PID controller tuning for unstable systems by optimization method

Simple Tuning formulae are provided for optimal PID controller settings for unstable first order plus time delay systems. The method is based on minim ization of integral squared errors (ISE). A method of calculating the set p oint weighting parameter is proposed to reduce the overshoot for servo prob lems. The performances of the proposed PID settings are compared with the s ettings recently proposed by Huang and Chen (1997, 1999) for both the servo and regulatory problems. The performance of the controller is also evaluat ed under parameter uncertainty in time delay and separately in process gain . Tuning formulae are given for PI controller along with the set point weig hting. The performance of the PI controller is compared with that of Poulin and Pomerleau (1996). Two simulation studies, one on control of an unstabl e nonlinear bioreactor and a second on an unstable chemical reactor using t he proposed PID controller settings, show improved performances both for se rvo and regulatory problems.