Controle PID de Vibrações em Sistemas de Segunda Ordem com Atraso Usando Receptância com Estabilidade Robusta e Otimização de Desempenho

Abstract

This work deals with the design of PID controllers for linear dynamic systems with time-delay, modeled by second-order matrix differential equations. The receptance approach is adopted, which, as it is based on the frequency response of the system, allows dealing with closed-loop stability exactly, without the need to resort to approximations of the delay term or a posteriori checks. An optimization problem is formulated to determine the controller gains that guarantee robustness, through a given stability margin, and performance, through the minimization of the Integral of the Absolute Error, relative to constant reference tracking. A Genetic Algorithm is implemented to solve the optimization problem. Unlike related works in the literature, the proposed method can also be applied to systems with open-loop poles in the right half-plane.