Estimação de parâmetros do modelo de Histerese L2P através de técnicas variadas de otimização

Abstract

Many sensors and actuators exhibit hysteresis in one of their characteristics of practical interest. Hysteresis often occurs in mechanical actuators due to friction and can cause many difficulties in the development of control applications. Another example is electrical transformers, which are simple current sensors that exhibit hysteresis between the magnetization and the magnetic field. There are several models to describe the hysteretic behavior, each of them having its own positive aspects and drawbacks. Recently, Almeida et al. (2003b), in studying the resistance-temperature characteristics of vanadium dioxide infrared detectors, proposed a simple algebraic hysteresis operator called the limiting loop proximity model (L2P). This model has lower mathematical complexity and is capable of describing asymmetric hysteresis phenomena. Like most hysteresis operators, the L2P model requires the use of search and optimization techniques to fit it to experimental data. To date, there is no independent mathematical procedure for extracting the L2P parameters. This dissertation focuses on the study of some traditional optimization techniques and their application to fit the LP model to hysteretic experimental data of vanadium dioxide thin films. Two main types of search methods are studied: calculus-based and random. Calculus-based methods search the optima near the initial point and are divided into two types: indirect and direct. The former search for local extrema solving a set of nonlinear equations, while the latter search for local optima in the steepest allowed direction using the local gradient. The two computational methods studied are: Gauss-Newton and Levenberg-Marquardt. Random search algorithms are not as specialized and efficient as calculus-based methods, but are more robust and usually able to explore a much larger search space. The genetic algorithm is an example of a random search based on the mechanisms of natural selection. The parameter extraction of the model L2P is also explored using the genetic algorithm. The performance of these optimization methods is compared and presented in terms of the normalized mean square error (e).