a b s t r a c t In this paper, a hybrid method using active control and a High Order Differentiator (HOD) methodology is proposed to synchronize chaotic systems. Compared to some traditional active control methods, this new method can synchronize chaotic systems where only output states of the master system are available, i.e. the system is considered a black box. The HOD is used to estimate the derivative information of the master system followed by an active control methodology relying on HOD information. The Qi hyperchaotic system is used to verify the performance of this hybrid method. The proposed method is also compared to some traditional methods. Experimental results show that the proposed method has high synchronization precision and speed and is robust against uncertainties in the master system. The circus implements of the proposed synchronizing scheme are included in this paper. The simulation results show the feasibility of the proposed scheme.

Precise velocity and acceleration information is required for many real time applications. A standalone GPS receiver can be used to derive such information; however, there are many unsolved problems in this regard. This thesis establishes the theoretical basis for precise velocity and acceleration determination using a standalone GPS receiver in real time. An intensive investigation has been conducted into the Doppler effect in GPS. A highly accurate Doppler shift one-way observation equation is developed based on a comprehensive error analysis of each contributing factor including relativistic effects. Various error mitigation/elimination methods have been developed to improve the measurement accuracy of both the Doppler and Doppler-rate. Algorithms and formulae are presented to obtain real-time satellite velocity and acceleration in the ECEF system from the broadcast ephemeris. Low order IIR differentiators are designed to derive Doppler and Doppler-rate measurements from the raw GPS data for real-time applications. Abnormalities and their corresponding treatments in real-time operations are also discussed. In addition to the velocity and acceleration determination, this thesis offers a good tool for GPS measurement modelling and for design of interpolators, differentiators, as well as Kalman filters. The relativistic terms presented by this thesis suggest that it is possible to measure the geopotential directly using Doppler shift measurements. This may lead to a foundation for the development of a next generation satellite system for geodesy in the future.

La qualité de la dérivation numérique en ligne d’un signal bruité joue un rôle primordial dans diverses applications touchant différents domaines (1D et 2D). Dans le travail présenté, nous nous sommes intéressés aux dérivateurs type "signal". Nos travaux s’inscrivent dans ce contexte et abordent des aspects théoriques et applicatifs. Du point de vue théorique, une étude de deux familles de dérivateurs a été effectuée. En premier lieu, nous avons étudié les dérivateurs de nature algébrique [travaux du projet INRIA-Non-A] et en deuxième lieu les différentiateurs modes glissants d’ordre supérieur [travaux de Levant]. Cette étude nous a permis de décrire les points forts et les points faibles de chacune de ces approches. Suite à cette étude, une nouvelle version des dérivateurs modes glissants a été proposée. Du point de vue applicatif, une première application dans le domaine 1D est présentée et qui consiste à utiliser le dérivateur proposé pour l’identification paramétrique en ligne d’un robot SCARA à deux axes. La méthode d’identification est validée expérimentalement par comparaison des résultats obtenus avec ceux donnés par d’autres méthodes (méthode en ligne et hors ligne). La deuxième application touche au domaine 2D. Dans ce cas, nous proposons l’application du différentiateur pour la détection des contours dans une image. Pour la validation des résultats, différents essais sont réalisés pour différents types de bruits. Une étude comparative avec des méthodes classiques est effectuée. Pour pouvoir tester l’efficacité du différentiateur dans des boucles de commande nous nous sommes intéressés aux systèmes électrohydrauliques. Le système physique étudié est un servo-vérin électrohydraulique à hautes performances ayant différents modes de fonctionnement. Après une succession d’hypothèses effectuées sur le modèle de simulation, des modèles de commande sont fournis. La dernière partie de ces travaux est dédiée à la synthèse de stratégie de commande via la technique du Backstepping pour le positionnement de l’axe électrohydraulique afin de tester l’efficacité l’algorithme proposé dans des boucles de commande. Comme base de comparaison, la version classique des algorithmes modes glissants est aussi utilisée. / The quality of the on-line differentiation with a noisy signal plays an important role in various applications involving different areas (1D and 2D). In the present work, we were interested particularly to differentiation method which requires a minimal knowledge on the noise and/or the input signal. Our work is registred in this context and address both aspects theoretical and applications. From the theoretical point of view, a study of two families of differentiation algorithm was performed. Firstly, we studied the algorithm based on the algebraic development [the work of the project INRIA-ALIEN] and secondly the differentiators of higher order sliding modes [work Levant] for detailed study. This study allowed us to describe the advantages and disadvantages of each approach. Following this study, a new version of sliding modes differentiator was proposed, this last one being the main theoretical contribution of this thesis. To test the efficiency of the proposed version, differents applications were carried out. The first application in 1D is shown, which consists in use the proposed differentiator for online parametric identification of a two-axis SCARA robot. The identification method is validated experimentally by comparing the results obtained with those given by other methods (method online and offline). The second application relates to the 2D domain. In this case, we propose the implementation of the differentiator for the edge detection in an image. To validate the results, various tests are carried out for different types of noise. In order to have some comparison basis, we use the filter Canny and Prewitt masks and the gradient. To test the effectiveness of the differentiator in control loops we are interested in electrohydraulic systems. For this, a model of the hydraulic and mechanical system is made. After a consideration of some assumptions on the simulation model, the control models are provided. To separate the dynamic servovalve/ actuator, a local study is performed. The last part of this work is dedicated to the synthesis of control strategy through the backstepping technique for the positioning of the electro-hydraulic axis in order to test the effectiveness of the proposed algorithm in the control loop. As a basis for comparison, the classic version of sliding mode algorithm is also used.

Microwave signal processing in the optical domain is investigated in this thesis. Two signal processors including an all-optical fractional Hilbert transformer and an all-optical microwave differentiator are investigated and experimentally demonstrated. Specifically, the photonic-assisted fractional Hilbert transformer with tunable fractional order is implemented based on a temporal pulse shaping system incorporating a phase modulator. By applying a step function to the phase modulator to introduce a phase jump, a real-time fractional Hilbert transformer with a tunable fractional order is achieved. The microwave bandpass differentiator is implemented based on a finite impulse response (FIR) photonic microwave delay-line filter with nonuniformly-spaced taps. A microwave bandpass differentiator based on a six-tap nonuniformly-spaced photonic microwave delay-line filter with all- positive coefficients is designed, simulated, and experimentally demonstrated. The reconfigurability of the microwave bandpass differentiator is experimentally investigated. The employment of the differentiator to perform differentiation of a bandpass microwave signal is also experimentally demonstrated.

Microwave signal processing in the optical domain is investigated in this thesis. Two signal processors including an all-optical fractional Hilbert transformer and an all-optical microwave differentiator are investigated and experimentally demonstrated. Specifically, the photonic-assisted fractional Hilbert transformer with tunable fractional order is implemented based on a temporal pulse shaping system incorporating a phase modulator. By applying a step function to the phase modulator to introduce a phase jump, a real-time fractional Hilbert transformer with a tunable fractional order is achieved. The microwave bandpass differentiator is implemented based on a finite impulse response (FIR) photonic microwave delay-line filter with nonuniformly-spaced taps. A microwave bandpass differentiator based on a six-tap nonuniformly-spaced photonic microwave delay-line filter with all- positive coefficients is designed, simulated, and experimentally demonstrated. The reconfigurability of the microwave bandpass differentiator is experimentally investigated. The employment of the differentiator to perform differentiation of a bandpass microwave signal is also experimentally demonstrated.

Microwave signal processing in the optical domain is investigated in this thesis. Two signal processors including an all-optical fractional Hilbert transformer and an all-optical microwave differentiator are investigated and experimentally demonstrated. Specifically, the photonic-assisted fractional Hilbert transformer with tunable fractional order is implemented based on a temporal pulse shaping system incorporating a phase modulator. By applying a step function to the phase modulator to introduce a phase jump, a real-time fractional Hilbert transformer with a tunable fractional order is achieved. The microwave bandpass differentiator is implemented based on a finite impulse response (FIR) photonic microwave delay-line filter with nonuniformly-spaced taps. A microwave bandpass differentiator based on a six-tap nonuniformly-spaced photonic microwave delay-line filter with all- positive coefficients is designed, simulated, and experimentally demonstrated. The reconfigurability of the microwave bandpass differentiator is experimentally investigated. The employment of the differentiator to perform differentiation of a bandpass microwave signal is also experimentally demonstrated.

Microwave signal processing in the optical domain is investigated in this thesis. Two signal processors including an all-optical fractional Hilbert transformer and an all-optical microwave differentiator are investigated and experimentally demonstrated. Specifically, the photonic-assisted fractional Hilbert transformer with tunable fractional order is implemented based on a temporal pulse shaping system incorporating a phase modulator. By applying a step function to the phase modulator to introduce a phase jump, a real-time fractional Hilbert transformer with a tunable fractional order is achieved. The microwave bandpass differentiator is implemented based on a finite impulse response (FIR) photonic microwave delay-line filter with nonuniformly-spaced taps. A microwave bandpass differentiator based on a six-tap nonuniformly-spaced photonic microwave delay-line filter with all- positive coefficients is designed, simulated, and experimentally demonstrated. The reconfigurability of the microwave bandpass differentiator is experimentally investigated. The employment of the differentiator to perform differentiation of a bandpass microwave signal is also experimentally demonstrated.

This thesis deals with the derivation of novel adaptive feed forward compensator, which will be used for the control of the electromechanical actuators used in automotive industry. The electromechnical actuators are an electronic throttle valve and an EGR valve. The introduced adaptive compensator is derived from an existing multiple model feedback control method. This work describes the derivation of this method and simulation and experimental verification. In addition, the most well known digital filter differentiators are presented and summarized in this paper because the feed forward compensator needs them for its operation. From these filters, one specific is chosen, whoose coefficients for the specific setting leads to integer multiplication and an integer implementation of the filter. This will be used to implement this filter to the FPGA and then we prove, that this implementation saves a lot of FPGA resources compared to filters implemented using fixed or floating-point arithmetic.

Les systèmes de régulation des turbomoteurs actuels sont basés sur des architectures complexes que les constructeurs tendent à rendre plus modulaires avec des technologies plus économiques tout en garantissant un niveau de fiabilité supérieur ou égal. Dans ce contexte, la surveillance du circuit carburant, qui a pour but de déceler les dysfonctionnements des composants hydrauliques critiques, permet de réduire le coût de maintenance, d'améliorer le niveau de maintenabilité et d'assurer la disponibilité des turbomoteurs. La présente étude porte sur l'élaboration de méthodes de diagnostic performantes et robustes permettant la détection et la localisation des défauts impactant les fonctions hydrauliques primaires du circuit carburant. Des méthodes existantes de génération de résidus à base de modèles non linéaires sont présentées et appliquées au cas du circuit carburant. L'approche analytique pour le découplage, combinée avec des filtres de Kalman étendus, permet la structuration des résidus pour assurer la localisation des défauts. Une nouvelle approche basée sur la théorie de platitude différentielle est proposée pour le diagnostic de défauts des systèmes non linéaires avec une application au cas du circuit carburant. Les différentiateurs à modes glissants sont utilisés pour l'estimation des dérivées de signaux nécessaires à l'application de certaines méthodes de génération de résidus. Des simulations numériques illustrent la pertinence des résultats obtenus. Une application expérimentale est présentée en utilisant un jeu de données réelles issues d'un banc d'essais partiel et fournies par la société Turbomeca du groupe SAFRAN. / The current gas turbine regulation systems are based on complex architectures that manufacturers tend to make more modular with more cost effective technologies while ensuring a greater or equal level of reliability. In this context, the fuel system health monitoring, which aims to identify critical hydraulic components dysfunction, allows to reduce maintenance costs, to improve maintainability level and to ensure gas turbine availability. The present study focuses on the development of performant and robust diagnosis methods for the detection and isolation of faults affecting primary fuel system hydraulic functions. Existing nonlinear model based residual generation methods are presented and applied to the fuel system. The analytical approach for decoupling, combined with extended Kalman filters, helps fault isolation by generating residual structures. A new approach based on differential flatness theory is proposed for nonlinear systems fault diagnosis with an application to the fuel system. Sliding mode differentiators are used to estimate derived signals that are necessary for the application of some residual generation methods. Numerical simulations illustrate the efficiency of obtained results. An experimental application is presented using a real data set from a partial test bench provided by Turbomeca company of the SAFRAN group.

Tato disertační práce pojednává o návrhu nových funkčních bloků použitelných v oblasti zpracování analogového signálu. Jde o obvody v proudové módu, které mohou ve vhodné konfiguraci pracovat v proudovém i v napěťovém módu. To umožnílo získat velmi nadějné výsledky v soustavách s nízkým napájecím napětím. Mnohostrannost těchto obvodů nalezne uplatnění v mnoha aplikacích. Zesilovač s proudovou zpětnou vazbou byl zavolen jako hlavní stavební blok pro detailní zkoumání funkce obvodů s RC operační sítí. Tato disertační práce pojednává o studiu, syntéze a návrhových aspektech realizace nových imitančních funkcí, jmenovitě induktivních a superkapacitních, proudových a napěťových konvejorech, kmitočtových filtrech s velkou jakostí, integrátorech a diferenciátorech, fázovacích členech s neminimální fází a napětím řízených oscilátorech. Disertační práce se detailně zabývá těmito novými bloky, které jsou popsány teoreticky a vyhodnoceny na základě simulací vlastností.