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Contribution à la modélisation et au contrôle d'une matrice d'AFM

Abstract : In this dissertation, we establish a two-scale model both for one-dimensional and two-dimensional Cantilever Arrays in elastodynamic operating regime with possible applications to Atomic Force Microscope (AFM) Arrays. Its derivation is based on an asymptotic analysis for thin elastic structures, a two-scale approximation and a scaling used for strongly heterogeneous media homogenization. We complete the theory of two-scale approximation for fourth order boundary value problems posed in thin periodic domains connected in some directions only. Our model reproduces the global dynamics as well as each of the cantilever motion. For the sake of simplicity, we present a simplified model of mechanical behavior of large cantilever arrays with decoupled rows in the dynamic operating regime. Since the supporting bases are assumed to be elastic, cross-talk effect between cantilevers is taken into account. The verification of the model is carefully conducted. We explain not only how each eigenmode is decomposed into products of a base mode with a cantilever mode but also the method used for its discretization, and report results of its numerical validation with full three-dimensional Finite Element simulations. We show new tools developed for Arrays of Microsystems and especially for AFM array design. A robust optimization toolbox is interfaced to aid for design before the microfabrication process. A model based algorithm of static state estimation using measurement of mechanical displacements by interferometry is presented. We also synthesize a controller based on Linear Quadratic Regulator (LQR) methodology for a one-dimensional cantilever array with regularly spaced actuators and sensors. With the purpose of implementing the control in real time, we propose a semi-decentralized approximation that may be realized by an analog distributed electronic circuit. More precisely, our analog processor is made by Periodic Network of Resistances (PNR). The control approximation method is based on two general concepts, namely on functions of operators and on the Dunford- Schwartz representation formula. This approximation method is extended to solve a robust H∞ filtering problem of the coupled cantilevers for time-invariant system with random noise effects.
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Contributor : Fabienne Cornu <>
Submitted on : Wednesday, May 29, 2013 - 4:03:55 PM
Last modification on : Thursday, November 12, 2020 - 9:42:06 AM
Long-term archiving on: : Friday, August 30, 2013 - 8:20:21 AM


  • HAL Id : tel-00827715, version 1


Hui Hui. Contribution à la modélisation et au contrôle d'une matrice d'AFM. Mécanique des structures [physics.class-ph]. Université de Franche-Comté, 2013. Français. ⟨tel-00827715⟩



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