Set-point weighted PID controllers for unstable systems

The methods proposed by Astrom and Hagglund (IFAC Adaptive Control of Chemi cal Processes, Pergamon Press, New York, 1985, pp. 205-210), Mantz and Tacc oni (Int. J. Control 49 (1989) 1465-1471; Ind. Eng. Chem. Res. 20 (1990) 12 49-1253) for selection of set-point weighting parameters for stable systems are extended to unstable first-order plus time-delay (FOPTD) systems. Sinc e these methods require the real part of the dominant pole, an analytical s olution is derived for calculation of dominant poles of the closed-loop sys tem given the PID controllers settings. For PID controller settings given b y DePaor and O'Malley (Int. J. Control 49 (1989) 1273-1284) and Clement and Chidambaram (Chem. Eng. Commun. 62 (1997) 63-74), the set-point weighting parameters are calculated and simple equations are given for the parameters in terms of epsilon (ratio of time delay to dominant time constant). Simul ation results on an unstable FOPTD transfer function model and higher-order transfer function model show that the overshoot is significantly reduced b y employing the set-point weighting parameters in the PID controller. The p erformances of the closed-loop servo responses for all the extended methods are compared. (C) 2000 The Franklin Institute. Published by Elsevier Scien ce Ltd. All rights reserved.