PROPOSTA DE CONTROLE BASEADO EM CRITÉRIO DE ESTABILIDADE ROBUSTA: UMA ABORDAGEM EM TERMOS DE FUNÇÃO DE TRANSFERÊNCIA APLICADA A SISTEMAS DINÂMICOS NO TEMPO CONTÍNUO COM ATRASO

Abstract

In this dissertation, a robust fuzzy PID Takagi-Sugeno control methodology based on gain and phase margins specifications for dynamic systems with time delay in continuous time domain is proposed. A fuzzy model based on the Takagi-Sugeno structure is used to represent the dynamic system to be controlled. Thus, from the input and output data of the dynamic system, the Gustafson-Kessel fuzzy clustering algorithm is used to estimate the parameters of the antecedent proposition (input space) and the rules number of the fuzzy model, while the least mean squares algorithm is used to estimate the parameters of the sub-linear models of the consequent proposition (output space) of the fuzzy model. A mathematical formulation based on PDC (parallel and distributed compensation) strategy is defined from the gain and phase margins specifications for the calculation of PID controllers sub-parameters, in the robust fuzzy PID controller rule base, the linear sub-models parameters of the dynamic system model fuzzy rule base to be controlled. An analysis of necessary and sufficient conditions for robust fuzzy PID controller design, with the proposal of one axiom and two theorems are presented. Computational results to validation of the proposal compared to others control methods widely cited in the literature, with the application in the angular position control of a robotic manipulator, are also presented.