Conversores analógico-digitais (ADCs) têm papel fundamental na implementação dos sistemas-em-chip, do inglês System-on-Chip (SoC), atuais. Em razão dos requisitos destes sistemas e dos compromissos entre as características fundamentais dos ADCs, como largura de banda, consumo de energia e exatidão, diversas topologias e estratégias para sua implementação em circuitos integrados (CIs) têm sido desenvolvidas através dos tempos. Dentre estas topologias, os conversores sigma-delta (SDC) têm se destacado pela versatilidade, aliada ao baixo consumo e excelente exatidão. Inicialmente desenvolvidos e empregados para a conversão de sinais de baixa frequência e com operação em tempo discreto (DT), esta classe de conversores têm evoluído e nos últimos anos está sendo desenvolvida para operar em tempo contínuo e ser empregada na conversão de sinais com frequências de centenas de kHz a dezenas de MHz. Neste trabalho, os moduladores sigma-delta em tempo contínuo (SDMs-CT) são estudados, visando sua aplicação à conversão analógico-digital (AD). Os SDMs-CT oferecem vantagens significativas sobre seus homólogos em tempo discreto, como menor consumo de energia, maior largura de banda do sinal de entrada e filtro anti-alias, do inglês anti-alias filter (AAF), implícito. Entretanto, os SDMs-CT apresentam limitações adicionais, responsáveis pela degradação de seu desempenho, como os efeitos do jitter do sinal de relógio, o atraso excessivo do laço de realimentação, do inglês Excess Loop Delay (ELD), e as limitações impostas aos integradores analógicos. Após o estudo e análise de SDMs-CT e de suas limitações, foi desenvolvido um modelo comportamental no ambiente Matlab/Simulink R , que permite a simulação do impacto destas limitações no modulador, possibilitando a obtenção de uma estimativa mais aproximada do seu desempenho. Com base nestas simulações foi possível a determinação das especificações mínimas de cada bloco analógico que compõe o modulador (como o slew rate, a frequência de ganho unitário (fu) e o ganho DC dos amplificadores operacionais utilizados nos integradores) e os valores toleráveis de ELD e jitter do sinal de relógio. Adicionalmente, neste trabalho foi desenvolvida uma metodologia para simulação de SDMs-CT compostos por DACs a capacitor chaveado e resistor, do inglês Switched-Capacitor-Resistor (SCR). Com base neste modelo e no estudo das diferentes topologias de SDMs, um circuito foi desenvolvido para aplicação em receptores de RF, sendo do tipo passa-baixas de laço único, do inglês single-loop, single-bit, de terceira ordem, voltado ao baixo consumo de energia. Este circuito foi desenvolvido em tecnologia CMOS IBM de 130 nanômetros, tendo sido enviado para fabricação. Através das simulações pós-leiaute realizadas espera-se que seu desempenho fique próximo ao que tem sido publicado recentemente sobre SDMs-CT passa-baixas de laço único e single-bit. / Analog-to-Digital Converters (ADCs) play a fundamental role in the implementation of current systems-on-chip (SoC). Due to the requirements of these systems and the tradeoffs between the main ADCs characteristics, such as signal bandwidth, power consumption and accuracy, many topologies and strategies for their implementation in integrated circuits (ICs) have been developed through the ages. Among these topologies, the sigmadelta converters (SDC) have highlighted the versatility combined with low power consumption and excellent accuracy. Initially developed and used for the conversion of low frequency signals and operation in the discrete time (DT) domain, this class of converters have been evolved and developed over the past to operate in continuous time domain for the conversion of signals with frequencies of hundreds of kHz up to tens of MHz. In this work, continuous time sigma-delta modulators (CT-SDMs) are studied focusing its application to the analog-to-digital (AD) conversion. CT-SDMs offer significant advantages over their discrete-time counterparts, such as lower power consumption, higher input signal bandwidth and implicit anti-alias filter (AAF). However, CT-SDMs present additional limitations that are responsible for their performance degradation, such as the clock jitter, Excess Loop Delay (ELD) and the limitations imposed on the analog integrators. After the study and analysis of CT-SDMs and their performance limitations, a behavioral model approach was developed in the Matlab/Simulink R environment, which allows the simulation of the limitations impact on the modulator, allowing the obteinment of a more accurate estimate of its performance. Based on these simulations it was possible to determine the minimum specifications for each block that composes the analog modulator (such as slew rate, the unity gain frequency (fu) and the DC gain of the operational amplifiers used in integrators) and tolerable values of ELD and clock jitter. Additionally, it was developed in this work a methodology for simulate CT-SDMs with Switched-Capacitor- Resistor (SCR) DACs that provide exponential waveforms. Based on this model and the study of different SDMs topologies, it was developed a low-pass, single-loop, single-bit, third order circuit focused on low-power intended for application in RF receivers. This circuit was developed in an IBM 130 nanometers CMOS technology, and was send to manufacturing. Based on the post-layout simulations it is expected to have performance close to what has been recently published of low-pass, single-loop, single-bit CT-SDMs.

Neste trabalho estudamos as noções de alcançabilidade e controlabilidade para sistemas lineares a tempo contínuo com perturbações aditivas e saltos nos parâmetros sujeitos a uma cadeia de Markov geral. Definimos conceitos de alcançabilidade e controlabilidade médios de maneira natural exigindo que os valores esperados dos gramianos correspondentes sejam definidos positivos. Visando obter uma condição testável para ambos os conceitos, introduzimos conjuntos de matrizes de alcançabilidade e de controlabilidade para esta classe de sistemas e usamos certas propriedades de invariância para mostrar que: o sistema é alcançável em média, e, analogamente, controlável em média, se e somente se as matrizes respectivas, de alcançabilidade e de controlabilidade, têm posto completo. Usamos alcançabilidade média de sistemas para mostrar que a matriz de segundo momento do estado é definida positiva com uma margem uniforme. Uma consequência deste resultado no problema de estimação linear do estado é que a matriz de covariância do erro de estimação é positiva definida em média, no sentido que existe um nível mínimo de ruído nas estimativas. Na sequência, para estimadores lineares markovianos, estudamos a limitação do valor esperado da matriz de covariância do erro para mostrar que o filtro é estável num certo sentido, sendo esta uma propriedade desejável em aplicações reais. Quanto às aplicações da controlabilidade média, usamos este conceito para estabelecer condições necessárias e suficientes que garantem a existência de um processo de controle que leva a componente contínua do estado do sistema para a origem em tempo finito e com probabilidade positiva. / In this work we study the reachability and controllability notions for continuous-time linear systems with exogenous inputs and jump parameters driven by a quite general Markov chain. We define a rather natural average reachability and controllability concepts by requiring that the associated gramians are average positive definite, respectively. Aiming at testable conditions for each concept, we introduce certain sets of matrices linked with the gramians, and employ some invariance properties to find rank-based conditions. We show for average reachable systems that the state second moment is positive definite. One consequence of this result in the context of linear estimation for reachable systems is that the expectation of the error covariance matrix is positive definite. Moreover, for linear markovian filters we study the average boundedness of the error covariance matrix to show that the filter is stable in an appropriate sense, which consists in a property that is desirable in real applications. Regarding the average controllability concept, we show that it is a necessary and sufficient condition for the feasibility of the following control problem: find a control process that drives the continuous component of the state to zero in finite time with positive probability.

Les principales contributions de cette thèse concernent l'identification à temps continu des systèmes par modèles non entiers dans un contexte à erreurs en les variables. Deux classes de méthodes sont développées : la première classe est fondée sur les statistiques d'ordre trois et la deuxième est fondée sur les statistiques d'ordre quatre. Dans chaque classe, deux cas différents sont distingués : le premier cas suppose que tous les ordres de dérivation non entiers sont connus a priori et seuls les coefficients de l'équation différentielle non entière sont estimés en utilisant les estimateurs fondés sur les statistiques d'ordre supérieur. Le deuxième cas suppose que les ordres de dérivation sont commensurables à un ordre nu estimé au même titre que les coefficients de l'équation différentielle non entière par des techniques d'optimisation non linéaire combinées aux estimateurs fondés sur les cumulants d'ordre trois et quatre. Des exemples de simulation numérique illustrent les développements théoriques. Des applications pratiques sur la modélisation du phénomène de diffusion de chaleur dans un barreau d'Aluminium et sur la modélisation d'un système électronique ont montré la pertinence des méthodes développées. / This thesis deals with continuous-time system identification by fractional models in the EIV context. Two classes of methods are developed : the first class is based on third-order statistics and the second one is based on fourth-order statistics. Firstly, all differentiation orders are known a priori and only the coefficients of the differential equation are estimated using the developed algorithms based on higher-order statistics. Then, they are extended to estimate both the fractional differential equation coefficients and the commensurate order. Simulation examples display the theoretical developments on system identification in the EIV context. A practical application for modeling heat transfer phenomena in an aluminium rod and for modeling an electronic real system have shown the efficiency of the developed methods.

La méthode d'identification développée dans cette thèse est inspirée des travaux de D. Rémond. On considérera les données d'entrée suivante : la réponse de la structure, qui sera mesurée de manière discrète, et qui dépendra des dimensions de la structure (temps, espace) le modèle de comportement, qui sera exprimé sous forme d'une équation différentielle ou d'une équation aux dérivées partielles, les conditions aux limites ainsi que la source d'excitation seront considérées comme non mesurées, ou inconnues. La procédure d'identification est composée de trois étapes : la projection sur une base polynomiale orthogonale (polynômes de Chebyshev) du signal mesuré, la différentiation du signal mesuré, l'estimation de paramètres, en transformant l'équation de comportement en une équation algébrique. La poutre de Bernoulli a permis d'établir un lien entre l'ordre de troncature de la base polynomiale et le nombre d'ondes contenu dans le signal projeté. Sur un signal bruité, nous avons pu établir une valeur de nombre d'onde et d'ordre de troncature minimum pour assurer une estimation précise du paramètre à identifier. Grâce à l'exemple de la poutre de Timoshenko, nous avons pu réadapter la procédure d'identification à l'estimation de plusieurs paramètres. Trois paramètres dont les valeurs ont des ordres radicalement différents ont été estimés. Cet exemple illustre également la stratégie de régularisation à adopter avec ce type de problèmes. L'estimation de l'amortissement sur une poutre a été réalisée avec succès, que ce soit à l'aide de sa réponse transitoire ou à l'aide du régime établi. Le cas bidimensionnel de la plaque a également été traité. Il a permis d'établir un lien similaire au cas de la poutre de Bernoulli entre le nombre d'onde et l'ordre de troncature. Deux cas d'applications expérimentales ont été traités au cours de cette thèse. Le premier se base sur le modèle de la poutre de Bernoulli, appliqué à la détection de défaut. En effet on applique un procédé d'identification ayant pour hypothèse initiale la continuité de la structure. Dans le cas où celle-ci ne le serait pas on s'attend à observer une valeur aberrante du paramètre reconstruit. Le procédé permet de localiser avec succès le lieu de la discontinuité. Le second cas applicatif vise à reconstruire l'amortissement d'une structure 2D : une plaque libre-libre. On compare les résultats obtenus à l'aide de notre procédé d'identification à ceux obtenus par Ablitzer à l'aide de la méthode RIFF. Les deux méthodes permettent d'obtenir des résultats sensiblement proches. / The purpose of this work is to adapt and improve the continuous time identification method proposed by D. Rémond for continuous structures. D. Rémond clearly separated this identification method into three steps: signal expansion, signal differentiation and parameter estimation. In this study, both expansion and differentiation steps are drastically improved. An original differentiation method is developed and adapted to partial differentiation. The existing identification process is firstly adapted to continuous structure. Then the expansion and differentiation principle are presented. For this identification purpose a novel differentiation model was proposed. The aim of this novel operator was to limit the sensitivity of the method to the tuning parameter (truncation number). The precision enhancement using this novel operator was highlighted through different examples. An interesting property of Chebyshev polynomials was also brought to the fore : the use of an exact discrete expansion with the polynomials Gauss points. The Gauss points permit an accurate identification using a restricted number of sensors, limiting de facto the signal acquisition duration. In order to reduce the noise sensitivity of the method, a regularization step was added. This regularization step, named the instrumental variable, was inspired from the automation domain. The instrumental variable works as a filter. The identified parameter is recursively filtered through the structure model. The final result is the optimal parameter estimation for a given model. Different numerical applications are depicted. A focus is made on different practical particularities, such as the use of the steady-state response, the identification of multiple parameters, etc. The first experimental application is a crack detection on a beam. The second experimental application is the identification of damping on a plate.

The objective of this project is to develop an operational scheduling model for Sasol Mining’s coal handling facility, Sasol Coal Supply (referred to as SCS), to optimise daily operations. In this document, the specific scheduling problem at SCS is presented and solved using Mixed Integer Non-Linear Programming (MINLP) continuous time representation techniques. The most recent MINLP scheduling techniques are presented and applied to an example problem. The assumption is made that the results from the example problem will display trends which will apply to the SCS scheduling problem as well. Based on this assumption, the unit-specific event based continuous time formulation is chosen to apply to the SCS scheduling problem. The detail mathematical formulation of the SCS scheduling problem, based on the chosen technique, is discussed and the necessary changes presented to customise the formulation for the SCS situation. The results presented show that the first phase model does not solve within 72 hours. A solution time of more than three days is not acceptable for an operational scheduling model in a dynamic system like SCS. Various improvement approaches are applied during the second phase of the model development. Special Ordered Sets of Type 1 (SOS1) variables are successfully applied in the model to reduce the amount of binary variables. The time and duration constraints are restructured to simplify the structure of the model. A specific linearization and solution technique is applied to the non-linear equations to ensure reduced model solution times and reliable results. The improved model for one period solves to optimality within two minutes. This dramatic improvement ensures that the model will be used operationally at SCS to optimise daily operations. The scheduling model is currently being implemented at SCS. Examples of the input variables and output results are presented. It is concluded that the unit-specific event based MINLP continuous time formulation method, as presented in the literature, is not robust enough to be applied to an operational industrial-sized scheduling problem such as the SCS problem. Customised modifications to the formulation are necessary to ensure that the model solves in a time acceptable for operational use. However, it is proved that Mixed Integer Non-linear Programming (MINLP) can successfully be applied to optimise the scheduling of an industrial-sized plant such as SCS. Although more research is required to derive robust formulation techniques, the principle of using mathematical methods to optimise operational scheduling in industry can dramatically impact the way plants are operated. The optimisation of daily schedules at SCS by applying the MINLP continuous time scheduling technique, has made a significant contribution to the coal handling industry. Finally, it can be concluded that the SCS scheduling problem was successfully modelled and the operational scheduling model will add significant value to the Sasol Group. / Dissertation (MEng (Industrial Engineering))--University of Pretoria, 2006. / Industrial and Systems Engineering / unrestricted

Cette thèse étudie certaines propriétés fractales et trajectorielles de processus de branchement en temps et espace continus. De façon informelle, ce type de processus est obtenu en considérant l'évolution d'une population où les individus se reproduisent et meurent au cours du temps, et ce de manière aléatoire. Le premier chapitre concerne la classe des processus de branchement avec immigration. On donne une formule semi-explicite pour la transformée de Laplace des temps d'atteinte ainsi qu'une condition nécessaire et suffisante de récurrence-transience. Ces deux résultats illustrent la compétition branchement/immigration. Le second chapitre considère l'arbre Brownien et ses mesures de temps local, dites mesures de niveau. On montre que celles-ci s'obtiennent comme restriction, à une constante près explicitée, d'une certaine mesure de Hausdorff sur l'arbre. Le résultat est montré simultanément pour tous niveaux. Le troisième chapitre étudie le Super-mouvement Brownien associé à un mécanisme de branchement général. Sa mesure d'occupation totale est obtenue comme restriction d'une certaine mesure de packing dans l'espace euclidien. Le résultat est valable en grande dimension. La condition sur la dimension de l'espace ambiant est discutée à travers le calcul, sous des hypothèse de régularité faibles pour le mécanisme de branchement, de la dimension de packing du range total du processus. / This thesis investigates some fractal and pathwise properties of branching processes with continuous time and state-space. Informally, this kind of process can be described by considering the evolution of a population where individuals reproduce and die over time, randomly. The first chapter deals with the class of continuous branching processes with immigration. We provide a semi-explicit formula for the hitting times and a necessary and sufficient condition for the process to be recurrent or transient. Those two results illustrate the competition between branching and immigration. The second chapter deals with the Brownian tree and its local time measures : the level-sets measures. We show that they can be obtained as the restriction, with an explicit multiplicative constant, of a Hausdorff measure on the tree. The result holds uniformly for all levels. The third chapter study the Super-Brownian motion associated with a general branching mechanism. Its total occupation measure is obtained as the restriction to the total range, of a given packing measure on the euclidean space. The result is valid for large dimensions. The condition on the dimension is discussed by computing the packing dimension of the total range. This is done under a weak assumption on the regularity of the branching mechanism.

Fatigue analysis is a critical stage in the design of any structural component. Typically fatigue is analysed during post-processing, but as the size of the analysed component increases, the amount of data stored for the analysis increases simultaneously. This increases the computational and memory requirements of the system, intensifying the work load on the engineer. A continuum mechanics approach namely ’Continuous time fatigue model’, for fatigue analysis is available in a prior study which reduces the computational requirements by simultaneously computing fatigue along with the stress. This model implements a moving endurance surface in the stress space along with the damage evolution equation to compute high-cycle fatigue. In this thesis the continuous time fatigue model is compared with conventional model (ie.Cycle counting) to study its feasibility. The thesis also aims to investigate the continuous time fatigue model and an evolved version of the model is developed for non-proportional load cases to identify its limitations and benefits.

Les mécanismes responsables du transport hydrodynamique anormal (non-Fickéen) peuvent être rattachés à la complexité de la géométrie du milieu à l'échelle des pores. Dans cette thèse, nous étudions la dynamique des vitesses de particules à l'échelle des pores. À l'aide de simulations de suivi de particules effectuées sur un échantillon numérisé de grès de Berea, nous présentons une analyse détaillée de l'évolution Lagrangienne et Eulérienne et de leur dépendance aux conditions initiales. Le long de leur ligne de courant, la vitesse des particules montre un signal intermittent complexe, alors que leur sériede vitesses spatiales présente des fluctuations régulières. La distribution spatiale des vitesses des particules converge rapidementvers l'état stationnaire. Ces résultats dénotent un processus Markovienqui permet de prédire les fluctuations de vitesse dans le réseau poral.Ces processus, associés à la tortuosité et à la distance de corrélation de vitesse permettent de paramétrer un modèle de marche aléatoire dans le temps (CTRW) et de réaliser le changement d’échelle pour simuler le transport à l’échelle de Darcy. Le modèle, comme tout modèle issu d’un changement d'échelle, repose sur la définition d'un volume élémentaire représentatif (VER). Nous montrons qu’un VER basé sur les statistiques de vitesse permet de définir un support pertinent pour la modélisation du transport hydrodynamique pré-asymptotique à asymptotique, et ainsi d’éviter les limitations associées à l’équation d’advection-dispersionFickéenne. Cette approche est utilisée pour étudier l’impact de l’hétérogénéité du réseau poral sur le volume de mélange et la masse du produit d’une réaction bimoléculaire. / The mechanisms responsible for anomalous (non-Fickian) hydrodynamictransport can be traced back to the complexity of the medium geometry atthe pore-scale. In this thesis, we investigate the dynamics of pore-scaleparticle velocities. Using particle tracking simulations performed on adigitized Berea sandstone sample, we present a detailed analysis of theevolution of the Lagrangian and Eulerian evolution and their dependenceon the initial conditions. The particles experience a complexintermittent temporal velocity signal along their streamline while theirspatial velocity series exhibit regular fluctuations. The spatialvelocity distribution of the particles converges quickly to thesteady-state. These results lead naturally to Markov processes for theprediction of these velocity series.These processes, together with the tortuosity and the velocitycorrelation distance that are properties of the medium, allow theparameterization of a continuous time random walk (CTRW) for theupscaling of the transport. The model, like any upscaled model, relieson the definition of a representative elementary volume (REV). We showthat an REV based on the velocity statistics allows defining a pertinentsupport for modeling pre-asymptotic to asymptotic hydrodynamictransport at Darcy scale using, for instance, CTRW, thus overcomingthe limitations associated with the Fickian advection dispersionequation. Finally, we investigate the impact of pore-scale heterogeneityon a bimolecular reaction and explore a methodology for the predictionof the mixing volume and the chemical mass produced.

In this paper, we examine the feasibility of extending the Akaike information criterion (AIC) for deterministic systems as a potential model selection criteria for stochastic models. We discuss the implementation method for three different classes of stochastic models: continuous time Markov chains (CTMC), stochastic differential equations (SDE), and random differential equations (RDE). The effectiveness and limitations of implementing the AIC for comparison of stochastic models is demonstrated using simulated data from the three types of models and then applied to experimental longitudinal growth data for algae.

Le marché des convertisseurs analogique-numérique peut être segmenté en deux catégories de circuits. Nous distinguons d’une part, les blocs de propriété intellectuelle (IP) qui sont généralement optimisés pour une application spécifique. Et d’autre part, les circuits intégrés discrets qui sont conçus pour répondre aux besoins d’une plus large gamme d’applications. Ce travail de thèse concerne la deuxième catégorie de composants. Il s’inscrit dans le cadre d'un programme de recherche et développement initié en 2010 dans le projet européen FP7 SACRA et dont le but était d'étudier la faisabilité d'un convertisseur analogique-numérique Delta-Sigma (DS) qui pourrait rivaliser avec l'architecture pipeline pour des applications nécessitant une large bande passante (≥10MHz) et une haute résolution (>10-bit) comme l’imagerie médicale, les communications numériques sans fils ou câblées, la vidéo ou encore l’instrumentation. Ce manuscrit synthétise les travaux de conception, fabrication et mesure d’un modulateur DS Passe-bas à temps continu avec une bande passante de 40MHz, et visant une résolution effective de 12-bit tout en consommant moins de 100mW. / The market of A/D converters can be segmented in two categories. From one side we distinguish the Intellectual Property (IP) blocks that are generally optimized for a specific application. On the other side, the general-purpose discrete Integrated Circuits (ICs) that are designed such as they could be used in different applications. This thesis work deals with the second category. It is part of a research and development program initiated in 2010 in the European project FP7 SACRA, whose purpose was to study the feasibility of a delta-sigma (DS) analog-to-digital converter that could compete with the pipeline architecture for applications that require high bandwidth (≥10MHz) and high resolution (>10-bit) such as medical imaging, wireless and wireline communications, video or instrumentation. Currently, the pipeline is still largely predominant for such applications and the few commercial wideband solutions based on a DS architecture have a signal bandwidth limited to 10 MHz or 25 MHz while consuming respectively 100mW and 20mW for an ENOB around 12-bit. This manuscript summarizes the design, fabrication and measurement of a low-pass CT DS modulator with a signal bandwidth of 40MHz, while targeting an effective resolution of 12-bit and a power consumption of less than 100mW.