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Indirect wind estimation onboard unmanned aerial systems (UASs) can be accomplished using existing air vehicle sensors along with a dynamic model of the UAS augmented with additional wind-related states. It is often desired to extract a mean component of the wind the from frequency fluctuations (i.e. turbulence). Commonly, a variation of the KALMAN filter is used, with explicit or implicit assumptions about the nature of the random wind velocity. This dissertation presents an H-infinity (H∞) filtering approach to wind estimation which requires no assumptions about the statistics of the process or measurement noise. To specify the wind frequency content of interest a low-pass filter is incorporated. We develop the augmented UAS model in continuous-time, derive the H∞ filter, and introduce a KALMAN-BUCY filter for comparison. The filters are applied to data gathered during UAS flight tests and validated using a vaned air data unit onboard the aircraft. The H∞ filter provides quantitatively better estimates of the wind than the KALMAN-BUCY filter, with approximately 10-40% less root-mean-square (RMS) error in the majority of cases. It is also shown that incorporating DRYDEN turbulence does not improve the KALMAN-BUCY results. Additionally, this dissertation describes the theory and process for using generalized polynomial chaos (gPC) to re-cast the dynamics of a system with non-deterministic parameters as a deterministic system. The concepts are applied to the problem of wind estimation and characterizing the precision of wind estimates over time due to known parametric uncertainties. A novel truncation method, known as Sensitivity-Informed Variable Reduction (SIVR) was developed. In the multivariate case presented here, gPC and the SIVR-derived reduced gPC (gPCr) exhibit a computational advantage over Monte Carlo sampling-based methods for uncertainty quantification (UQ) and sensitivity analysis (SA), with time reductions of 38% and 98%, respectively. Lastly, while many estimation approaches achieve desirable accuracy under the assumption of known system parameters, reducing the effect of parametric uncertainty on wind estimate precision is desirable and has not been thoroughly investigated. This dissertation describes the theory and process for combining gPC and H-infinity (H∞) filtering. In the multivariate case presented, the gPC H∞ filter shows superiority over a nominal H∞ filter in terms of variance in estimates due to model parametric uncertainty. The error due to parametric uncertainty, as characterized by the variance in estimates from the mean, is reduced by as much as 63%. / Doctor of Philosophy / On unmanned aerial systems (UASs), determining wind conditions indirectly, without direct measurements, is possible by utilizing onboard sensors and computational models. Often, the goal is to isolate the average wind speed while ignoring turbulent fluctuations. Conventionally, this is achieved using a mathematical tool called the KALMAN filter, which relies on assumptions about the wind. This dissertation introduces a novel approach called H-infinity (H∞) filtering, which does not rely on such assumptions and includes an additional mechanism to focus on specific wind frequencies of interest. The effectiveness of this method is evaluated using real-world data from UAS flights, comparing it with the traditional KALMAN-BUCY filter. Results show that the H∞ filter provides significantly improved wind estimates, with approximately 10-40% less error in most cases. Furthermore, the dissertation addresses the challenge of dealing with uncertainty in wind estimation. It introduces another mathematical technique called generalized polynomial chaos (gPC), which is used to quantify and manage uncertainties within the UAS system and their impact on the indirect wind estimates. By applying gPC, the dissertation shows that the amount and sources of uncertainty can be determined more efficiently than by traditional methods (up to 98% faster). Lastly, this dissertation shows the use of gPC to provide more precise wind estimates. In experimental scenarios, employing gPC in conjunction with H∞ filtering demonstrates superior performance compared to using a standard H∞ filter alone, reducing errors caused by uncertainty by as much as 63%.

Nos últimos anos, tem havido grande interesse em estudar manipuladores paralelos, aplicados principalmente em simuladores de voo, com seis graus de liberdade. O interesse em estruturas cinemáticas paralelas é motivado por sua alta rigidez e excelente capacidade de posicionamento em relação às estruturas cinemáticas seriais. Além disso, como os atuadores são posicionados em uma base, eles podem ser aplicados em cargas pesadas e ainda apresentam baixo consumo de energia, tendo em vista que vários atuadores atuam simultaneamente no mesmo corpo. A presente tese apresenta o projeto de três controladores, sendo eles, o controlador H infinito com realimentação de saída, o controlador PID e o controlador Fuzzy, com isto, esta metodologia poderá ser empregada na construção de um futuro simulador de voo. O modelo dos atuadores foi obtido através de uma entrada degrau de tensão nos motores, medindo os seus deslocamentos através dos encoders acoplados, individualmente, a cada um dos respectivos eixos dos motores. Sabendo-se a relação de transmissão do mecanismo de movimento entre o motor e cada haste dos atuadores obtém-se o deslocamento de cada haste a partir da rotação de cada motor medida pelo correspondente encoder e com isso obtém-se o modelo matemático de cada atuador em conjunto com seu sistema de transmissão. Entretanto, na prática, cada atuador é ligeiramente diferente dos outros, o que leva a comportamento e desempenho diferentes entre si. Isso afeta o comportamento da plataforma fazendo com que a trajetória final desejada não possa ser seguida adequadamente, algo que é extremamente necessário em simuladores de voo. Assim, uma das contribuições importantes deste trabalho é, em primeiro lugar, apresentar uma metodologia de padronização das respostas dos atuadores de modo a que todos eles tenham no final, um comportamento igual o mais próximo possível, particularmente em termos de velocidade e de posicionamento. Com os dados da cinemática e da dinâmica da plataforma compondo o modelo completo do sistema foram realizadas várias simulações que aplicadas na plataforma de Stewart real validaram o modelo e mostraram a eficiência das técnicas de controle aplicadas no controle de posição e orientação da plataforma. Para validar o projeto da Plataforma de Stewart como uma possível base de movimento de um simulador de voo, foi implementada a dinâmica longitudinal e lateral de um Boeing 747-100, e com o auxilio de um sensor inercial Xsens® MTi-G, foram realizadas as medições dos ângulos de Euler da Plataforma. Os resultados obtidos pelos três controladores foram satisfatórios e ilustram o desempenho e a robustez da metodologia proposta. / In recent years there has been great interest in studying parallel manipulators, mainly applied in flight simulators, with six degrees of freedom. The interest in parallel kinematic structures is motivated by its high stiffness and excellent positioning capability in relation to serial kinematic structures. Furthermore, since the actuators are positioned on a base, they can handle heavy loads and also have low power consumption, considering that several actuators act on the same platform. This thesis presents the design of three controllers, which are, H-infinity controller with output feedback, PID controller and Fuzzy controller, so that this methodology can be employed in building a future flight simulator. The actuators models were obtained by a step voltage input to the engines and measuring their displacements by the encoders that are coupled to each of the respective axes of the motors. Knowing the relation from the motion transmission mechanism between the motor and the spindle of each actuator, the displacement of each spindle is obtained from the rotation of each motor measured by the corresponding encoder and thus we obtain the mathematical model of each actuator together with its transmission system. However, in practice, each actuator is slightly different from others, which leads to different behavior and performance of each. This affects the behavior of the platform making the final desired trajectory cannot be properly followed something that is extremely necessary in flight simulators. Thus, one of the important contributions of this work is first to present a methodology to standardize the actuators responses so that they all have in the end a behavior equal a close as possible, particularly in terms of velocity and positioning. With the kinematics data and platform dynamics composing the complete system model, several simulations applied to the real Stewart Platform validate the model and show the effectiveness of control techniques applied to control the position and orientation of the platform. In order to validate the Stewart Platform design as a possible base for a motion flight simulator, the longitudinal and lateral dynamics of a Boeing 747-100 model were implemented, and with the aid of an inertial sensor Xsens® MTi-G, measurements of the Euler angles of the platform were performed. The results obtained by the three controllers were satisfactory and illustrate the performance and robustness of the proposed methodology.

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.

O uso de etanol combustível no Brasil é hoje considerado o mais importante programa de combustível comercial renovável do mundo, sendo um potencial substituto aos derivados de petróleo. O aumento de rendimento fermentativo e a diminuição das perdas são objetivos de estudo em diversos centros de pesquisa, sendo o estudo da modelagem matemática e simulação do processo de grande importância para tal. A presente pesquisa apresenta como função identificar um modelo matemático para a linhagem isolada de Saccharomyces cerevisiae PE-2, de maneira a otimizar a maneira como é realizada a sua alimentação através de um controle H∞ por representação quasi-LPV. São realizados 9 ensaios de fermentação em 3 temperaturas distintas sob mesmas condições de concentração de substrato entrante. Após a finalização dos experimentos e análises, realiza-se a estimativa dos parâmetros componentes das equações diferenciais que modelam a cinética fermentativa, através de um algoritmo Quasi-Newton. De posse do modelo matemático, desenvolve-se um controle otimizado para a temperatura de 33ºC (temperatura usual de controle no processo industrial), considerando os parâmetros \"s\" e \"v\" variantes no tempo e os parâmetros x = 150 g/L e p = 70 g/L fixados, sendo valores médios obtidos durante o experimento. A utilização do controle desenvolvido possibilita um aumento de produtividade na faixa de 10% com relação a alimentação realizada em laboratório. Os resultados finais comprovam a eficiência do modelo matemático desenvolvido, comparado a outros estudos semelhantes, a influência da temperatura nos parâmetros cinéticos e a possibilidade de otimizar o processo através de um controle avançado do processo. / The use of ethanol in Brazil is considered the most important commercial renewable fuel program in the world, with a potential substitute for oil products. The increase in fermentation yield and losses reduction are objectives of study in various research centers, where the study of mathematical modeling and simulation of the process is of significant importance. This research presents as function to identify a mathematical model for the isolated strain of Saccharomyces cerevisiae PE-2, in order to optimize the way their substrate is fed, through a H∞ control based on quasi-LPV representation. Nine fermentation tests are performed at three different temperatures under the same conditions for incoming substrate concentration. After the experiments and analysis, it is carried out the estimation of parameters which are components of the differential equations that explain the fermentation kinetics, through a Quasi-Newton algorithm. With the mathematical model obtained, it is developed an optimal control for temperature 33°C (usual temperature control in the industrial process), considering the parameters \"s\" e \"v\" variyng in time and the parameters x = 150 g/L e p = 70 g/L set, which are average values obtained over the tests. The use of the control developed, applied to the flow variation, allows increasing productivity in 10% when compared with the flow performed in the tests conditions. The final results demonstrated the efficacy of the developed mathematical model, compared to other similar studies, the influence of temperature on the kinetic parameters and the possibility to optimize the process through an advanced process control.

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.

This thesis represents the work that has been done by the author in the area of vibration analysis and control of smart structures during his PhD candidature. The research was concentrated on flexible structures, using piezoelectric materials as actuators and sensors. The thesis consists of four major parts. The first part (Chapter 2) is the modelling of piezoelectric laminate structures using modal analysis and finite element methods. The second part (Chapter 4) involves the model correction of pointwise and spatial models of resonant systems. The model correction solution compensates for the errors associated with the truncation of high frequency modes. The third part (Chapter 5) is the optimal placement methodology for general actuators and sensors. In particular, optimal placement of piezoelectric actuators and sensors over a thin plate are considered and implemented in the laboratory. The last part (Chapters 6 to 8) deals with vibration control of smart structures. Several different approaches for vibration control are considered. Vibration control using resonant, spatial H-2 and H-infinity control is proposed and implemented on real systems experimentally. It is possible, for certain modes, to obtain the very satisfactory result of up to 30 dB vibration reduction. / PhD Doctorate

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One of the main tasks for an industrial robot is to move the end-effector in a predefined path with a specified velocity and acceleration. Different applications have different requirements of the performance. For some applications it is essential that the tracking error is extremely small, whereas other applications require a time optimal tracking. Independent of the application, the controller is a crucial part of the robot system. The most common controller configuration uses only measurements of the motor angular positions and velocities, instead of the position and velocity of the end-effector. The development of new cost optimised robots has introduced unwanted flexibilities in the joints and the links. The consequence is that it is no longer possible to get the desired performance and robustness by only measuring the motor angular positions.  This thesis investigates if it is possible to estimate the end-effector position using Bayesian estimation methods for state estimation, here represented by the extended Kalman filter and the particle filter. The arm-side information is provided by an accelerometer mounted at the end-effector. The measurements consist of the motor angular positions and the acceleration of the end-effector. In a simulation study on a realistic flexible industrial robot, the angular position performance is shown to be close to the fundamental Cramér-Rao lower bound. The methods are also verified in experiments on an ABB IRB4600 robot, where the dynamic performance of the position for the end-effector is significantly improved. There is no significant difference in performance between the different methods. Instead, execution time, model complexities and implementation issues have to be considered when choosing the method. The estimation performance depends strongly on the tuning of the filters and the accuracy of the models that are used. Therefore, a method for estimating the process noise covariance matrix is proposed. Moreover, sampling methods are analysed and a low-complexity analytical solution for the continuous-time update in the Kalman filter, that does not involve oversampling, is proposed.  The thesis also investigates two types of control problems. First, the norm-optimal iterative learning control (ILC) algorithm for linear systems is extended to an estimation-based norm-optimal ILC algorithm where the controlled variables are not directly available as measurements. The algorithm can also be applied to non-linear systems. The objective function in the optimisation problem is modified to incorporate not only the mean value of the estimated variable, but also information about the uncertainty of the estimate. Second, H∞ controllers are designed and analysed on a linear four-mass flexible joint model. It is shown that the control performance can be increased, without adding new measurements, compared to previous controllers. Measuring the end-effector acceleration increases the control performance even more. A non-linear model has to be used to describe the behaviour of a real flexible joint. An H∞-synthesis method for control of a flexible joint, with non-linear spring characteristic, is therefore proposed. / En av de viktigaste uppgifterna för en industrirobot är att förflytta verktyget i en fördefinierad bana med en specificerad hastighet och acceleration. Exempel på användningsområden för en industrirobot är bland annat bågsvetsning eller limning. För dessa typer av applikationer är det viktigt att banföljningsfelet är extremt litet, men även hastighetsprofilen måste följas så att det till exempel inte appliceras för mycket eller för lite lim. Andra användningsområden kan vara punktsvetsning av bilkarosser och paketering av olika varor. För dess applikationer är banföljningen inte det viktiga, istället kan till exempel en tidsoptimal banföljning krävas eller att svängningarna vid en inbromsning minimeras. Oberoende av applikationen är regulatorn en avgörande del av robotsystemet. Den vanligaste regulatorkonfigurationen använder bara mätningar av motorernas vinkelpositioner och -hastigheter, istället för positionen och hastigheten för verktyget, som är det man egentligen vill styra.  En del av utvecklingsarbetet för nya generationers robotar är att reducera kostnaden men samtidigt förbättra prestandan. Ett sätt att minska kostnaden kan till exempel vara att minska dimensionerna på länkarna eller köpa in billigare växellådor. Den här utvecklingen av kostnadsoptimerade robotar har infört oönskade flexibiliteter i leder och länkar. Det är därför inte längre möjligt att få den önskade prestandan och robustheten genom att bara mäta motorernas vinkelpositioner och -hastigheter. Istället krävs det omfattande matematiska modeller som beskriver dessa oönskade flexibiliteter. Dessa modeller kräver mycket arbete att dels ta fram men även för att identifiera parametrarna. Det finns automatiska metoder för att beräkna modellparametrarna men oftast krävs det en manuell justering för att få bra prestanda.  Den här avhandlingen undersöker möjligheterna att beräkna verktygspositionen med hjälp av bayesianska metoder för tillståndsskattning. De bayesianska skattningsmetoderna beräknar tillstånden för ett system iterativt. Med hjälp av en matematisk modell över systemet predikteras vad tillståndet ska vara vid nästa tidpunkt. Efter att mätningar av systemet vid den nya tidpunkten har genomförts justeras skattningen med hjälp av dessa mätningar. De metoder som har använts i avhandlingen är det så kallade extended Kalman filtret samt partikelfiltret.  Informationen på armsidan av växellådan ges av en accelerometer som är monterad på verktyget. Med hjälp av accelerationen för verktyget och motorernas vinkelpositioner kan en skattning av verktygspositionen beräknas. I en simuleringsstudie för en realistisk vek robot har det visats att skattningsprestandan ligger nära den teoretiska undre gränsen, känd som Raooch mätstörningar som påverkar roboten. För att underlätta trimningen så har en metod för att skatta processbrusets kovariansmatris föreslagits. En annan viktig del som påverkar prestandan är modellerna som används i filtren. Modellerna för en industrirobot är vanligtvis framtagna i kontinuerlig tid medan filtren använder modeller i diskret tid. För att minska felen som uppkommer då de tidskontinuerliga modellerna överförs till diskret tid har olika samplingsmetoder studerats. Vanligtvis används enkla metoder för att diskretisera vilket innebär problem med prestanda och stabilitet. För att hantera dessa problem införs översampling vilket innebär att tidsuppdateringen sker med en mycket kortare sampeltid än vad mätuppdateringen gör. För att undvika översampling kan det motsvarande tidskontinuerliga filtret användas för att prediktera tillstånden vid nästa diskreta tidpunkt. En analytisk lösning med låg beräkningskomplexitet till detta problem har föreslagits.  Vidare innehåller avhandlingen två typer av reglerproblem relaterade till industrirobotar. För det första har den så kallade norm-optimala iterative learning control styrlagen utökats till att hantera fallet då en skattning av den önskade reglerstorheten används istället för en mätning. Med hjälp av skattningen av systemets tillståndsvektor kan metoden nu även användas till olinjära system vilket inte är fallet med standardformuleringen. Den föreslagna metoden utökar målfunktionen i optimeringsproblemet till att innehålla inte bara väntevärdet av den skattade reglerstorheten utan även skattningsfelets kovariansmatris. Det innebär att om skattningsfelet är stort vid en viss tidpunkt ska den skattade reglerstorheten vid den tidpunkten inte påverka resultatet mycket eftersom det finns en stor osäkerhet i var den sanna reglerstorheten befinner sig.  För det andra har design och analys av H∞-regulatorer för en linjär modell av en vek robotled, som beskrivs med fyra massor, genomförts. Det visar sig att reglerprestandan kan förbättras, utan att lägga till fler mätningar än motorns vinkelposition, jämfört med tidigare utvärderade regulatorer. Genom att mäta verktygets acceleration kan prestandan förbättras ännu mer. Modellen över leden är i själva verket olinjär. För att hantera detta har en H∞-syntesmetod föreslagits som kan hantera olinjäriteten i modellen. / Vinnova Excellence Center LINK-SIC