Uma variação do algoritmo de busca harmônica aplicada na determinação das matrizes de ponderação do regulador linear quadrático

Abstract

Linear Quadratic Regulator (LQR) is an important modern control technique with excellent properties associated to robust stability, as it can be applied to complex control systems in order to ensure stability against small perturbations. However, the controller design presents some difficulty regarding the definition of weighting matrices Q and R, which are responsible for ensuring the design specifications, although they require a large search space. Thus, the application of a computational intelligence technique is necessary to perform the optimized search for the aforementioned matrices automatically. For this purpose, the Harmony Search (HS) algorithm has been applied to define the matrices for the LQR controller. HS is a metaheuristic algorithm inspired by musical improvisation as a tool to create new harmonies, which has been widely used by scientific community in recent years and can be applied to this problem. However, some parameters must be defined by empirical means to ensure good convergence. Within this context, this work proposes a novel HS Algorithm that ensures the automatic adjustment of parameters. By adopting the CH-47 helicopter and an inverted pendulum system, several tests involving search and simulation have been performed with three HS algorithms i.e. standard HS and the modified methods known as Improved Harmony Search (IHS) and Statistical Dispersion Harmony Search (DHS). The latter one can be seen as the main contribution of this work, which also compares the results obtained from the HS algorithms. It can be stated that all approaches present satisfactory results when analyzing the system response, although the one introduced in this work presents superior performance in terms of convergence if compared with the consolidated techniques. Keywords: Linear Quadratic Regulator. Search and Optmization. Weighing matrices. Harmony Search Algorithm.