Real-time optimization for nonlinear processes including output saturation

Output saturation is observed in many chemical processes and microbial cultivation processes. In these processes, output saturation can cause a number of control problems near the saturation point due to the nonlinear continuous input multiplicity interval after the saturation point. In general, the widely used proportional-integral-derivative (PID) controller cannot perform its function due to the nonlinearity. In particular, the accumulated error due to the integration term in the saturation region may result in a reduction in the energy efficiency and in an overloading of the process. Two solutions to this optimization problem are presented in this study. The first is to eliminate input multiplicity through a modified PID controller that introduces a new output value with the input signal added. The second is to find the optimal point of the nonlinear saturation process using extremum seeking control with continuous perturbation. Overflow experiments and simulations involving the liquid level system were performed for both solutions. Both methods have different characteristics, but both exhibit remarkable performance and stability improvements over conventional control systems.