This thesis aims to develop control algorithms for irrigation canals in an experimental framework.These water transport systems are difficult to manage and present low efficiencies in practice. As a result, an important percentage of water is lost, maintenance costs increase and water users follow a rigid irrigation schedule.All these problems can be reduced by automating the operation of irrigation canals.In order to fulfil the objectives, a laboratory canal, called Canal PAC-UPC, was equipped and instrumented in parallel with the development of this thesis. In general, the methods and solutions proposed herein were extensively tested in this canal.In a broader context, three main contributions in different irrigation canal control areas are presented.Focusing on gate-discharge measurements, many submerged-discharge calculation methods are tested and compared using Canal PAC-UPC measurement data. It has been found that most of them present errors around ±10%, but there are notable exceptions. Specifically, using classical formulas with a constant 0.611 contraction value give very good results (error<±6%), but when data is available, a very simple calibration formula recently proposed in the literature significantly outperform the rest (error<±3%). As a consequence, the latter is encouragingly proposed as the basis of any gate discharge controller.With respect to irrigation canal modeling, a detailed procedure to obtain data-driven linear irrigation canal models is successfully developed. These models do not use physical parameters of the system, but are constructed from measurement data. In this case, these models are thought to be used in irrigation canal control issues like controller tuning, internal controller model in predictive controllers or simply as fast and simple simulation platforms. Much effort is employed in obtaining an adequate model structure from the linearized Saint-Venant equations, yielding to a mathematical procedure that verifies the existence of an integrator pole in any type of canal working under any hydraulic condition. Time-domain and frequency-domain results demonstrate the accuracy of the resulting models approximating a canal working around a particular operation condition both in simulation and experiment.Regarding to irrigation canal control, two research lines are exploited. First, a new water level control scheme is proposed as an alternative between decentralized and centralized control. It is called Semi-decentralized scheme and aims to resemble the centralized control performance while maintaining an almost decentralized structure. Second, different water level control schemes based on PI control and Predictive control are studied and compared. The simulation and laboratory results show that the response and performance of this new strategy against offtake discharge changes, are almost identical to the ones of the centralized control, outperforming the other tested schemes based on PI control and on Predictive control. In addition, it is verified that schemes based on Predictive control with good controller models can counteract offtake discharge variations with less level deviations and in almost half the time than PI-based schemes.In addition to these three main contributions, many other smaller developments, minor results and practical recommendations for irrigation canal automation are presented throughout this thesis.

Dans cette thèse, nous établissons un modèle à deux échelles à la fois pour desmatrices de cantilevers unidimensionnels et bidimensionnels en régime de fonctionnementélastodynamique avec des applications possibles aux réseaux de microscopesà force atomique (AFM). Son élaboration est basée sur une analyseasymptotique pour les structures minces élastiques, une approximation à deuxéchelles et une mise à l’échelle utilisée pour l’homogénéisation des milieux fortementhétérogènes. Nous complétons la théorie de l’approximation à deux échellespour les problèmes aux limites du quatrième ordre posés dans des domaines mincespériodiques connexes seulement dans certaines directions. Notre modèle reproduitla dynamique globale du support ainsi que les mouvements locaux des cantilevers.Pour simplifier la suite du travail, nous concentrons nos travaux à l’étude de matricesde leviers constituées de lignes découplées en régime dynamique. Comme lesupport des leviers est élastique, l’effet du couplage entre levier est pris en compte.La vérification du modèle est soigneusement réalisée. Nous montrons que chaquemode propre peut être décomposé en produits d’un mode de base avec un modede levier. Nous présentons une méthode de discrétisation du modèle et effectuonssa vérification numérique en la comparant avec des résultats de simulation paréléments finis du problème d’élasticité tridimensionnel. Par ailleurs, nous avonsélaboré de nouveaux outils d’aide à la conception de réseaux d’AFM. Une boîte àoutils d’optimisation robuste est interfacée avec le modèle permettant d’optimiserun design avant micro-Fabrication. Un algorithme d’estimation de l’état statiquecombinant la mesure de déplacements mécaniques par interférométrie et le modèlea été introduit. Nous avons également synthétisé un régulateur quadratiquelinéaire (LQR) pour un réseau de cantilevers en mode dynamique comprenant actionneurset capteurs régulièrement espacées. Dans le but de mettre en oeuvre lecontrôle en temps réel, nous proposons une approximation semi-Décentralisée quipeut être réalisé par un circuit électronique distribué analogique. Plus précisément,notre processeur analogique peut être réalisé par un réseau périodique derésistances (PNR). La méthode d’approximation de commande est basée sur deuxconcepts généraux, à savoir sur un calcul fonctionnel (c’est-À-Dire des fonctionsd’opérateurs) et sur la formule de représentation d’une fonction d’opérateur deDunford-Schwartz. Cette méthode d’approximation est étendue pour la résolutiond’un problème de filtrage optimal robuste de type H∞ de la dynamique d’un réseaude leviers couplés avec sources aléatoires de bruit. / In this dissertation, we establish a two-Scale model both for one-Dimensionaland two-Dimensional Cantilever Arrays in elastodynamic operating regime withpossible applications to Atomic Force Microscope (AFM) Arrays. Its derivationis based on an asymptotic analysis for thin elastic structures, a two-Scale approximationand a scaling used for strongly heterogeneous media homogenization. Wecomplete the theory of two-Scale approximation for fourth order boundary valueproblems posed in thin periodic domains connected in some directions only. Ourmodel reproduces the global dynamics as well as each of the cantilever motion. Forthe sake of simplicity, we present a simplified model of mechanical behavior of largecantilever arrays with decoupled rows in the dynamic operating regime. Since thesupporting bases are assumed to be elastic, cross-Talk effect between cantileversis taken into account. The verification of the model is carefully conducted. Weexplain not only how each eigenmode is decomposed into products of a base modewith a cantilever mode but also the method used for its discretization, and reportresults of its numerical validation with full three-Dimensional Finite Element simulations.We show new tools developed for Arrays of Microsystems and especiallyfor AFM array design. A robust optimization toolbox is interfaced to aid for designbefore the microfabrication process. A model based algorithm of static stateestimation using measurement of mechanical displacements by interferometry ispresented. We also synthesize a controller based on Linear Quadratic Regulator(LQR) methodology for a one-Dimensional cantilever array with regularly spacedactuators and sensors. With the purpose of implementing the control in real time,we propose a semi-Decentralized approximation that may be realized by an analogdistributed electronic circuit. More precisely, our analog processor is made by PeriodicNetwork of Resistances (PNR). The control approximation method is basedon two general concepts, namely on functions of operators and on the Dunford-Schwartz representation formula. This approximation method is extended to solvea robust H∞ filtering problem of the coupled cantilevers for time-Invariant systemwith random noise effects.