Robust PID Controller for Second-Order Systems plus Time Delay

  • Danielle S. Gontijo Programa de Pós-graduação em Engenharia Elétrica, Universidade Federal de Minas Gerais, MG
  • Fernando O. Souza Departamento de Engenharia Eletrônica, Universidade Federal de Minas Gerais, MG
  • José M. Araújo Grupo de Pesquisa em Sinais e Sistemas, Instituto Federal da Bahia, BA
Keywords: Robust Control, Time Delay, Linear Matrix Inequalities, Second-Order Systems, Proportional-Integral-Derivative controller (PID)


This paper presents a design methodology for obtaining a robust proportional- integral-derivative (PID) multivariable controller for second-order linear systems with time- varying delay, guaranteeing a pre-established exponential decay rate. Relevant control challenges such as stabilization, modeling error and constant reference tracking are addressed within the proposed Linear Matrix Inequality (LMI) design approach. The design strategy is derived from a transformation that can be applied to obtain constant reference tracking for an actuated subspace of underacted systems. Furthermore, the integral action has an additional objective which is to increase the degree of design. Simulation case studies are used to highlight the benefits of the proposed results.