Stabilising PID tuning for a class of fourth-order integrating nonminimum-phase systems

Fed-batch fermentation processes are commonly used in bioprocessing industry. A fed-batch fermentation process often exhibits integrating/unstable type of dynamics with multiple right-half plane zeros. A class of fourth-order integrating model can be used to adequately represent such a complex dynamics of the fed-batch fermentation process. In this paper, rigorous stability analysis of proportional-integral-derivative (PID) controller based on the Routh-Hurwitz criteria for the fourth-order integrating system is presented. A set of all stabilising PID controller parameter regions is established. Based on these stabilising regions, a general PID controller tuning procedure is proposed for the fourth-order integrating system with two right-half plane zeros. Numerical study shows that based on the proposed tuning procedure, a low-order PID controller can outperform a fifth-order optimal LQG controller in terms of servo and regulatory controls.