With the rapid development in today&rsquo / s technology, reliability and performance requirements on components of various mechanical systems, which tend to be much lighter and work under much more severe working conditions, dramatically increased. In general, analysis techniques based on simplified model of structural components with linearity assumption may provide time saving for solutions with reasonable accuracy. However, since most engineering structures are often very complex and intrinsically nonlinear, in some cases they may behave in a different manner which cannot be fully described by linear mathematical models, or linear treatments may not be applicable at all. In fact, some studies revealed that deviations in the modal properties of dynamic structures gathered from measured data are due to nonlinearities in the structure. Hence, in problems where accuracy is the primary concern, taking the nonlinear effects into account becomes inevitable. In this thesis, it is aimed to analyze the harmonic response characteristics of multi degree of freedom nonlinear structures having different type of nonlinearities. The amplitude dependencies of nonlinearities are modelled by using describing function method. To increase the accuracy of the results, effect of the higher order harmonic terms will be considered by using multi harmonic describing function theory. Mathematical formulations are embedded in a computer program developed in MATLAB&reg / with graphical user interface. The program gets the system matricies from the file which is obtained by using substructuring analysis in ANSYS&reg / , and nonlinearities in the system can easily be defined through the graphical user interface of the MATLAB&reg / program.

This dissertation seeks to merge the ideas from robust control theory such as H-Infinity control design and the Small Gain Theorem, L stability theory and Lyapunov stability from nonlinear control, and recent theoretical achievements in adaptive control. The fusion of frequency domain and linear time domain ideas allows the derivation of an H-Infinity Norm Minimization Approach (H-Infinity-NMA) for adaptive control architecture that permits a control designer to simplify the adaptive tuning process and tune the uncertainty compensation characteristics via linear control design techniques, band limit the adaptive control signal, efficiently handle redundant actuators, and handle unmatched uncertainty and matched uncertainty in a single design framework. The two stage design framework is similar to that used in robust control, but without sacrificing performance. The first stage of the design considers an ideal system with the system uncertainty completely known. For this system, a control law is designed using linear H-Infinity theory. Then in the second stage, an adaptive process is implemented that emulates the behavior of the ideal system. If the linear H-Infinity design is applied to control the emulated system, it then guarantees closed loop system stability of the actual system. All of this is accomplished while providing notions of transient performance bounds between the ideal system and the true system. Extensions to the theory include architectures for a class of output feedback systems, limiting the authority of an adaptive control system, and a method for improving the performance of an adaptive system with slow dynamics without any modification terms. Applications focus on using aerodynamic flow control for aircraft flight control and the Crew Launch Vehicle.

The work concerns the "observability problem"--the reconstruction of a dynamic process's full state from a partially measured state-- for nonlinear dynamic systems. The Extended Kalman Filter (EKF) is a widely-used observer for such nonlinear systems. However it suffers from a lack of theoretical justifications and displays poor performance when the estimated state is far from the real state, e.g. due to large perturbations, a poor initial state estimate, etc. . . We propose a solution to these problems, the Adaptive High-Gain (EKF). Observability theory reveals the existence of special representations characterizing nonlinear systems having the observability property. Such representations are called observability normal forms. A EKF variant based on the usage of a single scalar parameter, combined with an observability normal form, leads to an observer, the High-Gain EKF, with improved performance when the estimated state is far from the actual state. Its convergence for any initial estimated state is proven. Unfortunately, and contrary to the EKF, this latter observer is very sensitive to measurement noise. Our observer combines the behaviors of the EKF and of the high-gain EKF. Our aim is to take advantage of both efficiency with respect to noise smoothing and reactivity to large estimation errors. In order to achieve this, the parameter that is the heart of the high-gain technique is made adaptive. Voila, the Adaptive High-Gain EKF. A measure of the quality of the estimation is needed in order to drive the adaptation. We propose such an index and prove the relevance of its usage. We provide a proof of convergence for the resulting observer, and the final algorithm is demonstrated via both simulations and a real-time implementation. Finally, extensions to multiple output and to continuous-discrete systems are given.

The process of quantifying the robustness of a given nonlinear system is not necessarily trivial. If the dynamics of the system in question are not sufficiently involved, then a tight estimate of a bound on system performance may be obtained. As the dynamics of the system concerned become more and more involved, it is often found that using the results existing in the literature provides a very conservative bound on system performance. Therefore, the motivation for this work is to develop a general method to obtain a less conservative estimate of a bound on system performance, compared to the results already available in literature. The scope of this work is limited to two dimensions at present. Note that working in a two dimensional space does not necessarily make the objective easily achievable. This is because quantifying the robustness of a general nonlinear system perturbed by disturbances can very easily become intractable, even on a space with dimension as low as two. The primary contribution of this work is a computational algorithm, the points generated by which are conjectured to lie on the boundary of the smallest robust forward invariant set for a given nonlinear system. A well known path-planning algorithm, available in existing literature, is leveraged to make the algorithm developed computationally efficient. If the system dynamics are not accurately known, then the above computed approximation of an invariant set may cease to be invariant over the given finite time interval for which the computed set is expected to be invariant. Therefore, the secondary contribution of this work is an algorithm monitoring a computed approximation of an invariant set. It is shown that for a certain type of systems, this secondary monitoring algorithm can be used to detect that a computed approximation of an invariant set is about to cease to be invariant, even if the primary algorithm computed the set based on an unsophisticated dynamical model of a system under consideration. The work related to computing approximations of invariant sets is tested mainly with the curve tracking problem in two dimensions. The algorithm monitoring whether a computed approximation of an invariant set is about to cease to be invariant is inspired by work related to detecting Lithium-ion (Li-ion) battery terminal voltage collapse detection.

This thesis is concerned with the sampled-data control of non-linear continuous-time systems. Sampled-data systems are present in all computer controlled, hybrid or embedded systems. The design and computation of suitable digital controllers represent unavoidable tasks since both continuous and discrete-time components interact. The basic framework of this work takes part of a wide research activity performed by S. Monaco and D. Normand-Cyrot regarding non-linear sampled-data systems. The underlying idea is to design digital controllers that recover certain continuous-time properties that are usually degraded through sampling as it is the case when continuous-time controllers are implemented by means of zero-order holder devices (emulated control). This thesis brings contributions into three different directions. The first one regards theoretical developments: a new digital backstepping-like strategy design for strict-feedback systems is proposed. This method is compared with other strategies proposed in the literature. The second contribution is the development of a control designer and of a simulation toolbox (in Matlab) for non-linear sampled-data systems. This toolbox includes different digital design strategies such as: multi-rate control, input-output/Lyapunov matching, digital backstepping design, etc. The third contribution concerns several case studies conducted to highlight the performances of the sampled-data controller designs, computed by the means of the software toolbox. Experimental and simulation results are described for various real examples especially in the area of electrical and mechanical processes.

Orientador: Marcelo Carvalho Minhoto Teixeira / Banca: Edvaldo Assunção / Banca: Celso Pascoli Bottura / Resumo: Em alguns problemas práticos, por exemplo, no controle de vibrações de sistemas mecânicos utilizando acelerômetros como sensores, é mais fácil obter a da derivada do vetor de estado do que o vetor de estado. Esta dissertação mostra que plantas lineares e invariantes no tempo descritas pelas matrizes {A,B,C,D}, cuja saída é a derivada do vetor de estado, são não observáveis e não estabilizáveis com realimentação da saída, quando det(A)=0. A impossibilidade de rejeição de distúrbios constantes, somados à entrada da planta quando det(A) 6= 0, realimentando-se a saída com controladores estáticos, foi também demonstrada. Adicionalmente, são propostas novas técnicas de controle para uma classe de sistemas não lineares com incertezas variantes no tempo. Condições na forma de desigualdades matriciais lineares, em inglês Linear Matrix Inequalities (LMIs), para o projeto de sistemas de controle empregando realimentação derivativa estática da derivada do vetor de estado, que ao mesmo tempo estabiliza a planta e maximiza o limite de incerteza do termo não linear, são estabelecidas com base em funções quadráticas de Lyapunov. Posteriormente estendem-se as condições de estabilidade robusta para sistemas não lineares com incertezas variantes no tempo e incertezas politópicas, que podem também representar falhas estruturais. O projeto do controlador é realizado através de condições baseadas em LMIs que, quando factíveis, podem ser resolvidas facilmente utilizando técnicas de programação convexa. Essa metodologia permite a inclusão de restrições de desempenho no projeto, como por exemplo, na taxa de decaimento e na norma de ganho dos controladores, de modo a atender às restrições do projeto. São apresentadas análises e resultados considerando o sinal de controle nulo e empregando realimentação derivativa estática do vetor de estado... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: In some practical problems, for instance in the control of mechanical systems using accelerometers as sensors, it is easier to obtain the state-derivative vectors than the state vectors. This dissertation shows that (i) linear time-invariant plants given by the state-space model matrices {A,B,C,D} with output equal to the state-derivative vector are not observable and can not be stabilizable by using an output feedback if det(A) = 0 and (ii) the rejection of a constant disturbance added to the input of the aforementioned plants, considering det(A) 6= 0, and a static output feedback controller is not possible. The proposed results can be useful in the analysis and design of control systems with state-derivative feedback. Additionally, a new procedure for the control of a class of nonlinear systems with time-varying uncertainties using static statederivative feedback is proposed. Conditions based on Linear Matrix Inequalities (LMIs) for the design of robust controllers using state-derivative feedback, which simultaneously stabilizes the system and maximizes the uncertainty bound of the nonlinear term are proposed. Robust stability conditions for nonlinear systems with uncertainties and time-varying polytopic uncertainties, known as structural failures, are also presented. The controller design are based on LMIs which, when feasible, can be easily solved using convex programming techniques. This methodology allows the inclusion of performance constraints on the design, such as the decay rate and gain bounds in order to meet the design requirements. The dissertation considered cases where the control signal is equal to zero and with a state-derivative feedback. The elaboration of the theory for systems with n nonlinearities is illustrated through examples covering a single nonlinearity, with and without two polytopic uncertainties (and structural failures), and two nonlinearities... (Complete abstract click electronic access below) / Mestre

Systems which exhibit nonreciprocal transmission or that can be used as logic functions are of great interest for the development of essential devices to nanotechnology. In this work, we investigate the transmission properties for two kinds of coupled discrete nonlinear chains configurations. In the first structure, it was explored the diode-like behavior, while in the other, it was showed the performance of different logic gates. The two systems were described by a set of the discrete nonlinear Schrödinger equations within a tight-binding approach. We determine their respective transmission spectrum. The first system is a nonlinear dimer coupled to linear side chains. We investigate the influence of the saturation of the nonlinear response on the nonreciprocal transmission, which had not been well studied in the previous literature. Through the analysis of the transmission spectrum, we unveil that, in regions of bistable behavior (windows), the difference between transport from right to left and transport from left to right is greater. Moreover these windows widen and displace to regions where the incident amplitude is larger as saturation is considered. The calculation of rectifying factor showed that, in the second bistability window, the influence of the saturation parameter has distinct actions over short- and long-wavelength. In the first window, the rectifying action is not compromised by the saturation. So weak saturation can improve the efficiency of the nonreciprocal transmission. The second system is a Y-shaped structure, on which three linear chains are joined by a nonlinear site. This kind of structure has been studied in the context of DNA-based devices. We investigated the capability of our model system to perform logic gate operations based on the transmission of phase-shifted incoming waves. Using a digitalization scheme of the output signal based on amplitude modulation, we show that AND, OR and XOR logic gate can be achieved. The phase-shifting between the incoming waves is required for the OR logic gate to be realizable and strong nonlinearity favors the existence of logic gates in the regime of short wavevectors. The analysis of the contrast ratio shows that optimal operation of the AND and OR logic gates takes place when the nonlinear response is the predominant physical property distinguishing the coupling and regular sites. We concluded that Y-shaped structures can potentially perform distinct logic functions. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Sistemas que apresentam transmissão não reciproca ou que possam ser usados em funções lógicas são de grande interesse para a construção de dispositivos essenciais ao desenvolvimento da nanotecnologia. Neste trabalho, investigamos as propriedades de transmissão em duas configurações de cadeias quase unidimensionais, discretas e não lineares. Em uma delas foi explorado o comportamento tipo diodo, e na outra, o surgimento de diferentes tipos de portas lógicas. Ambos os sistemas foram modelados através de um conjunto de equações de Schrödinger discretas não lineares dentro de aproximação tight binding e obtidos seus respectivos espectros de transmissão. O primeiro sistema consiste em um dímero não linear acoplado a duas cadeias lineares no qual investigamos a influência da saturação da resposta não linear na obtenção de transmissão não recíproca, até então ainda não estudada. Através da análise do espectro de transmissão, pudemos mostrar que nas regiões de comportamento biestável (chamados de janelas de biestabilidade), a diferença entre o transporte da direita para esquerda e o transporte da esquerda para direita é mais pronunciada a medida que se aumenta o coeficiente de saturação da não linearidade. Estas janelas se ampliam e são deslocadas para regiões onde a amplitude das ondas incidentes são maiores. O cálculo do fator de retificação nos permitiu mostrar ainda que a influência da saturação se dá de maneira diferente nas janelas de biestabilidade. Enquanto na segunda janela o comportamento é diferente em pequeno e grande comprimento de onda, na primeira isso não ocorre. Portanto, pudemos concluir que valores intermediários da saturação favorecem o transporte unidirecional. O segundo sistema consiste de uma estrutura tipo Y, na qual três cadeias lineares são unidas por um sítio não linear. Esse tipo de estrutura tem sido muito investigado em nanoestruturas de DNA. Investigamos a capacidade deste sistema realizar operações de portas lógicas baseadas na transmissão de ondas incidentes com diferença de fase. Usando um esquema de digitalização do sinal de saída baseado na modulação da amplitude, mostramos que portas AND, OR, e XOR podem ser encontradas. A diferença de fase entre as ondas incidentes é responsável pela existência das portas tipo OR enquanto que fortes não linearidades favorecem a realização de portas lógicas na região de pequeno vetor de onda. A análise do contraste, grandeza que mede a eficiência da porta lógica, mostrou que portas lógicas AND e OR são melhores quando os sítios regulares e o de acoplamento são distintos apenas pela resposta não linear. Concluímos que estruturas tipo Y têm grande potencial para realização de portas lógicas.

La miniaturisation de circuits intégrés, les hautes fréquences de fonctionnement, la baisse des potentiels d'alimentation, les fortes densités d'intégration rendent les signaux numériques propagés sur les interconnexions très susceptibles à la dégradation voire à la corruption. En vue d’évaluer la compatibilité électromagnétique et l’intégrité du signal il est nécessaire de disposer dès les premières phases de développement de modèles précis de ces interconnexions pour les insérer dans les simulateurs temporels. Nos travaux s'inscrivent dans ce contexte et concernent plus particulièrement la modélisation comportementale des buffers et drivers de ligne de transmission. Ils ont abouti à une approche originale de modélisation notamment basée sur les séries de Volterra-Laguerre. Les modèles boites noires développés disposent d’une implémentation SPICE assez simple autorisant ainsi une très bonne portabilité. Ils sont faciles à identifier et disposent d’une complexité paramétrique permettant un gain important de temps de simulation vis-à-vis des modèles transistors des drivers. En outre les méthodes développées permettent une modélisation dynamique non linéaire plus précise du port de sortie, et une gestion plus générale des entrées autorisant notamment une très bonne prise en compte du régime de sur-cadencement ce que par exemple ne fait pas le standard IBIS. / Integrated circuits miniaturization, high operating frequencies, lower supply voltages, high-density integration make digital signals propagating on interconnects highly vulnerable to degradation. Assessing EMC and signal integrity in the early stages of the design flow requires accurate interconnect models allowing for efficient time-domain simulations. In this context, our work addressed the issue of behavioral modeling of transmission line buffers, and particularly that of drivers. The main result is an original modeling approach partially based on Volterra-Laguerre series. The black box models we developed have a fairly simple implementation in SPICE thus allowing a very good portability. They are easy to identify and have a parametric complexity allowing a large gain in simulation time with respect to transistor driver models. In addition, the developed methods allow a more accurate output port nonlinear dynamics modeling, and a more general management of inputs. A very good reproduction of driver behaviour in overclocking conditions provides a significant advantage over standard IBIS models.

This work presents an investigation into the parameter estimation of suspension components and the vertical motions of wheeled vehicles from experimental data. The estimation problems considered were for suspension dampers, a single wheel station and a full vehicle. Using conventional methods (gradient-based (GB), Downhill Simplex (DS)) and stochastic methods (Genetic Algorithm (GA) and Differential Evolution (DE)), three major problems were encountered. These were concerned with the ability and consistency of finding the global optimum solution, time consumption in the estimation process, and the difficulties in setting the algorithm's control parameters. To overcome these problems, a new technique named the discrete variable Hybrid Differential Evolution (dvHDE) method is presented. The new dvHDE method employs an integer-encoding technique and treats all parameters involved in the same unified way as discrete variables, and embeds two mechanisms that can be used to deal with convergence difficulties and reduce the time consumed in the optimisation process. The dvHDE algorithm has been validated against the conventional GB, DS and DE techniques and was shown to be more efficient and effective in all but the simplest cases. Its robustness was demonstrated by its application to a number of vehicle related problems of increasing complexity. These include case studies involving parameter estimation using experimental data from tests on automotive dampers, a single wheel station and a full vehicle. The investigation has shown that the proposed dvHDE method, when compared to the other methods, was the best for finding the global optimum solutions in a short time. It is recommended for nonlinear vehicle suspension models and other similar systems.

Un de nos grands défis actuels est la décarbonisation du réseau électrique en éliminant les générateurs d'électricité à base de carburant, et de les remplacer de préférence par des ressources publiquement acceptés et qui respectent la nature de l'environnement. C'est où les ressources énergétiques renouvelables soulèvent comme une solution prometteuse. Les Systèmes de génération d'électricité à cycle de relaxation représentent notamment une classe intéressante des énergies renouvelables. Un tel système doit retrouver périodiquement un état qui permet la production d'énergie, ce qui entraîne un cycle à deux phases : une phase de génération et une phase de récupération qui consomme l'énergie. L'intérêt principal de cette thèse est focaliser sur le système de traction à base de cerf-volant, appelé par la suite le Kite Generator System (KGS). Il s'agit d'une solution proposée pour extraire l'énergie du vent stable et forte dans les hautes altitudes. Son principe de fonctionnement est d'entraîner mécaniquement un générateur électrique au sol en utilisant un ou plusieurs cerfs-volants captifs. La problématique est divisée en deux objectifs : 1 - L'optimisation et le contrôle du cycle de relaxation afin de maximiser la puissance moyenne produite par le système. Deux stratégies de contrôle sont proposées à cet effet : une basée sur un contrôle du modèle non linéaire prédictif (Nonlinear model predictive control - NMPC), et la deuxième basée sur l'application des contraintes virtuel (Virtual Constraints Control - VCC). 2 - L'Intégration du système sur le réseau électrique ou l'employer pour alimenter une charge isolée. Ces problèmes sont abordés dans cette thèse, réalisée au laboratoire de génie électrique de Grenoble (G2ELab) en collaboration avec le laboratoire d'Image Parole Signal Automatique de Grenoble (GIPSA-Lab). / One of our current major challenges is decarbonizing the electric grid by eliminating fuel based electricity generators, and replacing them preferably by nature-friendly publicly accepted resources. That is where renewable energy resources raise as a promising solution. Power relaxation-cycle systems represent an interesting and particular class of renewable. Such a system needs to regain periodically a state that allows energy production. Hence, it has two phases: A generation during which the system is working in its "power" region and is able to generate power and a recovery phase that starts when the system reaches its power region boundaries and resets the system's state to start a new generation phase, which results in power consumption. The main focus of this PhD dissertation is the kite-based traction system, named thereafter the kite generator system (KGS), which emerged as an important class of renewable energy systems that uses relaxation phases. It is a solution proposed to extract energy from the steady and strong wind found in high altitudes. Its operation principle is to mechanically drive a ground-based electric generator using one or several tethered kites. The problematic is divided into two objectives: 1 - Optimization and control of the relaxation cycle to maximize the system's average produced power. Two control strategies are proposed for this purpose: A nonlinear model predictive control (NMPC) based and virtual constraints control (VCC) based one. 2 - Integration of the system on the electric grid or employing it to supply an isolated load. These problems are addressed in this thesis, realized in Grenoble Electrical Engineering laboratory (G2ELab) with collaboration with Grenoble Image Parole Signal Automatique laboratory (GIPSA-Lab).