This thesis focuses on the theory, design, simulation and implementation of several digital controllers for periodic signals on a laser scanning galvanometer. A model for the galvanometer was obtained and veri ed using closed loop identi cation techniques. Using this model, controllers were designed and simulated using MATLAB and then implemented on a custom FPGA control processor with a focus on tracking performance. The types of controllers used were: an Iterative Learning Controller, an RST pole placement controller, an Adaptive Feed-forward cancellation controller, a combined Iterative Learning and Adaptive Feed-forward cancellation controller and a simple PID controller. The simulated results were better than the experimental results because of system noise and modelling uncertainties but the relative performance between each of the controllers was similar for both the simulation and experimental setup. The experimental results achieved were very good with one controller reaching errors under 50 rad. / Graduate / 0537 / t_Torres_bonet@hotmail.com

La classe des systèmes non-linéaires dont la dynamique est définie par un champ de vecteurs polynomial est étudié. Des modèles polynomiaux peuvent représenter différents systèmes réels ou bien définir des approximations plus riches que des modèles linéaires pour des systèmes non-linéaires différentiables. Des techniques de programmation semi-définie développées récemment ont rendu possible l'étude de cette classe de systèmes avec des outils numériques. Le problème d'analyse en stabilité locale est résolu via des conditions basées sur la positivité de polynomes. Dans le cadre de la synthèse de lois de commande nous proposons un changement de variables linéaire pour traiter la synthèse de lois de commande non-linéaire qui garantissent la stabilité locale. Les ensembles définissant des estimations de la région d'attraction, définis par des courbes de niveau de la fonction de Lyapunov pour le système, sont également donnés par des fonctions polynomiales / We study the class of nonlinear dynamical systems which vector field is defined by polynomial functions. A large set of systems can be modeled using such class of functions. Tests for stability are formulated as semidefinite programming problems by considering positive polinomials to belong to the class of Sum of Squares polynomials. Polynomial control law gains are computed based on a linear change of coordinates and guarantee the local stability of the closed-loop system. Lyapunov theory is then applied in order to obtain estimates of the region of attraction for stable equilibrium points. Such estimates are given by level sets of polynomial positive functions