No que segue, propõe-se uma classe de sistemas robóticos multi-corpos, cujos corpos componentes estão fisicamente acoplados através de juntas rotativas ativas. Os sistemas da classe considerada possuem mobilidade irrestrita no espaço plano uma vez que propulsores distribuídos ao longo dos corpos do sistema. A modelagem dinâmica destes sistemas é apresentada sob as abordagens Hamiltoniana e Lagrangiana da mecânica analítica. A descrição destes métodos de modelagem, assim como os modelos por eles obtidos, é realizada com ênfase na interpretação geométrica da matemática envolvida. Alguns exemplos de parametrizações do espaço de fase do sistema são discutidos e exemplos de modelagem em função destas parametrizações são obtidos. Ademais, alguns critérios de análise de controlabilidade não-linear são revisados e aplicados aos modelos do sistema com a estrutura de entradas considerada. Alguns casos de estabilização da classe de sistemas são também discutidos. Resultados de simulação de estabilização são obtidos para sistemas através de estudos de casos. Sistemas completamente controlados no espaço de estados podem ser linearizados através de uma técnica de linearização por realimentação e estabilizados com uma realimentação de estados. Para os sistemas cuja controlabilidade é deficiente, propõe-se a modificação de um método de controle de sistemas sub-atuados e uma lei de controle por realimentação é obtida pela teoria de estabilidade de Lyapunov. A classe de sistemas aqui discutida possui grande potencial de aplicação nos ambientes espacial e submarino. / In the following, a class of multi-body robotic systems is proposed in which its system component bodies are physically coupled by active rotating joints. The systems belonging to the proposed class have unrestricted mobility on the plane since thrusters are distributed along the system. System dynamical modeling is obtained through the analytic mechanical Hamiltonian and Lagrangian methods. The presentation of these methods, as well as the dynamical models obtained by them, is realized with an emphasis in the geometrical interpretation of the corresponding mathematics. A few different system phase space parameterizations approaches are discussed and modeling examples are presented under these parameterizations. Additionally, some nonlinear controllability analysis criteria are reviewed and applied to system dynamical models composed by the input structure mentioned above. A few stabilization case studies for the class of systems are also discussed and simulation results are presented. Totally controlled systems in the phase space can be linearized by feedback linearization techniques and stabilized through a state feedback. For partially controllable systems a modification of a stabilization method for under-actuated systems is proposed which renders feedback control via Lypunov stability theory. The class of systems discussed has great potential for space and underwater applications.

Orientador: Samuel da Silva / Co-orientador: Fábio Roberto Chavarette / Banca: João Antonio Pereira / Banca: Marcelo Amorim Savi / Resumo: Captação de energia a partir de vibrações tem sido uma área de grande expansão nos últimos anos. Dispositivos lineares tem recebido maior atenção na literatura, no entanto, pesquisadores utilizam cada vez mais, dispositivos não-lineares para a transdução de banda larga. O processo de captação de energia possui duas etapas: a extração de energia e a utilização desta energia gerada para alimentar dispositivos eletrônicos. Assim, este trabalho descreve a utilização de um dispositivo mecânico não-linear caótico para captação de energia, acoplado a um circuito de retificação de meia-onda para transformar a tensão alternada gerada pelo PZT para tensão contínua para possível alimentação de um dispositivo eletrônico. A análise da interação dinˆamica entre os dois dispositivos é feita e pode-se concluir que é possível a utilização de um dispositivo mecânico, que opera no caos acoplado a um circuito de retificação, a fim de gerar mais energia / Abstract: Energy harvesting from vibrations has been an area of enormous expansion in the last years. While linear vibratory energy harvesters have received the majority of the literature's attention, some current research is focused on the concept of purposeful inclusion of nonlinearities for broadband transduction. The process of harvesting energy must have two steps: the extraction of energy and the utilization of this energy to feed in electronic devices. Thus, this work discusses the use of a non-linear mechanical device which has chaos to capture energy coupled to half-wave rectifier circuit to transform the alternating voltage generated by the PZT for continuous voltage to a possible device electronic. An analysis of the dynamic interaction between the two devices is done and it can be concluded that it is possible to use a mechanical device that operates in chaos coupled to a rectification circuit in order to generate more power / Mestre

Este trabalho apresenta uma abordagem para a identificação da dinâmica não linear do modelo matemático de uma pá de helicóptero em rotação. Durante a simulação, foi considerado o helicóptero em voo pairado. Foi usada a representação bilinear para o modelo, uma das formas mais simples de representação de um modelo não linear. O modelo matemático da pá foi implementado através do método de elementos finitos e simulado em ambiente Matlab. Foi suada na identificação, uma rede neural artificial como técnica não convencional, já que demonstra grande capacidade de aproximação de modelos não lineares, grande desempenho em análise da dinâmica de sistemas flexíveis e implementação e rapidez consideráveis. As redes neurais com processamento temporal são usadas para aproximar componentes da dinâmica não linear sobre um conjunto de entradas prescritas, e são usadas em simulação como meio rápido de obter a resposta no tempo. Para capturar a natureza recursiva dos componentes dinâmicos do sistema foi usada uma rede feedforward com processamento temporal, com uma camada intermediária de neurônios e com entradas na rede atrasadas. Para verificar o desempenho da rede, foi feita a comparação entre os dados de simulação obtidos originalmente e os dados resultantes de simulação da rede. Este trabalho foi desenvolvido visando futuramente aplicação de técnicas de controle de vibrações em pás rotativas. / This work presents an approach for non-linear dynamics identification of a rotating helicopter blade mathematical model. During simulation, the helicopter was considered in hovering flight. A bilinear representation was used for the model, since it is known as one of the simplest forms of representation of a non linear model. Mathematical model of blade was implemented using finite elements method and simulated in Matlab. A neural network is used in the identification process as a non conventional technique, since it demonstrates good capacity for approximation non-linear models and good performance in terms of the analysis of the dynamics of flexible systems. It also presents good performance in terms of implementation and processing speed. The neural networks with time dependent processing are used to approximate the components of the non-linear dynamics over a prescribed inputs set, and they are used in simulation as a rapid way of obtaining the time response. In order to capture the recursive nature of the dynamic components of the system, a feedforward network with time dependent processing, with an intermediate layer of neurons and delayed inputs is used. The performance of the net was verified comparing the results obtained originally by simulation with those resulting from the network emulation. This work was developed in order to apply vibration control techniques to rotating blades.

Orientador: José Manoel Balthazar / Banca: Angelo Marcelo Tusset / Banca: Bento Rodrigues de Pontes Junior / Resumo: O propósito deste trabalho é o de obter modelos matemáticos que sirvam de referência, para que se possa efetuar os estudos relacionados aos efeitos não-lineares presentes no comportamento dinâmico envolvido na perfuração de petróleo, executada por navios perfuradores. As diversas modelagens matemáticas adotadas e abordadas neste trabalho, para esse tipo de problema, baseiam-se em sistemas pendulares invertidos e que possuem excitação harmônica ou excitação por meio de um EDS-Vibrador Eletrodinâmico (electrodynamics Shaker), na forma de um circuito RLC com uma fonte de tensão harmônica. A investigação do problema em questão, se fez por meio de simulações numérico-computacionais, fazendo-se uso do método Runge-Kutta de 4ª ordem para a integração numérica das equações de movimento dos sistemas, aproximando suas soluções. O controle aplicado nas possíveis irregularidades associadas ao movimento do sistema é do tipo retroalimentação de ajuste de energia de oscilação, proposto anteriormente por TERESHKO (2011) e daí adaptado ao modelo matemático, adotado / Abstract: The purpose of this paper is to obtain mathematical models that serve as a reference for the studies related to the nonlinear effects present in the dynamic behavior involved in oil drilling, performance by drill ships. The various mathematical models adopted and raised in this paper for this problem, were based on inverted pendulum systems and have harmonic excitation or through an EDS-electrodynamics vibrator (Electrodynamics Shaker) simplified ma form of an RLC circuit with a harmonic voltage source. The investigation of the problem in question was made by means of numerical and computational simulations, making use of the Runge-Kutta 4th order for the direct numerical integration of the equations of motion of systems approaching their solutions. The control applied on possible irregularities associated with the motion of the the system is the type of feedback adjustment oscillation energy, previously proposed by TERESHKO (2011) and then adapted to the mathematical model adopted / Mestre

ii) An adaptive output regulation design is proposed for the systems with ISS inverse dynamics and an uncertain exosystem. When the exosystem contains uncertain parameters, the direct approach can not be implemented any longer. To deal with this issue in the general case, by introducing an observer, we first derive an extended system composed of the plant and the observer. Then the output regulation problem of the extended system is solved. It is further shown that the unknown parameter vector of the exosystem can be exactly estimated if a controller containing a minimal internal model is employed. / iii) A sufficient solvability condition of the global output regulation for the systems with iISS inverse dynamics is proposed. Since the concept of iISS is strictly weaker than the ISS one, the result allows us to handle a much larger class of nonlinear systems. / In the past ten years or so, the output regulation of the strict output feedback systems has attracted a lot of attention. In contrast with the strict output feedback systems, the output feedback systems is more general since it not only involves the nonlinearity of the system output but also the unmodeled dynamics. Therefore, the usual design method is not applicable, which motivates us to develop some new methodology for the output regulation design of the output feedback systems. / One of the motivations of the case study is to deal with the output regulation problem of a shunt-connected DC motor whose inverse dynamics is iISS but not ISS. As an illustration, a disturbance rejection problem of the shunt-connected DC motor is solved. / The application of the result leads to the solution of several interesting control problems such as the global disturbance rejection of the FitzHugh-Nagumo (FHN) system and the robust output synchronization of the generalized third and fourth-order Lorenz system and the Harmonic system. / The main results of the thesis are outlined as follows. i) A direct approach is proposed for the output regulation of the systems with ISS inverse dynamics and unknown control directions. The internal model is first designed for the control input. The output feedback control design is further achieved based on a type of partial state observer which is designed for the transformed augmented system. The Nussbaum function technique is successfully incorporated in the stabilization design to deal with the case of unknown control directions. / The nonlinear output regulation is a central control problem that involves nonlinear stabilization, tracking control and disturbance rejection as special cases. The control objective is to find a feedback controller to achieve asymptotic tracking and/or disturbance rejection while maintaining closed-loop stability. The output regulation study has experienced rapid developments in the past two decades or so. It is now well known that the problem can be systematically approached according to the general framework of tackling nonlinear output regulation that is composed of the following two steps. The first step is the problem conversion: from nonlinear output regulation to stabilization. The output regulation is generally more complicated than the stabilization problem. Therefore the problem conversion indeed reduces the complexity and makes it possible to be handled. In this step, the output regulation is converted into the stabilization of an augmented system consisting of the original plant and a suitable dynamic compensator called internal model. The second step is the stabilization of the augmented system whose solvability implies solvability of the output regulation problem. / The result is applied to solve a tracking control problem associated with the well known Lorenz system and a class of generalized fourth-order Lorenz systems. By certain system decomposition, it is proved that the Lorenz system contains certain ISS inverse dynamics and the output feedback control is successfully realized. / The thesis is concerned with the global robust output regulation for nonlinear systems in the output feedback form by using output feedback control. For the nonlinear output feedback systems, we mainly study three typical output regulation problems. The first one is the output regulation problem with unknown control directions and input-to-state stable (ISS) inverse dynamics using a direct approach. The second one is the adaptive output regulation problem with an uncertain exosystem and ISS inverse dynamics. The third one is a case study on the solvability of the systems with integral input-to-state stable (iISS) inverse dynamics. / Xu, Dabo. / Adviser: Jie Huang. / Source: Dissertation Abstracts International, Volume: 72-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 107-113). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Zhao, Jin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 79-83). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Synchronization of Master-slave Systems --- p.1 / Chapter 1.2 --- Output Regulation --- p.2 / Chapter 1.3 --- Typical Nonlinear Systems --- p.4 / Chapter 1.4 --- Organization --- p.4 / Chapter 2 --- Synchronization of Chua's Circuit and Van der Pol Oscillator via Inter- nal Model Approach --- p.6 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Problem Formulation --- p.8 / Chapter 2.3 --- Preliminaries --- p.10 / Chapter 2.4 --- Solvability of the Problem --- p.13 / Chapter 2.4.1 --- The solution of the regulator equations --- p.14 / Chapter 2.4.2 --- Steady-state generator --- p.15 / Chapter 2.4.3 --- Internal model --- p.19 / Chapter 2.4.4 --- Stabilization --- p.20 / Chapter 2.4.5 --- Simulation --- p.22 / Chapter 2.5 --- Conclusions --- p.27 / Chapter 3 --- Robust Output Regulation of Output Feedback Systems with Nonlinear Exosystems --- p.28 / Chapter 3.1 --- Introduction --- p.28 / Chapter 3.2 --- Assumptions and Preliminaries --- p.29 / Chapter 3.3 --- Solvability of the Synchronization Problem --- p.33 / Chapter 3.4 --- Comparing Two Approaches for Output Regulation --- p.42 / Chapter 3.4.1 --- Differences between the two approaches for the output regulation problem --- p.42 / Chapter 3.4.2 --- Solvability of the regulator equations --- p.43 / Chapter 3.4.3 --- Solvability of stabilization --- p.47 / Chapter 3.5 --- Conclusions --- p.49 / Chapter 4 --- Applications of Robust Regional Synchronization via Output Regulation Techniques --- p.50 / Chapter 4.1 --- Problem Formulation --- p.50 / Chapter 4.2 --- Duffing Oscillator Synchronizes with Chua's Circuit --- p.51 / Chapter 4.2.1 --- Transfer the synchronization problem into the stabilization problem --- p.53 / Chapter 4.2.2 --- Boundedness of Chua's circuit --- p.57 / Chapter 4.2.3 --- Stabilization --- p.59 / Chapter 4.2.4 --- Simulation Results --- p.64 / Chapter 4.3 --- The Chaotic SMIB Power System Synchronizes with Van der Pol Oscillator --- p.64 / Chapter 4.3.1 --- Transfer the synchronization problem into the stabilization problem --- p.68 / Chapter 4.3.2 --- Stabilization --- p.71 / Chapter 4.3.3 --- Simulation Results --- p.74 / Chapter 4.4 --- Conclusions --- p.76 / Chapter 5 --- Conclusions --- p.77 / Bibliography --- p.79

Neste trabalho se estuda o comportamento dinâmico não linear de um pórtico plano submetido à excitação não ideal de suportes, sendo isto aplicável a estruturas civis dele derivadas. Neste sentido, um edifício pode ser considerado uma justaposição de pórticos. Modelos físicos simples aplicáveis a estruturas civis ou mecânicas com grau de dificuldade crescente são resolvidos individualmente com a utilização das equações diferenciais de Lagrange para determinar as equações do movimento do sistema. A análise qualitativa de cada problema permite determinar os valores que os parâmetros físicos podem assumir. Cada modelo simples fornece um conjunto de parâmetros, que vão sendo utilizados progressivamente nas integrações numéricas. Em sistemas com fonte de energia limitada, ocorre uma interação entre o movimento da estrutura e da fonte de energia; matematicamente é acrescentada uma equação diferencial acoplada adicional ao correspondente sistema livre de excitações. No caso de pórticos planos de grande esbelteza, as cargas axiais induzem grandes deslocamentos, sendo importante considerar na estrutura a não-linearidade geométrica. Neste caso, uma discretização da estrutura precisa ser feita para identificar os graus de liberdade do sistema. Nas análises dos problemas, busca-se o regime permanente de trabalho, no qual as amplitudes da estrutura variam lentamente com o tempo e a fonte de energia trabalha com freqüência constante. / In this work we study the dynamical nonlinear behavior of plane frame under non ideal support excitation, being this applicable to civil structures derived from it. In this sense, a building can be considered as a contiguous series of frames. Simple physical models that are applicable to civil or mechanical structures with increasing difficulty degree are solved individually, with the use of differential Lagrange\'s equations to determine the systems equations of motion. Qualitative analysis of each problem allows the determination of the values that the physical parameters can take. Each model provides a simple set of parameters, which are being progressively used in numerical integrations. On systems with limited power supply, there is an interaction between the structures and the energy sources movement; mathematically an extra equation of motion is coupled to its corresponding excitements free system. Because in plane frames of high slenderness the axial loads induce large displacements, it is important to consider the structures geometric nonlinearity. In this case, in order to identify systems degrees of freedom, the structure must be discretized. In the problems analysis, we seek the steady state, in which the structures amplitudes vary slowly with time and the power supply works with constant frequency.

Este trabalho apresenta uma abordagem para a identificação da dinâmica não linear do modelo matemático de uma pá de helicóptero em rotação. Durante a simulação, foi considerado o helicóptero em voo pairado. Foi usada a representação bilinear para o modelo, uma das formas mais simples de representação de um modelo não linear. O modelo matemático da pá foi implementado através do método de elementos finitos e simulado em ambiente Matlab. Foi suada na identificação, uma rede neural artificial como técnica não convencional, já que demonstra grande capacidade de aproximação de modelos não lineares, grande desempenho em análise da dinâmica de sistemas flexíveis e implementação e rapidez consideráveis. As redes neurais com processamento temporal são usadas para aproximar componentes da dinâmica não linear sobre um conjunto de entradas prescritas, e são usadas em simulação como meio rápido de obter a resposta no tempo. Para capturar a natureza recursiva dos componentes dinâmicos do sistema foi usada uma rede feedforward com processamento temporal, com uma camada intermediária de neurônios e com entradas na rede atrasadas. Para verificar o desempenho da rede, foi feita a comparação entre os dados de simulação obtidos originalmente e os dados resultantes de simulação da rede. Este trabalho foi desenvolvido visando futuramente aplicação de técnicas de controle de vibrações em pás rotativas. / This work presents an approach for non-linear dynamics identification of a rotating helicopter blade mathematical model. During simulation, the helicopter was considered in hovering flight. A bilinear representation was used for the model, since it is known as one of the simplest forms of representation of a non linear model. Mathematical model of blade was implemented using finite elements method and simulated in Matlab. A neural network is used in the identification process as a non conventional technique, since it demonstrates good capacity for approximation non-linear models and good performance in terms of the analysis of the dynamics of flexible systems. It also presents good performance in terms of implementation and processing speed. The neural networks with time dependent processing are used to approximate the components of the non-linear dynamics over a prescribed inputs set, and they are used in simulation as a rapid way of obtaining the time response. In order to capture the recursive nature of the dynamic components of the system, a feedforward network with time dependent processing, with an intermediate layer of neurons and delayed inputs is used. The performance of the net was verified comparing the results obtained originally by simulation with those resulting from the network emulation. This work was developed in order to apply vibration control techniques to rotating blades.

The nonlinearity of RF power amplifiers (PA) is one of critical concerns for RF designers because it causes spectral regrowth related to in-band and out-of-band spurious emissions control in communication standards. Traditionally, RF power amplifiers must be backed off considerably from the peak of their power level in order to prevent spectral regrowth. The digital predistortion (DPD) technique is being widely used for compensation of the nonlinearity of RF power amplifiers, as the high power efficiency becomes increasely important in wireless communication systems. However, the latest generations of communication systems, such as Wi-Fi, WiMAX, and LTE, using wider bandwidth have some additional memory distortion, other than the traditional memoryless distortion. The distortion caused by memory effect makes the traditional predistorter not precise any more for the PA linearization. In this dissertation, the traditional prediction of 3rd order memoryless spectrum regrowth is applied to 4G communication signals in terms of the 3rd intercept point of PAs, based on the previous researches in Portland State University led by Professor Fu Li. Then, the spectrum regrowth prediction is extended to an arbitrarily high order with intercept points of an RF power amplifier. A simple predistortion method which enables direct calculation of the predistorter coefficients from the intercept points is also proposed. Furthermore, the memory effect is taken into account for both PA modeling and predistortion. A simplified Hammerstein structure based method is proposed to analyze the nonlinear characteristic of PAs more precisely and completely. By applying the inverse structures of the PA model, the proposed predistorter corrects both the traditional memoryless nonlinear distortions and the memory effect that may exist in RF power amplifiers. The order of nonlinearity and depth of memory of a predistorter can be chosen from 0 to any arbitrarily high number. This increases the flexibility for designers to decide how to linearize power amplifier effectively and efficiently.

The ability to construct accurate mathematical models of real systems is an important part of control systems design. A block oriented systems identification approach models the unknown system as interconnected linear and nonlinear blocks. The subject of this thesis is a particular configuration of these blocks referred to as a Wiener model. The Wiener model studied here is a cascade of a one input linear block followed by a nonlinear block which then provides one output. We assume that the signal between the linear and nonlinear block is always unknown, only the Wiener model input and output can be sampled. This thesis investigates identification of the linear transfer function in a Wiener model. The question examined throughout the thesis is: given some small amount of a priori information on the nonlinear part, what can we determine about the linear part? Examples of minimal a priori information are knowledge of only one point on the nonlinear transfer characteristic, or simply that the transfer characteristic is monotonic over a certain range. Nonlinear blocks with and without memory are discussed. Several algorithms for identifying the linear transfer function of a block oriented Wiener system are presented and analyzed in detail. Linear blocks identified have both finite and infinite impulse response (i.e. FIR and IIR). Each algorithm has a carefully defined set of minimal a priori information on the nonlinearity. Also, each approach has a minimally restrictive set of assumptions on the input excitation. The universal applicability of each algorithm is established by providing rigorous proofs of identifiability and in some cases convergence. Extensive simulation testing of each algorithm has been performed. Simulation techniques and results are discussed in detail.