Identificação e controle de sistemas dinâmicos utilizando uma Fuzzy Wavelet Neural Network

Abstract

Mathematical modeling is a task of vital importance for the development of science and technology, since its objective is to obtain a mathematical description of a real phenomenon. Regardless of their nature, real systems need to be studied and their dynamics must be known in order for their functioning to take place as desired. The classical way of obtaining a mathematical representation is by analyzing the physical laws governing systems. However, in this case, in addition, they are (often) difficult or even impossible to follow this path, and a plausible alternative is the identification of systems. The identification of dynamic systems aims to obtain a mathematical representation of the dynamics of a system based on input and output data. Real dynamic systems are nonlinear. In some applications, as linear approximations are sufficient, however, when linear representations do not express a dynamic process, it is necessary to use a nonlinear model. In the last decades, as neural networks have been installed as one of the main tools for an identification of nonlinear dynamic systems, as they have characteristics that make them attractive for identification, due to nonlinearity and generalization and learning. From the possession of a model that satisfactorily represents the dynamics of a system, it can be used for applications such as control, prediction, inference, among others. The present work proposes the application of a Fuzzy Wavelet Neural Network in the identification of nonlinear dynamic systems. This hybrid technique combines the multiresolution features of the Wavelet theory with the learning ability and the generalization of the neural networks together with the ability to deal with Fuzzy logic uncertainties. The obtained model is used for the tuning of a PID controller. In the course of the work, the concepts and techniques necessary to perform identification and controller tuning will be presented. And the results obtained attest to the efficiency of the techniques used.