A simple method of tuning PID controllers for stable and unstable FOPTD systems

Abstract

A simple method is proposed to design PI/PID controllers for stable first-order plus time delay (FOPTD) systems. The method is based on matching the coefficient of corresponding powers of s in the numerator and that in the denominator of the closed loop transfer function for a servo problem. This method gives simple equations for the controller settings in terms of the FOPTD model parameters. Simulation results show that the method gives a similar response as that of Ziegler–Nichols (Z–N) method and better response than that of IMC method. Controllers are also designed by using two tuning parameters and the performance is best when compared to that of Z–N [ASME Trans. 64 (1942) 759] and Abbas [ISA Trans. 36 (1997) 183]. The controller settings give a robust performance for uncertainty in the process model parameters. The method is also extended to design PI/PID controllers for an unstable FOPTD system. Simulation results show that the present method gives improved performances: (i) for PID controllers over that of the controllers designed by Huang and Chen [J. Chem. Eng. Jpn. 32 (1999) 579], IMC method and that proposed by Visioli [IEE Proc. CTA 148 (2001) 180] and (ii) for PI controllers over the method of Jung et al. [J. Process Contr. 9 (1999) 265]. Theoretical analysis of stability and robustness of the proposed controller are also provided.