Robust optimal proportional-integral-derivative controller design for a class of uncertain second-order delay-free and time-delay systems Articles uri icon

publication date

  • August 2022

start page

  • 2061

end page

  • 2073


  • 15-16


  • 28

International Standard Serial Number (ISSN)

  • 1077-5463

Electronic International Standard Serial Number (EISSN)

  • 1741-2986


  • The second-order systems can capture the dynamics of a vast majority of industrial processes. However, the existence of uncertainty in second-order approximation of such processes is inevitable because the approximation may not be accurate or the operating condition changes, resulting in performance degradation or even instability. This article aims at designing a novel robust proportional–integral–derivative controller for the uncertain second-order delay-free and time-delay systems in an optimal manner. The method is simple, effective, and can efficiently improve the performance of the uncertain systems. The approach is based on the linear quadratic theory, in which by adding a new matrix in the quadratic cost function regarding the uncertainties, the stability of the perturbed system is guaranteed and proven for both time-delay and delay-free second-order cases. The comparison with the recent works in the literature supports the effectiveness of the proposed methodology


  • Aeronautics
  • Electronics
  • Robotics and Industrial Informatics


  • optimal control; proportional–integral–derivative controller; linear quadratic; second-order systems; robustness