Set-point weighted PID controllers for unstable systems

The methods proposed by Astrom and Hagglund (IFAC Adaptive Control of Chemical Processes, Pergamon Press, New York, 1985, pp. 205–210), Mantz and Tacconi (Int. J. Control 49 (1989) 1465–1471; Ind. Eng. Chem. Res. 20 (1990) 1249–1253) for selection of set-point weighting parameters for stable systems are extended to unstable first-order plus time-delay (FOPTD) systems. Since these methods require the real part of the dominant pole, an analytical solution is derived for calculation of dominant poles of the closed-loop system given the PID controllers settings. For PID controller settings given by DePaor and OʹMalley (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 ε (ratio of time delay to dominant time constant). Simulation results on an unstable FOPTD transfer function model and higher-order transfer function model show that the overshoot is significantly reduced by employing the set-point weighting parameters in the PID controller. The performances of the closed-loop servo responses for all the extended methods are compared.