A Simple and Robust Method of Tuning PID Controllers for Integrator/Dead Time Processes

Abstract

A simple method is proposed for PID controller settings for an integrating plus dead-time system and a stable FOPTD system with an integrator. The method is based on matching the coefficients of corresponding powers of s, s2, s3 in the numerator to α1, α2, and α2 times that in the denominator of the closed-loop transfer function, respectively, for the servo problem. Here α1 and α2 are tuning parameters, and α1 is greater than 1. It is found by simulation on various transfer function models that the use of α2 = 0.6α1 gives good results. The robustness of the controller is evaluated theoretically by Kharitonov’s theorem. The method is used to design a PID controller for an isothermal continuous copolymerization reactor, and the performance of the controller designed by the present method is compared with a modified gain margin method (Luyben, 1996). The method is extended to design a PID controller for a stable FOPTD system with an integrator. The performance of the method is better than the method proposed by Zhang et al. (1999) for the servo problem, and it is superior to their method for the regulatory problem.