No description available.

No description available.

This dissertation aims to develop a formal foundation to design an adaptive output feedback predictor for a class of unknown systems where parameters and order are unknown or high-dimensional. We present a reduced-order adaptive output-predictor scheme based on modal reduction and Lyapunov's method. Moreover, the credibility of the proposed reduced-order adaptive output-predictor scheme is validated by mathematical proof, and numerical and experimental studies, such as single pendulum, double pendulum, six-link pendulum, rope as a high-dimensional rope, and EEG data. Then the dissertation goal is to experimentally validate the proposed reduced-order model parameterization technique for tracking uncertain linear time-invariant (LTI) single-input, single-output (SISO) systems. The proposed theory focuses on parameterizing a high-dimensional, uncertain model and introduces a reduced-order adaptive output predictor capable of forecasting the system's output. This predictor utilizes auto-regressive filtered vectors, incorporating the input and output history. The adaptive output predictor is a simplified and known model, making it suitable for controlling high-dimensional, uncertain SISO systems without access to full-state measurements. Specifically, this work establishes the foundation for parameterizing uncertain models, creating a virtual structure that emulates the actual system, and offering a more manageable model for control when the objective is solely to regulate the system's output. The primary focus of this research is to assess the effectiveness and output-tracking capabilities of the proposed approach. These capabilities are extensively examined across diverse platforms and hardware configurations, relying solely on input and output data from the models without incorporating any additional information on the system dynamics. In the first experiment, the predictor's ability to track the angle of a single pendulum, including additional dynamics, is evaluated using only input-output data. The second experiment targets tracking the endpoint of a rope connected to a single pendulum, where the rope emulates a high-dimensional model. A vision system is designed and employed to acquire the rope endpoint position data. Before the rope experiment, a set of experiments is conducted on single pendulum hardware to ensure the accuracy of the vision system's data collection. Comparative analysis between data from object tracking via vision and data acquired through an encoder demonstrates negligible error. Finally, the input and the endpoint output data from the rope experiment are fed into the predictor to assess its capability to track the rope endpoint position without utilizing specific knowledge of the experimental hardware. Achieving negligible error in tracking implies that the predictor provides a simple and accurate representation of the rope dynamics. Consequently, designing a controller for this known model is equivalent to designing a controller for the actual rope system dynamics. The predictor, by closely emulating the behavior of the rope, becomes a reliable surrogate model for control design, simplifying the task of controller design for the complex and uncertain high-dimensional system. Finally, this study introduces a novel approach to enhance controller design for complex brain dynamics by employing a reduced-order adaptive output predictor proposed in [1], fine-tuned with chirp binaural beats. The proposed technique is promising for developing closed-loop controllers in non-invasive brain stimulation therapies, such as binaural beats stimulation, to improve working memory. The study focuses on parameterizing uncertain models and creates a predictor that utilizes auto-regressive filtered vectors to forecast mean phase lock values generated by binaural beats stimulation. The simplified and known model of the predictor proves effective in tracking brain responses, as demonstrated in experiments evaluating its ability to track mean phase locking values. The results indicate negligible tracking error, suggesting the predictor's reliability in representing brain dynamics and simplifying the task of controller design for the complex and uncertain high-dimensional system. / Doctor of Philosophy / This dissertation explores the development of a reduced-order adaptive output predictor for unknown systems with unknown or high-dimensional parameters and order. A reduced-order adaptive output predictor scheme is introduced, validated through mathematical proof, and tested in diverse scenarios, including pendulum systems and EEG data. The focus is on parameterizing uncertain models and creating a simplified adaptive output predictor capable of forecasting system output, specifically for SISO systems. Experimental validation involves tracking the angle of a single pendulum and the endpoint of a high-dimensional rope, demonstrating the predictor's accuracy without detailed knowledge of system dynamics. The study extends its application to complex brain dynamics, using the predictor fine-tuned with chirp binaural beats. Results show promise for developing closed-loop controllers in non-invasive brain stimulation therapies, offering a novel approach to improve working memory via helping to design closed-loop controllers.

Le présent document a pour objet la modélisation transitoire non linéaire du comportement vibratoire des systèmes de frein aéronautiques. Le but est de reproduire numériquement l’apparition et le niveau des vibrations au cours du temps, afin de les maîtriser et d’adapter la conception du frein. Les essais de freinage mettent en évidence deux modes de vibration que sont le whirl et le squeal. Si les niveaux de ces vibrations deviennent trop importants, la structure de la roue et du train d’atterrissage peut être endommagée. Afin d’éviter de tels dommages, la conception du frein doit être adaptée. Pour réaliser cela, Messier-Bugatti-Dowty doit disposer d’un modèle capable de prédire les niveaux de vibration du frein au cours du temps pendant la phase de freinage. Le modèle doit avoir une précision suffisante, être en lien avec la maquette numérique et ne doit pas exiger de recalage. Un premier travail vise à améliorer le modèle éléments finis existant qui se révèle être trop imprécis. Une étude portant sur les effets gyroscopiques permet d’évaluer leur impact sur la fréquence et la stabilité des modes de whirl. Une modélisation plus complète du bâti d’essai améliore la précision de la fréquence du mode de squeal. Enfin, le mode de whirl est mieux simulé grâce au développement d’un modèle de pneumatique à partir de son analyse modale. Ce modèle est ensuite réduit afin de réaliser une intégration temporelle. Une sous-structuration permet de séparer l’ensemble des disques du frein, où le frottement et la non-linéarité se situent, du reste de la structure considérée comme linéaire. Trois techniques de réduction de l’ensemble des disques sont exposées. On évalue leur représentativité par rapport au modèle non-réduit en comparant les fréquences et la stabilité des modes propres. La première méthode est une représentation nodale de l’ensemble des disques. Les équations décrivant la non-linéarité et le frottement sont analytiques. Pour la deuxième méthode, la non-linéarité est déplacée à l’extrémité de l’ensemble des disques pour la découpler du frottement. La troisième méthode, plus ambitieuse et complexe, conserve à la fois l’emplacement de la nonlinéarité aux interfaces frottantes et la géométrie des disques. Une technique de réduction modale permet d’abaisser le nombre de degrés de liberté non linéaires. Pour clore ce rapport, des simulations transitoires sont calculées à partir des modèles réduits. Des études d’influences sont réalisées. Les paramètres étudiés sont le type d’algorithme d’intégration temporelle, l’amortissement introduit, la loi non linéaire, la pression hydraulique d’entrée et le coefficient de frottement. Leurs impacts sur les niveaux et la durée d’apparition des vibrations est évalué. / This report deals with the non-linear transient simulation of the dynamic behaviour of aeronautic brake systems. The objective is to reproduce the occurrence and level of vibrations versus time in order to control and adjust design consequently. The braking tests highlight two eigenmodes, which are called whirl and squeal. If the level of these vibrations becomes too high, the structures of the wheel and the landing gear may be damaged. To avoid damage, the design has to be adjusted. To achieve this, Messier-Bugatti-Dowty requires a model that is able to predict the levels of vibrations of the brake when it is braking. This model must have an adequate accuracy, be linked to the digital mockup and not require tuning. First, the existing finite element model has to be improved because its initial accuracy is not acceptable. A study about gyroscopic effects allows to assess their impact on the frequency and the stability of whirl modes. A complete modelling of the test frame improves the squeal modes’ frequency accuracy. At last, the whirl modes are better simulated due to the development of a tyre model based on modal analysis data. Then, the finite element model is reduced in order to perform a temporal integration. A substructuring allows to separate the set of brake discs (heat sink), where friction and non-linearities are located, from the rest of the structure which is considered linear. Three heat sink reduction techniques are proposed. Their representativeness are estimated compared to the non-reduced model. The first technique is a nodal description of the heat sink. The equations of friction and non-linearity are analytical. For the second technique, the non-linearity is displaced to the extremity of the heat sink to uncouple it from friction. The third technique, more ambitious and complex, keeps the location and non-linearity in friction interfaces and discs geometry. A reduction technique enables to decrease the number of non-linear degrees of freedom. As a conclusion, transient simulations are computed from reduced models. Sensitivity studies are performed. Studied parameters are the type of integration solver, introduced damping, non-linearities, hydraulic pressure, and friction coefficient. Their impacts on level and duration of occurrence of vibrations is estimated.