This thesis presents a novel modulation scheme, called feedback dithering modulation, for DC to AC power converters. The feedback dithering modulator consists of a quantizer and a recently reported feedback dithering circuit, performing multilevel modulation with improved linearity and signal quality as opposed to the conventional modulation schemes. By combining the feedback dithering modulation and optimal control, a single-phase DC to AC power converter is built and tested. The resulting total harmonic distortion can be as low as 0.38% for a 25£[ load, or 0.47% when the output is open. Under the various operating conditions with DC voltages source varying from 190 V to 300 V and output powers from 0 to 600 W, the power converter always maintains a total harmonic distortion less than 1%, exhibiting high performance and excellent robustness.

The purpose of this thesis is to design and implement a linear quadratic optimal controller for a twin-buck converter with zero-voltage-transition (ZVT). The controller calculates duty ratio every cycle based on voltage and current feedback, as well as estimates the time instances when the synchronous rectification power switch current is zero. These time instances are crucial for ZVT operation. Via frequency modulation, the controller is designed to automatically regulate the output voltage to a desired value under load and voltage source variation. Simulations indicate that the proposed control design works. The controller is implemented using a Field Programmable Gate Array (FPGA). The experimental results match the simulations, which further verifies the applicability of the proposed voltage regulation strategy.

During the uniform locomotion of legged robots with compliant legs, the body of the robot exhibits quasi-periodic oscillations that have a disturbing eect on dierent onboard sensors. Of particular interest is the camera sensor which suers from image degradation in the form of motion-blur as a result of this camera motion. The eect of angular disturbances on the camera are pronounced due to the perspective projection property of the camera. The thesis focuses on the particular problem of legged robots exhibiting angular body motions and attempts to analyze and overcome the resulting disturbances on a camera carrying platform (head). Although the full problem is in 3D with three independent axes of rotation, a planar analysis provides signicant insight into the problem and is the approach taken in the thesis. A carefully modeled planar version of an actual camera platform with realistic mechanical and actuator selections is presented. Passive (ltering) and active (controller) approaches are discussed to compensate/cancel motion generated disturbances. We consider and comparatively evaluate PID and LQR based active control. Since PID has the limitation of controlling only one output, PID-PID control is considered to iv control two states of the model. Due to its state-space formulation and the capability of controlling an arbitrary number of states, LQR is considered. In addition to standard reference signals, Gyroscope measured disturbance signals are collected from the actual robot platform to analyze the bandwidth and test the performance of the controllers. Inverted pendulum control performance is evaluated both on a Matlab-Simulink as well as a precise electro-mechanical test setup. Since construction of the planar head test setup is in progress, tests are conducted on simulation.

Matrix Lyapunov and Riccati equations are an important tool in mathematical systems theory. They are the key ingredients in balancing based model order reduction techniques and linear quadratic regulator problems. For small and moderately sized problems these equations are solved by techniques with at least cubic complexity which prohibits their usage in large scale applications. Around the year 2000 solvers for large scale problems have been introduced. The basic idea there is to compute a low rank decomposition of the quadratic and dense solution matrix and in turn reduce the memory and computational complexity of the algorithms. In this thesis efficiency enhancing techniques for the low rank alternating directions implicit iteration based solution of large scale matrix equations are introduced and discussed. Also the applicability in the context of real world systems is demonstrated. The thesis is structured in seven central chapters. After the introduction chapter 2 introduces the basic concepts and notations needed as fundamental tools for the remainder of the thesis. The next chapter then introduces a collection of test examples spanning from easily scalable academic test systems to badly conditioned technical applications which are used to demonstrate the features of the solvers. Chapter four and five describe the basic solvers and the modifications taken to make them applicable to an even larger class of problems. The following two chapters treat the application of the solvers in the context of model order reduction and linear quadratic optimal control of PDEs. The final chapter then presents the extensive numerical testing undertaken with the solvers proposed in the prior chapters. Some conclusions and an appendix complete the thesis.

Extremely large telescopes (ELTs) are the next generation of ground-based reflecting telescopes of optical wavelengths. ELTs possess an aperture of more than 20 meters and share a number of common features, particularly the use of a segmented primary mirror and the use of adaptive optics systems. In 2005, the European Southern Observatory introduced a new giant telescope concept, named the European Extremely Large Telescope (E-ELT), which is scheduled for operation in 2018. The E-ELT will address key scientific challenges and will aim for a number of notable firsts, including discovering Earth-like planets around other stars in the ``habitable zones'' where life could exist, attempting to uncover the relationship between black holes and galaxies, measuring the properties of the first stars and galaxies, and probing the nature of dark matter and dark energy. In 2009, a feasibility study, conducted by National Instruments, proved the feasibility of the real-time (RT) control system architecture for the E-ELT's nearly 1,000 mirror segments with 3,000 actuators and 6,000 sensors. The goal of the RT control system was to maintain a perfectly aligned field of mirrors at all times with a loop-time of 1 ms. The study assumed a prescribed controller algorithm. This research report prescribes the optimal controller algorithms for large segmented telescopes. In this respect, optimal controller designs for the primary mirror of the E-ELT, where optimality is formulated in the [H-2] and [H-infinity] frameworks are derived. Moreover, the designed controllers are simulated to show that the desired performance metrics are met. / text

abstract: The development of a Solid State Transformer (SST) that incorporates a DC-DC multiport converter to integrate both photovoltaic (PV) power generation and battery energy storage is presented in this dissertation. The DC-DC stage is based on a quad-active-bridge (QAB) converter which not only provides isolation for the load, but also for the PV and storage. The AC-DC stage is implemented with a pulse-width-modulated (PWM) single phase rectifier. A unified gyrator-based average model is developed for a general multi-active-bridge (MAB) converter controlled through phase-shift modulation (PSM). Expressions to determine the power rating of the MAB ports are also derived. The developed gyrator-based average model is applied to the QAB converter for faster simulations of the proposed SST during the control design process as well for deriving the state-space representation of the plant. Both linear quadratic regulator (LQR) and single-input-single-output (SISO) types of controllers are designed for the DC-DC stage. A novel technique that complements the SISO controller by taking into account the cross-coupling characteristics of the QAB converter is also presented herein. Cascaded SISO controllers are designed for the AC-DC stage. The QAB demanded power is calculated at the QAB controls and then fed into the rectifier controls in order to minimize the effect of the interaction between the two SST stages. The dynamic performance of the designed control loops based on the proposed control strategies are verified through extensive simulation of the SST average and switching models. The experimental results presented herein show that the transient responses for each control strategy match those from the simulations results thus validating them. / Dissertation/Thesis / Ph.D. Electrical Engineering 2011

O presente trabalho implementa a otimização dos ganhos de um controle ativo com regulador linear quadrático (LQR), em um modelo veicular completo sujeito a um perfil de estrada proposto pela ISO 8608, para atenuação das acelerações RMS transmitidas para a carroceria e o assento do motorista. Dado que o ganho do controle LQR é formulado a partir das matrizes Q e R, o procedimento determina as matrizes ótimas do controle para a minimização das acelerações RMS transmitidas. O modelo é analisado no domínio do tempo por meio da formulação de espaço-estado, e o procedimento de otimização é avaliado pelo método dos algoritmos genéticos. Os parâmetros Q e R, que fornecem o melhor ganho para minimização do problema de otimização, reduzem em até 1000 vezes as acelerações RMS quando comparadas à situação sem atuação do controle. Após otimizar Q e R, são analisadas a influência nos demais graus de liberdade e as forças necessárias para os resultados obtidos. / This work aims to optimize the gains of an active control with linear quadratic regulator (LQR), applied in a full vehicle model subject to a random road surface profile proposed by ISO 8608, for reduction of RMS accelerations transmitted to the driver’s seat and the vehicle body. Since the gain of LQR control is formulated from the matrices Q and R, the procedure determines the optimal control matrices that minimize the RMS accelerations transmitted. The model is analyzed in the time domain through state-space formulation, and the optimization process evaluated by the method of genetic algorithms. The parameters Q and R, which provide the best gain for minimizing the optimization problem, reduce by up to 1000 times the RMS accelerations when compared to the situation without active control. Finally, after optimizing Q e R, are analyzed the influence to the other degrees of freedom and the forces necessary for the results obtained.

O presente trabalho implementa a otimização dos ganhos de um controle ativo com regulador linear quadrático (LQR), em um modelo veicular completo sujeito a um perfil de estrada proposto pela ISO 8608, para atenuação das acelerações RMS transmitidas para a carroceria e o assento do motorista. Dado que o ganho do controle LQR é formulado a partir das matrizes Q e R, o procedimento determina as matrizes ótimas do controle para a minimização das acelerações RMS transmitidas. O modelo é analisado no domínio do tempo por meio da formulação de espaço-estado, e o procedimento de otimização é avaliado pelo método dos algoritmos genéticos. Os parâmetros Q e R, que fornecem o melhor ganho para minimização do problema de otimização, reduzem em até 1000 vezes as acelerações RMS quando comparadas à situação sem atuação do controle. Após otimizar Q e R, são analisadas a influência nos demais graus de liberdade e as forças necessárias para os resultados obtidos. / This work aims to optimize the gains of an active control with linear quadratic regulator (LQR), applied in a full vehicle model subject to a random road surface profile proposed by ISO 8608, for reduction of RMS accelerations transmitted to the driver’s seat and the vehicle body. Since the gain of LQR control is formulated from the matrices Q and R, the procedure determines the optimal control matrices that minimize the RMS accelerations transmitted. The model is analyzed in the time domain through state-space formulation, and the optimization process evaluated by the method of genetic algorithms. The parameters Q and R, which provide the best gain for minimizing the optimization problem, reduce by up to 1000 times the RMS accelerations when compared to the situation without active control. Finally, after optimizing Q e R, are analyzed the influence to the other degrees of freedom and the forces necessary for the results obtained.

Orientador: Prof. Dr. Marat Rafikov / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Engenharia Mecânica, 2016. / O objetivo desta dissertação é o controle de trajetória e navegação de um robô móvel autônomo subaquático. O robô abordado nesta dissertação faz parte de uma nova classe de AUV¿s (Autonomous Underwater Vehicles) chamados de planadores subaquáticos. Os planadores subaquáticos se destacam por substituírem os propulsores por um mecanismo de translação e rotação de massas internas e variação de flutuabilidade, para se locomoverem. Essa nova classe de veículos visa superar o problema de autonomia, encontrado em outros tipos de AUV¿s, devido à limitada duração das baterias. O controle de posicionamento é realizado através da linearização do modelo não ¿linear e aplicada a estratégia de controle ótimo conhecida por LQR (Regulador Linear Quadrático). Essa estratégia é aplicada ao problema de regulação do robô a uma referência e a eficácia do método de controle do robô é verificada através de simulações numéricas. Nas simulações verificou ¿ se que o controle LQR foi capaz de fazer com que o veículo convergisse para a trajetória de referência desejada, demonstrando assim que a aplicação de um controlador linear para o modelo não ¿ linear do veículo é uma opção de aplicação em missões reais. / Within the structures optimization study area, one of the extensively explored methods is the TO objetivo desta dissertação é o controle de trajetória e navegação de um robô móvel autônomo subaquático. O robô abordado nesta dissertação faz parte de uma nova classe de AUV¿s (Autonomous Underwater Vehicles) chamados de planadores subaquáticos. Os planadores subaquáticos se destacam por substituírem os propulsores por um mecanismo de translação e rotação de massas internas e variação de flutuabilidade, para se locomoverem. Essa nova classe de veículos visa superar o problema de autonomia, encontrado em outros tipos de AUV¿s, devido à limitada duração das baterias. O controle de posicionamento é realizado através da linearização do modelo não ¿linear e aplicada a estratégia de controle ótimo conhecida por LQR (Regulador Linear Quadrático). Essa estratégia é aplicada ao problema de regulação do robô a uma referência e a eficácia do método de controle do robô é verificada através de simulações numéricas. Nas simulações verificou ¿ se que o controle LQR foi capaz de fazer com que o veículo convergisse para a trajetória de referência desejada, demonstrando assim que a aplicação de um controlador linear para o modelo não ¿ linear do veículo é uma opção de aplicação em missões reais.

In this work, a unicycle system with reaction wheel is presented, considering the construction, the modeling, the design and test of the controllers. Firstly, a mechanical model considering a tridimensional computer aided design (3D CAD) is built in order to assist the construction and, after that, the modeling using the Lagrange method. In this work, linear controllers are designed and, therefore, the linearization of the system is done by the Jacobian, that is, assuming small variations around the equilibrium point. In this situation, there is no coupling between the pitch and the roll angles, thus resembling two inverted pendulums. The prototype is constructed by attaching the electronic components, the battery, the wheels and the motors to a body, to make it fully autonomous. The positioning of the parts has to balanced in order to maintain the position of the center of mass along the vertical and horizontal axis of symmetry. Then, a linear control project is done to stabilize the plant using two techniques that are validated considering simulations of the nonlinear coupled system. Then, the techniques were tested in the built prototype. The first one consists of the optimal LQR control that, although it worked, presented some problems due to parametric uncertainties. Therefore, the H2 control is used via LMI in such a way that the project becomes similar to the LQR, but in this way it is possible to insert parametric uncertainties and find a controller with some degree of robustness to them. / Neste trabalho, é apresentado um sistema de um monociclo com roda de reação, mostrando desde a construção, passando pela modelagem até o projeto e teste dos controladores. Primeiramente, é feito o projeto mecânico por meio de um desenho assistido por computador tridimensional (3D CAD), para auxiliar a construção e, em seguida, a modelagem por meio do método de Lagrange. Naturalmente, o sistema é não linear e os ângulos de arfagem e rolamento são acoplados. Neste trabalho, controladores lineares são projetados e, portanto, a linearização do sistema é feita pelo Jacobiano, ou seja, assumindo pequenas variações em torno do ponto de equilíbrio. Nesta situação, o modelo desacopla os ângulos de arfagem e rolamento. O protótipo é construído fixando os componentes eletrônicos, a bateria, as rodas e os motores a um corpo, de forma a ser totalmente autônomo. O posicionamento das peças precisa ser equilibrado, de forma a manter a posição do centro de massa ao longo dos eixos de simetria vertical e horizontal. Em seguida, é feito um projeto de controle linear para estabilização da planta usando duas técnicas que são validadas via simulações do sistema não linear acoplado. Depois, as técnicas são testadas no protótipo construído. A primeira consiste do controle ótimo LQR que, apesar de ter funcionado, apresentou alguns problemas devidos a incertezas paramétricas. Logo, é usado o controle H2 via LMI, de tal forma que o projeto equivalha ao LQR, mas desta forma é possível inserir incertezas paramétricas e achar um controlador com algum grau de robustez a elas.