Dinâmica não linear e controle de osciladores inteligentes

Abstract

Problems involving mechanical vibrations are common in virtually all branches of industry. In order to try to suppress or control these vibrations, several methods and techniques have been developed over the last decades and continue today, mainly due to the growing needs of engineering. Among the techniques used can be cited the use of intelligent materials and smart structures. These materials exhibit a non-linear behavior, and depending on the parameters of the dynamic system that employ them, they may present periodic, almost periodic and chaotic responses. Given this wealth of responses, there is an increase in the complexity of predicting their behavior and applying an effective control technique. The present work presents a study of the nonlinear dynamics of an oscillator with intelligent materials and seeks to bring the system to a desired state using a robust control technique aided by an Radial-Basis Function Networks. A demonstration of the robustness of the technique is presented using Lyapunov’s theory of stability and Barbalat’s lemma. Before applying this control technique, a prior study of the static behavior of Shape Memory Alloys Composites (SMAC) is carried out, followed by a dynamic study where tools such as the Bifurcation Diagram and the Largest Lyapunov Exponent are explored to extract more information about the dynamics presented by oscillators with such materials. Specific cases are presented to verify the effectiveness of the control technique, which must be robust, capable of learning, adapting and predicting. As a result, the control technique used was able to control oscillators with Shape Memory Alloys (SMA) and Shape Memory Alloy Composites in the face of non-linearities such as hysteresis, dead-zone and saturation, with fluctuations in the parameters and and the lack of system dynamics. The control technique was also able to control the chaotic oscillator responses.