as indicated by our numerical results. We use Sum-of-Squares (SOS) polynomials to parametrize the set of positive, linear and bounded operators on Hilbert spaces. As the name indicates, an SOS polynomial is one which can be represented as a sum of squared polynomials. The most important property of an SOS polynomial is that it can be represented using a positive (semi)-definite matrix. This implies that even though the problem of polynomial (semi)-positivity is NP-hard, the problem of checking if polynomial is SOS (and hence (semi)-positive) can be solved using SDP. Therefore, we aim to construct quadratic Lyapunov functions parametrized by positive operators. These positive operators are in turn parametrized by SOS polynomials. This parametrization using SOS allows us to cast the feasibility problem for the existence of a quadratic Lyapunov function as the feasibility problem of LMIs. The feasibility problem of LMIs can then be addressed using SDP. In the first part of the thesis we consider stability analysis and boundary controller synthesis for a large class of parabolic PDEs. The PDEs have spatially distributed coefficients. Such PDEs are used to model processes of diffusion, convection and reaction of physical quantities in anisotropic media. We consider boundary controller synthesis for both the state feedback case and the output feedback case (using and observer design). IN the second part of thesis we design distributed controllers for the regulation of poloidal magnetic flux in a tokamak (a thermonuclear fusion devise). First, we design the controllers to regulate the magnetic field line pitch (the safety factor). The regulation of the safety factor profile is important to suppress the magnetohydrodynamic instabilities in a tokamak. Then, we design controllers to maximize the internally generated bootstrap current density. An increased proportion of bootstrap current would lead to a reduction in the external energy requirements for the operation of a tokamak.

abstract: In this dissertation, we present a H-infinity based multivariable control design methodology that can be used to systematically address design specifications at distinct feedback loop-breaking points. It is well understood that for multivariable systems, obtaining good/acceptable closed loop properties at one loop-breaking point does not mean the same at another. This is especially true for multivariable systems that are ill-conditioned (having high condition number and/or relative gain array and/or scaled condition number). We analyze the tradeoffs involved in shaping closed loop properties at these distinct loop-breaking points and illustrate through examples the existence of pareto optimal points associated with them. Further, we study the limitations and tradeoffs associated with shaping the properties in the presence of right half plane poles/zeros, limited available bandwidth and peak time-domain constraints. To address the above tradeoffs, we present a methodology for designing multiobjective constrained H-infinity based controllers, called Generalized Mixed Sensitivity (GMS), to effectively and efficiently shape properties at distinct loop-breaking points. The methodology accommodates a broad class of convex frequency- and time-domain design specifications. This is accomplished by exploiting the Youla-Jabr-Bongiorno-Kucera parameterization that transforms the nonlinear problem in the controller to an affine one in the Youla et al. parameter. Basis parameters that result in efficient approximation (using lesser number of basis terms) of the infinite-dimensional parameter are studied. Three state-of-the-art subgradient-based non-differentiable constrained convex optimization solvers, namely Analytic Center Cutting Plane Method (ACCPM), Kelley's CPM and SolvOpt are implemented and compared. The above approach is used to design controllers for and tradeoff between several control properties of longitudinal dynamics of 3-DOF Hypersonic vehicle model -– one that is unstable, non-minimum phase and possesses significant coupling between channels. A hierarchical inner-outer loop control architecture is used to exploit additional feedback information in order to significantly help in making reasonable tradeoffs between properties at distinct loop-breaking points. The methodology is shown to generate very good designs –- designs that would be difficult to obtain without our presented methodology. Critical control tradeoffs associated are studied and compared with other design methods (e.g., classically motivated, standard mixed sensitivity) to further illustrate its power and transparency. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2018

Neste trabalho, o equacionamento dinâmico de um manipulador espacial de base livre flutuante é descrito a partir do conceito do manipulador dinamicamente equivalente para que as técnicas de controle desenvolvidas sejam experimentalmente validadas em um manipulador convencional de base fixa. Dois tipos de controle de movimento são considerados. O primeiro foi desenvolvido no espaço das juntas e realiza o comando direto de posicionamento das juntas do manipulador; o segundo foi desenvolvido no espaço inercial e o controle é direcionado para o posicionamento do efetuador no espaço Cartesiano. Nos dois casos, o problema de acompanhamento de trajetória de um manipulador espacial com base livre flutuante sujeito a incertezas na planta e perturbações externas é proposto e solucionado sob o ponto de vista do critério de desempenho H \'INFINITO\'. Considerando métodos de controle para sistemas subatuados, três técnicas adaptativas foram desenvolvidas a partir de um controlador H \'INFINITO\' não-linear baseado na teoria dos jogos. A primeira técnica foi proposta considerando a estrutura do modelo bem definida, porém calculada com base em parâmetros incertos. Uma lei adaptativa foi aplicada para estimar esses parâmetros utilizando parametrização linear. Redes neurais artificiais são aplicadas nas outras duas abordagens adaptativas. A primeira utiliza uma rede neural para aprender o comportamento dinâmico do sistema robótico, considerado totalmente desconhecido. Nenhum dado cinemático ou dinâmico da base é utilizado neste caso. A segunda abordagem considera a estrutura do modelo nominal do manipulador bem definida e a rede neural é aplicada para estimar o comportamento das incertezas paramétricas e da dinâmica não-modelada da base. O critério H \'INFINITO\' é aplicado nas três técnicas para atenuar o efeito dos erros de estimativa. Resultados experimentais foram obtidos com um robô manipulador de base fixa subatuado (UArmII) e apresentaram melhor desempenho no acompanhamento da trajetória e no consumo de energia para as abordagens baseadas em redes neurais. / In the present work, the dynamics of a free-floating space manipulator is described through the dynamically equivalent manipulator approach in order to obtain experimental results in a planar fixed base manipulator. Control in joint and Cartesian spaces are considered. The first acts directly on joints positioning; the second control scheme acts on positioning the end-effector in some inertially fixed position. In both cases, the problem of tracking control with a guaranteed H-infinity performance for free-floating manipulator systems with plant uncertainties and external disturbances is proposed and solved. Considering control methods for underactuated systems, three adaptive techniques were developed from a nonlinear H-infinity controller based on game theory. The first approach was proposed considering a well defined structure for the plant, however it was computed based on uncertain parameters. An adaptive law was applied to estimate these parameters using linear parametrization. Artificial neural networks were applied in the two other approaches. The first one uses a neural network to learn the dynamic behavior from the robotic system, which is considered totally unknown. No kinematics or dynamics data from the spacecraft are necessary in this case. The second approach considers the nominal model structure well defined and the neural network is applied to estimate the behavior of the parametric uncertainties and of the spacecraft non-modeled dynamics. The H-infinity criterion was applied to attenuate the effect of estimation errors in the three techniques. Experimental results were obtained with an underactuated fixed-base planar manipulator (UArmII) and presented better performance in tracking and energy consumption for the neural based approaches.