Thesis (Ph.D.(Electronic Engineering))--University of Pretoria, 2009. / Summaries in Afrikaans and English. Includes bibliographical references.

State dependent Riccati equation (SDRE) plays an important role in nonlinear controller design. For autonomous nonlinear systems that can be expressed in linear form with state-dependent coefficients (SDC), SDRE-based controllers guarantee local asymptotic stability of the closed-loop system, under pointwise stabilizability and detectability conditions. Moreover, the optimal control for a quadratic cost function, when it exists, corresponds to an SDRE-based control design for a specific SDC parameterization of the associated nonlinear system. Unfortunately, the implementation of the SDRE-based controllers is computationally expensive. Various techniques have been developed for solving the SDRE, which are either computationally expensive or lack acceptable precision. In this dissertation, a modified state-dependent differential Riccati equation (MSDDRE) is proposed for approximating the solution of the SDRE, which is easy to implement with moderate computation power and its solution can be made arbitrarily close to that of the SDRE. Therefore, it can be used for real-time implementation of near-optimal controllers for nonlinear systems in state-dependent linear form. The proposed technique is then extended to SDRE-based filter design and its application to SDRE-based output feedback control technique. The proposed technique is also extended to state-dependent H-inf; robust control design for a constant noise attenuation bound, when the solution exists. To reduce the design conservativeness, the technique is further extended to state-dependent H-inf; robust control design with adaptive noise attenuation bound, using gain-scheduling technique and linear matrix inequality (LMI) optimization, to approximate H-inf; optimal control with state-dependent noise-attenuation bound. Local asymptotic stability of the closed-loop system is proven for all proposed techniques. Simulation results further confirm the validity of the development and demonstrate the efficiency of the proposed techniques.

Space missions increasingly require sophisticated guidance, navigation and control algorithms, the development of which is reliant on verification and validation (V&V) techniques to ensure mission safety and success. A crucial element of V&V is the assessment of control system robust performance in the presence of uncertainty. In addition to estimating average performance under uncertainty, it is critical to determine the worst case performance. Industrial V&V approaches typically employ mu-analysis in the early control design stages, and Monte Carlo simulations on high-fidelity full engineering simulators at advanced stages of the design cycle. While highly capable, such techniques present a critical gap between pessimistic worst case estimates found using analytical methods, and the optimistic outlook often presented by Monte Carlo runs. Conservative worst case estimates are problematic because they can demand a controller redesign procedure, which is not justified if the poor performance is unlikely to occur. Gaining insight into the probability associated with the worst case performance is valuable in bridging this gap. It should be noted that due to the complexity of industrial-scale systems, V&V techniques are required to be capable of efficiently analysing non-linear models in the presence of significant uncertainty. As well, they must be computationally tractable. It is desirable that such techniques demand little engineering effort before each analysis, to be applied widely in industrial systems. Motivated by these factors, this thesis proposes and develops an efficient algorithm, based on the cross entropy simulation method. The proposed algorithm efficiently estimates the probabilities associated with various performance levels, from nominal performance up to degraded performance values, resulting in a curve of probabilities associated with various performance values. Such a curve is termed the probability profile of performance (PPoP), and is introduced as a tool that offers insight into a control system's performance, principally the probability associated with the worst case performance. The cross entropy-based robust performance analysis is implemented here on various industrial systems in European Space Agency-funded research projects. The implementation on autonomous rendezvous and docking models for the Mars Sample Return mission constitutes the core of the thesis. The proposed technique is implemented on high-fidelity models of the Vega launcher, as well as on a generic long coasting launcher upper stage. In summary, this thesis (a) develops an algorithm based on the cross entropy simulation method to estimate the probability associated with the worst case, (b) proposes the cross entropy-based PPoP tool to gain insight into system performance, (c) presents results of the robust performance analysis of three space industry systems using the proposed technique in conjunction with existing methods, and (d) proposes an integrated template for conducting robust performance analysis of linearised aerospace systems.

[pt] Nesta dissertação, um transportador pessoal robótico auto-equilibrante (TPRE) foi desenvolvido, consistindo de uma plataforma com duas rodas que funciona a partir do equilíbrio do indivíduo que o utiliza, assemelhando-se ao funcionamento do clássico pêndulo invertido. Entre as características que o TPRE tem, podem-se destacar a rapidez na movimentação, o uso de um espaço reduzido, alta capacidade de carga, e capacidade de fazer curvas de raio nulo. Ao contrário de veículos motorizados tradicionais, o TPRE utiliza alimentação elétrica, portanto não gera emissões poluentes e, além disso, não contribui com poluição sonora. Para a locomoção, são utilizados dois motores de corrente contínua de potências entre 0,7HP e 1,6HP. Para medir o ângulo de inclinação e a velocidade da variação do ângulo de inclinação, é utilizado um acelerômetro de três eixos e um girômetro de um eixo. Para indicar a direção do TPRE, foi utilizado um potenciômetro deslizante. A modelagem dinâmica do sistema foi feita usando o método de Kane, utilizada posteriormente em simulações na plataforma Matlab. O controlador lê os sinais provenientes do acelerômetro, do girômetro e do potenciômetro deslizante, e envia o sinal de controle, em forma de PWM, a placas controladoras de velocidade dos motores, usando a linguagem eLua. Os algoritmos de controle desenvolvidos neste trabalho foram PID, Fuzzy e Robusto, tendo como variáveis de controle o erro e a velocidade da variação do erro do ângulo de inclinação. Experimentos demonstram que os controles Fuzzy e Robusto reduzem significativamente as oscilações do sistema em terrenos planos em relação ao PID. Verifica-se também uma maior estabilidade para terrenos irregulares ou inclinados. / [en] A Self Balancing Personal Transporter (SBPT) is a robotic platform with two wheels that functions from the balance of the individual who uses it, resembling the operation of classic inverted pendulum. In this thesis, a SBPT is designed, built and controlled. Among the features from the developed SBPT, it can be mentioned: relatively high speeds, agility, compact aluminum structure, zero turn radius, and high load capacity, when compared to other SBPT in the market. Unlike traditional motor vehicles, the SBPT uses electric power, so there is no polluent emissions to the environment and no noise pollution. It is powered by two motors with output powers between 0.7HP and 1.6HP. To measure the tilt angle and its rate of change, a three-axis accelerometer and a gyroscope are used. The turning commands to the SBPT are sent through a potentiometer attached to the handle bars. The method of Kane is used to obtain the system dynamic equations, which are then used in Matlab simulations. The controller, programmed in eLua, reads the signals from the accelerometer, gyroscope and potentiometer slider, process them, and then sends PWM output signals to the speed controller of the drive motors. This thesis studies three control implementations: PID, Fuzzy and Robust Control. The control variables are the error and error variation of the tilt angle. It is found that the Fuzzy and Robust controls are more efficient than the PID to stabilize the system on inclined planes and on rough terrain.

L'utilisation de correcteur discret à période d'échantillonnage variable peut être intéressante dans plusieurs cas, par exemple lorsque la mesure, bien qu'envoyée de façon périodique, est reçue à intervalle variable. C'est le cas en milieu marin lorsque la mesure d'altitude est effectuée avec un capteur à ultrason (la durée du trajet du signal dans l'eau dépend de la distance par rapport au fond). Le délai variable entre deux réceptions de mesures, peut être vu comme une variation de période d'échantillonnage pour le contrôleur. La synthèse de lois de commande discrète à période d'échantillonnage variable a déjà été étudiée pour des systèmes stationnaires. On se propose ici d'étendre cette méthode pour des systèmes Linéaires à Paramètres Variants (LPV), qui permettent de conserver des paramètres importants d'un système non-linéaire en temps que paramètres d'un système linéaires. La synthèse de contrôleur repose sur le méthodologie H∞, appliquée aux systèmes LPV. En particulier, on s'intéressera à deux approches existantes dans la littérature : l'approche polytopique (où le paramètre variant évolue dans un volume convexe) et la Représentation Linéaire Fractionnelle (LFR). La méthode proposée est appliquée au contrôle d'un AUV (Autonomous Underwater Vehicle), qui est système difficile à contrôler du fait d'importantes non-linéarités. Des résultats de simulations permettront de montrer l'intérêt de la méthode pour le contrôle d'altitude d'un AUV, et notamment les améliorations apportées par l'ajout de paramètres issus du système non-linéaire au modèle utilisé pour la synthèse des régulateurs. / Discrete time controller using variable sampling can ba interesting in several cases, for axample when the measure, even if send periodically, is received with a variable interval. This is the case in submarine environement, when the altitude measurement is done using an ultrasonic sensor. Discrete control laws synthesis with variable sampling period have already been studied for LTI systems. The results are here extended to Linear Parameter Varying systems, that allow to keep some non-linearities as parameters of a linear system. In particular, two approaches are investigated : the polytopic and the LFR. The proposed method is applied for the altitude control of an autonomous underwater vehicle (AUV). Simulations results will show the interest of the method, in particular how results are improved by adding some parameters coming from the non linear model.

Un des enjeux actuels de la réduction des émissions polluantes pour les véhicules automobiles concerne l'utilisation de moyens de propulsion hybride (électrique+thermique). Les problématiques principales, pour l'automatique, sont alors d'optimiser l'efficacité énergétique globale du véhicule, mais aussi d'améliorer les performances du véhicule hybride. Nous envisageons ici de développer des méthodes de commande robuste dans cet objectif, tout en prenant en compte les contraintes liées à la mise en oeuvre pratique. / In the recent years, growing public concern has been given both on the energy problem and on the environment problem resulted from dramatically increased vehicles equipped with Internal Combustion Engine (ICE). Subsequently, intensive contributions have been made by the automotive industries and research institutes on vehicles that depend less on the fossil fuels, and introduce less pollutant emissions. This has led to the emergence of environment-friendly and energy-saving vehicles such as the Hybrid Electric Vehicle (HEV) that is usually equipped with one or more additional electric motors and the associated power battery compared with the Conventional vehicles (CVs) propelled solely by the ICE. The key point of an HEV is to design a proper Energy Management Strategy (EMS) that decides how to split the demanded power between the engine and the motor (battery). As the most important and expensive part of an HEV, it is important to take into account battery states, such as battery State of Charge (SOC) and battery ageing, aiming at maintain the optimality of the achieved EMS, as well as prolonging the battery life. In this dissertation, an HEV of parallel structure, which is equipped with a Lithiumion battery is considered. This dissertation is focused on accounting for battery related items, i.e. battery SOC and SOH indicated by battery parameters, in the EMS developments leading to a kind of fault tolerant EMS. Some brief introduction on the control methods and realization approaches involved in this work is presented first, followed by two big parts: the first part is focused on the battery modeling and estimation, while the second part is concerned by the vehicle modeling and few kinds of EMS development methods.

Made available in DSpace on 2014-06-11T19:22:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-06-21Bitstream added on 2014-06-13T19:26:17Z : No. of bitstreams: 1 iliuk_i_me_bauru.pdf: 2013927 bytes, checksum: e94fef7f2a027b1dc8fe2b2da4ecc240 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Nos últimos anos, a pesquisa sobre captura de energia, tem aumentado substancialmente. Muitos pesquisadores têm concentrado seus esforços em encontrar a melor configuração para estes sistemas e para otimizar sua potência de saída. No processo de captura de energia, a energia elétrica é obtida através da conversão de energia mecânica, criado por uma fonte de vibração do ambiente através de um transdutor, por exemplo, um fino filme piezocerâmico. Diferentes mecanismos de acoplamento eletromecânico têm sido desenvolvidos para dispositivos de captura, e um interesse particular tem sido dado ao uso de modelos que transformam a vibração mecânica em corrente elétrica utilizando um elemento piezoelétrico. Neste trabalho, foi proposto um modelo de captura de energia de vibrações, incluindo não-linearidades no acoplamento piezoelétrico e uma excitação não-ideal. Demonstrou-se que a potência capturada foi influenciada pelo efeito das não-linearidades do acoplamento piezoelétrico, alterando o comportamento dinâmico do sistema. Com o acoplamento fraco, um comportamento caótico foi encontrado causando instabilidade. Com o aumento do acoplamento ocorreu um aumento da energia capturada até um certo limite onde o aumento da não-linearidade teve um efeito amortecimento sobre as vibrações não-lineares da estrutura causando a perda de energia. Realizando simulações numéricas o comportamento do modelo foi analisado através dos expoentes de Lyapunov, retratos de fase, históricos de deslocamentos no tempo onde um comportamento caótico também foi observado, causando a perda de energia ao longo do tempo de simulação. Usando uma técnica de perturbação, foi encontrada uma solução analítica aproximada para o sistema não-ideal. Então, aplicou-se três técnicas de... / In recent years, research on energy harvesting, has increased substantially. Many researchers have concentrated their efforts on finding the best configuration for these systems and to optimize its power output. In the process of energy harvesting, electric power is obtained by converting mechanical energy created by a vibration source from the environment through a transducer, for example, a thin film piezoceramic. Different mechanisms of electromechanical coupling devices have been developd to harvesting, and a particular interest has been given to the use of models that tranform the mechanical vibration into electrical current using a piezoelectric element. In this paper we propose a model to energy harvesting from vibrations, including non-linearities in the piezoelectric doupling and a non-ideal excitation. It was demonstrated that the power captured was influenced by the effect of the nonlinearities of the piezoelectric coupling, modifying the dynamic behavior of the system. With a weak coupling, a chaotic behavior was found causing instability. With the increase of the coupling has ocurred an increase in the energy captured until a limit, where the increase of non-linearity has a damping effect on vibrations of the non-linear structure causing the loss of energy. Performing numerical simulations the behavior of the model was analyzed using the Lyapunov exponents, phase portraits, historical displacements in time where a a chaotic behavior was also observed, causing the loss os energy throughout the simulation time. Using a perturbation technique, found an approximate analytical solution for the non-ideal system. Then, we applied three control techniques to maintain the proposed system in a stable condition. Both the method of equations of state-dependent Riccati (SDRE), the method (LQR) and the feedback... (Complete abstract click electronic access below)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This dissertation presents as the main contribution the design and experimental validation of a robust H2 controller applied to boost converters with variations on the parameters load resistance, input voltage and operating point duty cycle. First, a polytopic model of the plant is presented, allowing to represent all the possible variations of the parameters within intervals previously established. Design conditions for a robust H2 controller, optimal under the quadratic stability, are detailed and used, allowing to efficiently calculate the controller gains. These gains are implemented with analog circuitry and the closed-loop system is tested by means of simulation and experimental results, which show a good match and illustrate a good performance. Finally, the small perturbation rejection capacity of the closed-loop system subject to parametric variations is evaluated using the H∞ guaranteed cost. / Esta dissertação apresenta como principal contribuição o projeto e a validação experimental de um controlador robusto H2 aplicado a conversores boost com variações nos parâmetros resistência de carga, tensão de entrada e razão cíclica do ponto de operação. Primeiramente, um modelo politópico da planta é apresentado, permitindo representar todas as situações de variações possíveis dos parâmetros mencionados, dentro de intervalos previamente estabelecidos. Condições de projeto de um controlador robusto H2, ótimo sob a estabilidade quadrática, são detalhadas e utilizadas, permitindo calcular eficientemente os ganhos do controlador. Estes ganhos são implementados de forma analógica e o sistema em malha fechada é testado por meio de resultados experimentais e de simulação, que apresentam uma boa correspondência e ilustram um bom desempenho. Por fim, a capacidade de rejeição de pequenas perturbações do sistema em malha fechada sujeito a variações paramétricas é avaliada utilizando o custo garantido H∞.

Orientador: José Manoel Balthazar / Banca: Angelo Marcelo Tusset / Banca: Bento Rodrigues de Pontes Junior / Resumo: Nos últimos anos, a pesquisa sobre captura de energia, tem aumentado substancialmente. Muitos pesquisadores têm concentrado seus esforços em encontrar a melor configuração para estes sistemas e para otimizar sua potência de saída. No processo de captura de energia, a energia elétrica é obtida através da conversão de energia mecânica, criado por uma fonte de vibração do ambiente através de um transdutor, por exemplo, um fino filme piezocerâmico. Diferentes mecanismos de acoplamento eletromecânico têm sido desenvolvidos para dispositivos de captura, e um interesse particular tem sido dado ao uso de modelos que transformam a vibração mecânica em corrente elétrica utilizando um elemento piezoelétrico. Neste trabalho, foi proposto um modelo de captura de energia de vibrações, incluindo não-linearidades no acoplamento piezoelétrico e uma excitação não-ideal. Demonstrou-se que a potência capturada foi influenciada pelo efeito das não-linearidades do acoplamento piezoelétrico, alterando o comportamento dinâmico do sistema. Com o acoplamento fraco, um comportamento caótico foi encontrado causando instabilidade. Com o aumento do acoplamento ocorreu um aumento da energia capturada até um certo limite onde o aumento da não-linearidade teve um efeito amortecimento sobre as vibrações não-lineares da estrutura causando a perda de energia. Realizando simulações numéricas o comportamento do modelo foi analisado através dos expoentes de Lyapunov, retratos de fase, históricos de deslocamentos no tempo onde um comportamento caótico também foi observado, causando a perda de energia ao longo do tempo de simulação. Usando uma técnica de perturbação, foi encontrada uma solução analítica aproximada para o sistema não-ideal. Então, aplicou-se três técnicas de... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: In recent years, research on energy harvesting, has increased substantially. Many researchers have concentrated their efforts on finding the best configuration for these systems and to optimize its power output. In the process of energy harvesting, electric power is obtained by converting mechanical energy created by a vibration source from the environment through a transducer, for example, a thin film piezoceramic. Different mechanisms of electromechanical coupling devices have been developd to harvesting, and a particular interest has been given to the use of models that tranform the mechanical vibration into electrical current using a piezoelectric element. In this paper we propose a model to energy harvesting from vibrations, including non-linearities in the piezoelectric doupling and a non-ideal excitation. It was demonstrated that the power captured was influenced by the effect of the nonlinearities of the piezoelectric coupling, modifying the dynamic behavior of the system. With a weak coupling, a chaotic behavior was found causing instability. With the increase of the coupling has ocurred an increase in the energy captured until a limit, where the increase of non-linearity has a damping effect on vibrations of the non-linear structure causing the loss of energy. Performing numerical simulations the behavior of the model was analyzed using the Lyapunov exponents, phase portraits, historical displacements in time where a a chaotic behavior was also observed, causing the loss os energy throughout the simulation time. Using a perturbation technique, found an approximate analytical solution for the non-ideal system. Then, we applied three control techniques to maintain the proposed system in a stable condition. Both the method of equations of state-dependent Riccati (SDRE), the method (LQR) and the feedback... (Complete abstract click electronic access below) / Mestre

abstract: In the past decade, real-world applications of Vertical Take-Off and Landing (VTOL) Unmanned Aerial Vehicles (UAV) have increased significantly. There has been growing interest in one of these types of UAVs, called a tail-sitter UAV, due to its VTOL and cruise capabilities. This thesis presents the fabrication of a spherical tail-sitter UAV and derives a nonlinear mathematical model of its dynamics. The singularity in the attitude kinematics of the vehicle is avoided using Modified Rodrigues Parameters (MRP). The model parameters of the fabricated vehicle are calculated using the bifilar pendulum method, a motor stand, and ANSYS simulation software. Then the trim conditions at hover are calculated for the nonlinear model, and the rotational dynamics of the model are linearized around the equilibrium state with the calculated trim conditions. Robust controllers are designed to stabilize the UAV in hover using the H2 control and H-infinity control methodologies. For H2 control design, Linear Quadratic Gaussian (LQG) control is used. For the H infinity control design, Linear Matrix Inequalities (LMI) with frequency-dependent weights are derived and solved using the MATLAB toolbox YALMIP. In addition, a nonlinear controller is designed using the Sum-of-Squares (SOS) method to implement large-angle maneuvers for transitions between horizontal flight and vertical flight. Finally, the linear controllers are implemented in the fabricated spherical tail-sitter UAV for experimental validation. The performance trade-offs and the response of the UAV with the linear and nonlinear controllers are discussed in detail. / Dissertation/Thesis / Masters Thesis Aerospace Engineering 2018