Enhanced Performance and Robustness of PID Controllers for Unstable Time Delay Systems Using Pole Placement Method

Abstract

Multiple dominant pole placement (MDP) method was used to design a PID controller with a lead/lag filter for unstable first-order plus time delay (FOPTD) systems and second-order plus time delay (SOPTD) systems. No approximation for time delay term was used which is the biggest advantage of the MDP method. Five equations are formulated with the characteristic equation and first-order, second-order, third-order and fourth-order derivatives of the characteristic equation. The equations are solved for five unknown parameters of PID controller and filter parameters. The location of closed loop pole is to be specified, and it is the tuning parameter. Tuning rules for the closed loop pole were given for the unstable FOPTD systems as a function of the ratio between time delay and time constant. Simulation results on various unstable systems along with nonlinear models of bioreactor are given to demonstrate the efficiency of the PID controller parameters obtained by the proposed method. Real-time experimentation on inverted pendulum illustrates the applicability of the PID controller designed by the proposed method to real-time systems. Performance comparison is given in terms of integral absolute error (IAE), and the controllers designed by the present method give good and robust performance.