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

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. © 2004 Elsevier Ltd. All rights reserved.