Projeto de Controladores PID Multivariáveis para Sistemas de Segunda Ordem com Atraso

Abstract

This study aims to develop multivariable PID controllers for linear dynamic systems with multiple inputs and outputs (MIMO) that present actuation delay and are described by a system of second-order differential equations. The proposed technique uses the frequency domain model known as reception matrix, and which allows the effect of delay to be treated without approximations. Closed-loop stability is ensured using the so-called generalized Nyquist criterion, verified by the so-called eigenloci plots. A given margin of stability is obtained by imposing a minimum distance between the eigenloci and the critical point. An optimization problem is formulated to calculate the PID gains that achieve this margin and optimizes the performance of the time response, which is solved by Genetic Algorithm. Two numerical examples are presented to illustrate the merit of the proposal.