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