Les travaux de cette thèse portent sur les problèmes d'analyse de stabilité et de synthèse de commande de systèmes non-linéaires à commutations en temps discret. Nos résultats obtenus sont fondés sur une nouvelle fonction de Lyapunov-Lur'e adaptée au temps discret. Nous reprenons le problème classique d'analyse de stabilité globale de systèmes linéaires connectés à une non-linéarité du type secteur borné. Notre fonction permet de traiter une classe de non-linéarités plus générale que celle des approches fondées sur la fonction de Lur'e classique. Ensuite, la stabilité locale et la synthèse de commande de ces systèmes avec une loi de commande non-linéaire saturée sont résolues en considérant les lignes de niveau de notre fonction de Lyapunov comme estimation du bassin d'attraction de l'origine. Notre estimation est composée par des ensembles non-connexes et non-convexes qui s'adaptent bien à l'allure du bassin d'attraction et donc est moins conservative que les ensembles ellipsoïdaux. Nous étendons nos résultats pour étudier les systèmes à commutations lorsque chacun des modes présente une non-linéarité du type secteur et la saturation. D'une part, en supposant que la loi de commutation est arbitraire, nous obtenons des conditions suffisantes pour assurer la propriété de stabilité pour toute loi de commutation. Dans ce cadre, notre fonction s'avère intéressante afin de fournir une estimation bien adaptée au bassin d'attraction. D'autre part, en considérant la loi de commutation comme une variable de commande, nous proposons une stratégie de commutation sur le minimum des fonctions de Lyapunov modales. Cette stratégie définit des partitions de l'espace d'état relatives à l'activation des modes qui ne sont pas uniquement des régions coniques, normalement exhibées par des approches fondées sur les fonctions quadratiques commutées.

Quantification of blood fraction (fblood), blood oxygenation (S<img src="http://onlinelibrary.wiley.com/store/10.1002/jbio.201200055/asset/equation/tex2gif-inf-2.gif?v=1&amp;t=h70man4a&amp;s=4a6d004ec608a2a6ec8e8597f73bdb6be30286e8" />), melanin, lipofuscin and oxidised and reduced Cytochrome aa 3 and c was done from diffuse reflectance spectra captured in cortex, white matter, globus pallidus internus (GPi) and subthalamus during stereotactic implantations of 29 deep brain stimulation (DBS) electrodes with the aim of investigating whether the chromophores can give physiological information about the targets for DBS. Double-sided Mann-Whitney U -tests showed more lipofuscin in GPi compared to white matter and subthalamus (p &lt; 0.05). Compared to the other structures, fbloodwas significantly higher in cortex (p &lt; 0.05) and S<img src="http://onlinelibrary.wiley.com/store/10.1002/jbio.201200055/asset/equation/tex2gif-inf-4.gif?v=1&amp;t=h70man4c&amp;s=855c70105e88a292de25618487573dfc7d30e08a" /> lower in GPi (p &lt; 0.05). Median values and range for fblood were 1.0 [0.2–6.0]% in the cortex, 0.3 [0.1–8.2]% in white matter, 0.2 [0.1–0.8]% in the GPi and 0.2 [0.1–11.7]% in the subthalamus. Corresponding values for S<img src="http://onlinelibrary.wiley.com/store/10.1002/jbio.201200055/asset/equation/tex2gif-inf-6.gif?v=1&amp;t=h70man4e&amp;s=151ec25bee7270bcfc2292e70d6f4aea18348dbc" /> was 20 [0–81]% in the cortex, 29 [0–78]% in white matter, 0 [0–0]% in the GPi and 0 [0–92]% in the subthalamus. In conclusion, the measurements indicate very low oxygenation and blood volume for DBS patients, especially in the GPi. It would be of great interest to investigate whether this is due to the disease, the normal situation or an artefact of doing invasive measurements.

This thesis deals with the design of multivariable controllers for stable linear time-invariant multi-input multi-output systems, with an unknown mathematical model, subject to constant reference/disturbance signals and actuator saturation constraints. A new controller parameter optimization approach, which can be carried out experimentally with no knowledge of the plant model nor of the order of the system, is proposed. The approach has the advantage that controllers can be optimized by perturbing only the initial conditions of the servocompensator, and that the order of the resulting controller obtained can be specified by the designer. Implementation of the proposed controller design approach is described, and an experimental application study of the proposed method applied to a multivariable system with industrial sensor/actuator components is presented to illustrate the feasibility of the design method in an industrial environment.

This thesis deals with the design of multivariable controllers for stable linear time-invariant multi-input multi-output systems, with an unknown mathematical model, subject to constant reference/disturbance signals and actuator saturation constraints. A new controller parameter optimization approach, which can be carried out experimentally with no knowledge of the plant model nor of the order of the system, is proposed. The approach has the advantage that controllers can be optimized by perturbing only the initial conditions of the servocompensator, and that the order of the resulting controller obtained can be specified by the designer. Implementation of the proposed controller design approach is described, and an experimental application study of the proposed method applied to a multivariable system with industrial sensor/actuator components is presented to illustrate the feasibility of the design method in an industrial environment.

Le tissu est réalisé par un entrecroisement, appelé armure [1], de 2 réseaux de fils, un longitudinal et un transversal 2D et de plus de 2 réseaux 3D. Les propriétés de ces tissus seront fonction de la quantité de fil insérable dans l'armure, quantité dont la limite doit être déterminée de façon précise. Hors, à ce jour, cette limite est très mal connue [2]. Donc, l'utilité principale du calcul des limites de tissabilité est de savoir si un tissu 2D ou 3D est réalisable ou non sur une machine à tisser. Les coefficients de difficulté permettent d'éviter des productions endommageant le matériel et aussi d'apprécier a priori les problèmes de rendement de production des articles proches des limites de tissabilité tel que les tissus techniques. Il est d'autre part possible de déduire certaines caractéristiques techniques de l'article réalisé. Ces calculs peuvent en effet quantifier le serrage des fils entre eux et permettre de déduire les caractéristiques mécaniques et physiques. Les raisons motivant ces recherches sont d'une part d'éviter un surcoût de production en essayant de tisser un article, 2D ou 3D, impossible à tisser et d'autre part de diminuer les casses des fils et l'usure des éléments de la machine à tisser à cause d'une surcharge sur le métier à tisser pendant l'opération de tissage. Après la mise en place d'un plan d'expérience de tissage, l'étude des propriétés mécaniques et physiques d'un nombre représentatifs de tissus 2D et 3D et la modélisation des structures tissées a permis de proposer de nouvelles équations de saturations et de limite de tissabilité en particulier pour le 3D [3]. Par ailleurs, à partir de ces équations, il est possible de prévoir, pour une contexture et une armure donnée en 2D ou 3D, la masse maximale de fil insérable dans le tissu ainsi que la difficulté qui sera rencontrée lors du tissage. Les relations théoriques nouvelles proposées, indices de saturation numérique et indice de saturation massique ont été confirmées par les résultats expérimentaux et Il a été conclu que les équations et abaques qui en découlent sont des outils utiles pour l'industrie de tissage traditionnel et technique.

In this paper we examine the stabilization of LTI discrete-time systems with control input constraints in the form of saturation nonlinearities. This kind of constraint is usually introduced to simulate the effect of actuator limitations. Since global controllability can not be assumed in the presence of constrained control, the controllable regions and their characterizations are analyzed first. We present an efficient algorithm for finding controllable regions in terms of their boundary hyperplanes (inequality constraints). A previously open question about the exact number of irredundant boundary hyperplanes is also resolved here. The main result of this research is a time-optimal nonlinear controller which stabilizes the system on its controllable region. We give analgorithm for on-line computation of control which is also implementable for high-order systems. Simulation results show superior response even in the presence of disturbances.

The bulk modulus of pure hydraulic oil and its dependency on pressure and temperature has been studied extensively over the past years. A comprehensive review of some of the more common definitions of fluid bulk modulus is conducted and comments on some of the confusion over definitions and different methods of measuring the fluid bulk modulus are presented in this thesis. In practice, it is known that there is always some form of air present in hydraulic systems which substantially decreases the oil bulk modulus. The term effective bulk modulus is used to account for the effect of air and/or the compliance of transmission lines. A summary from the literature of the effective bulk modulus models for a mixture of hydraulic oil and air is presented. Based on the reviews, these models are divided into two groups: “compression only” models and “compression and dissolve” models. A comparison of various “compression only” models, where only the volumetric compression of air is considered, shows that the models do not match each other at the same operating conditions. The reason for this difference is explained and after applying some modifications to the models, a theoretical model of the “compression only” model is suggested. The “compression and dissolve” models, obtained from the literature review, include the effects of the volumetric compression of air and the volumetric reduction of air due to the dissolving of air into the oil. It is found that the existing “compression and dissolve” models have a discontinuity at some critical pressure and as a result do not match the experimental results very well. The reason for the discontinuity is discussed and a new “compression and dissolve” model is proposed by introducing some new parameters to the theoretical model. A new critical pressure (PC) definition is presented based on the saturation limit of oil. In the new definition, the air stops dissolving into the oil after this critical pressure is reached and any remaining air will be only compressed afterwards. An experimental procedure is successfully designed and fabricated to verify the new proposed models and to reproduce the operating conditions that underlie the model assumptions. The pressure range is 0 to 6.9 MPa and the temperature is kept constant at °C. Air is added to the oil in different forms and the amount of air varies from about 1 to 5%. Experiments are conducted in three different phases: baseline (without adding air to the oil), lumped air (air added as a pocket of air to the top of the oil column) and distributed air (air is distributed in the oil in the form of small air bubbles). The effect of different forms and amounts of air and various volume change rates are investigated experimentally and it is shown that the value of PC is strongly affected by the volume change rate, the form, and the amount of air. It is also shown that the new model can represent the experimental data with great accuracy. The new proposed “compression and dissolve” model can be considered as a general model of the effective bulk modulus of a mixture of oil and air where it is applicable to any form of a mixture of hydraulic oil and air. However, it is required to identify model parameters using experimental measurements. A method of identifying the model parameters is introduced and the modeling errors are evaluated. An attempt is also made to verify independently the value of some of the parameters. The new proposed model can be used in analyzing pressure variations and improving the accuracy of the simulations in low pressure hydraulic systems. The new method of modeling the air dissolving into the oil can be also used to improve the modeling of cavitation phenomena in hydraulic systems.

In this paper we examine the stabilization of LTI discrete-time systems with control input constraints in the form of saturation nonlinearities. This kind of constraint is usually introduced to simulate the effect of actuator limitations. Since global controllability can not be assumed in the presence of constrained control, the controllable regions and their characterizations are analyzed first. We present an efficient algorithm for finding controllable regions in terms of their boundary hyperplanes (inequality constraints). A previously open question about the exact number of irredundant boundary hyperplanes is also resolved here. The main result of this research is a time-optimal nonlinear controller which stabilizes the system on its controllable region. We give analgorithm for on-line computation of control which is also implementable for high-order systems. Simulation results show superior response even in the presence of disturbances.

<p>The problem is two fold: how does natural selection operate on systems of interacting genes and how does natural selection operate in natural populations. To address the first problem, I have conducted a theoretical investigation into the evolution of control and the distribution of mutations in a simple system of interacting genes, a linear metabolic pathway. I found that control is distributed unevenly between enzymes, with upstream enzymes possessing the greatest control and accumulating the most beneficial mutations during adaptive evolution. To address the second problem, I investigated the evolution of copper tolerance in the common yellow monkeyflower, Mimulus guttatus. I genetically mapped a major locus controlling copper tolerance, Tol1. A Dobzhansky-Muller incompatibility was hypothesized to also be controlled by Tol1, however, we have demonstrated that it maps to another, tightly linked locus, Nec1. Finally, we investigated the parallel evolution of copper tolerance in multiple new discovered mine populations. We found that copper tolerance has evolved in parallel multiple times via at least two distinct physiological mechanisms. In four mine populations, there was a strong signal of selection at markers linked to Tol1, implying that copper tolerance has evolved via the same genetic mechanisms in these populations.</p> / Dissertation

An experimental study of the effect of initial conditions on the development of Rayleigh Taylor Instabilities (RTI) at low Atwood numbers (order of 10-4) was performed in the water channel facility at TAMU. Initial conditions of the flow were generated using a controllable, highly reliable Servo motor. The uniqueness of the study is the system’s capability of generating the required initial conditions precisely as compared to the previous endeavors. Backlit photography was used for imaging and ensemble averaging of the images was performed to study mixing width characteristics in different regimes of evolution of Rayleigh-Taylor Instability (RTI). High-speed imaging of the flows was performed to provide insights into the growth of bubble and spikes in the linear and non-linear regime of instability development. RTI are observed in astrophysics, geophysics and in many instances in nature. The vital role of RTI in the feasibility and efficiency of the Inertial Confinement Fusion (ICF) experiment warrants a comprehensive study of the effect of mixing characteristics of RTI and its dependence on defining parameters. With this broader objective in perspective, the objectives of this present investigation were mainly threefold: First was the validation of the novel setup of the Water channel system. Towards this objective, validation of Servo motor, splitter plate thickness effects, density and temperature measurements and single-mode experiments were performed. The second objective was to study the mixing and growth characteristics of binary and multi-mode initial perturbations seeking an explanation of behavior of the resultant flow structures by performing the first ever set of such highly controlled experiments. The first-ever set of experiments with highly controlled multi-mode initial conditions was performed. The final objective of this study was to measure and compare the bubble and spike velocities with single-mode initial conditions with existing analytical models. The data derived from these experiments would qualitatively and quantitatively enhance the understanding of dependence of mixing width on parametric initial conditions. The knowledge would contribute towards a generalized theory for RTI mixing with specified dependence on various parameters, which has a wide range of applications. The system setup was validated to provide a reliable platform for the novel multi-modal experiments to be performed in the future. It was observed that the ensemble averaged mixing width of the binary system does not vary significantly with the phase-difference between the modes of a binary mode initial condition experiment, whereas it varies with the amplitudes of the component modes. In the exponential and non-linear regimes of evolution, growth rates of multi-mode perturbations were found to be higher than the component modes, whereas saturation growth rates correspond to the dominant wavelength. Quadratic saturation growth rate constants, alpha were found to be about 0.07 ± 0.01 for binary and multi modes whereas single-mode data measured alpha about 0.06 ± 0.01. High-speed imaging was performed to measure bubble and spike amplitudes to obtain velocities and growth rates. It was concluded that higher temporal and spatial resolution was required for accurate measurement. The knowledge gained from the above study will facilitate a better understanding of the physics underlying Rayleigh-Taylor instability. The results of this study will also help validating numerical models for simulation of this instability, thereby providing predictive capability for more complex configurations.