Stabilization of second-order systems using PI controllers with delayed proportional and integral parts

Abstract

The present paper deals with the stabilization, optimization, and control of second-order systems using a PI delayed controller. This study analyzes the control of linear-time invariant (LTI) systems with time delay in the integral and proportional parts of the PI delayed controller and obtains the region of global stability in the two-dimensional plane. The proposed stabilization method is verified through software simulations with two benchmark examples: the control of an inverted pendulum and the control of the stick-slip vibration. The results show the effectiveness and practical applicability of the proposed method in all analyses and control. Additionally, the optimization of LTI systems with time delay in the integral and proportional parts of the PI delayed controller is discussed, and selected heuristic methods are compared. Future research aims to implement modern optimization algorithms for solving non-smooth, non-convex, and non-Lipschitz optimization problems in this field.