PI and PID Stabilization of Neutral and Retarded Systems with Time Delay

Abstract Stabilization using fixed order controllers is one of the key topics in control system design for the linear time-invariant (LTI) systems. In this paper, the stabilization of LTI neutral and retarded time delay systems by means of PI and PID controllers is investigated in detail. The basic theme of the presented approach is to obtain the global stability region in two-dimensional (kp, ki)-plane for the PI controller and in threedimensional (kp, ki, kd)-space for the PID controllers. This region is formed by stability boundaries that are defined as real root boundary, infinite root boundary and complex root boundary. The 3-D global stability region for the PID case is made up the set of 2-D stability regions which are obtained in (kp, ki)-plane, (kp, kd)-plane or (ki, kd)-plane by changing the other third parameter. To achieve this, the stability boundary locus approach is incorporated into the D-decomposition method. Thus, the complete set of stabilizing PI and PID controllers for the system is obtained. The simulation results indicate that the presented stabilization method is effective and practically useful in the analysis and control of the neutral and retarded time delay systems.