Uma nova condição quase-LMI para projeto de controladores PID multivariáveis

Caio Augusto Campos; Pedro Henrique Silva Coutinho; Víctor Costa da Silva Campos

doi:10.20906/SBAI-SBSE-2023/3839

Caio Augusto Campos Graduação em Engenharia de Controle & Automação, Universidade Federal de Minas Gerais, MG
Pedro Henrique Silva Coutinho Departamento de Engenharia Eletrônica, Universidade Federal de Minas Gerais, MG / Programa de Pós-Graduação em Engenharia Elétrica, Universidade Federal de Minas Gerais, MG
Víctor Costa da Silva Campos Departamento de Engenharia Eletrônica, Universidade Federal de Minas Gerais, MG

DOI: https://doi.org/10.20906/SBAI-SBSE-2023/3839

Keywords: PID control, Linear multivariable systems, Convex optimization, Asymptotic stabilization, Lyapunov methods

Abstract

This paper addresses the multivariable PID control design for linear systems in the state-space representation. The proposed design condition can be applied to multiple-input and multiple-output systems and does not require a state-space realization in any specific canonical form. In particular, the condition proposed in the form of linear matrix inequalities ensures the D-stability of the closed-loop system. It can be solved without resorting to iterative procedures. The condition is evaluated numerically and experimentally. The numerical simulations illustrate the advantages of the proposed approach, including the conservativeness reduction compared with related works. In the experimental evaluation, the PID controller was designed to stabilize the pitch angle dynamics of a twin-rotor system.