Extremum Seeking Control for Wastewater Treatment Plant with Prioritized Output Constraints

This paper is concerned with the applicability of extremum seeking (ES) control for wastewater treatment plants (WWTPs) under several practical constraints such as effluent regulations and/or operational constraints. Considering such constraints to optimize a trade-off between effluent improvement and operational cost reduction is important in real WWTP operation. To meet such practical requirements, this paper proposes a novel ES scheme incorporating multiple output constraints where the priority of each constraint is also considered. Such priority becomes important when one or more of the constraints cannot be satisfied, which will not be the exception in control problems of real WWTP due in part to the considerably large inflow load variation. To make ES be effective even in such situation, the paper proposes a prioritized output constraints ES scheme incorporating switching functions to change the performance index for minimization depending on the active constraints. It is suggested that such switching mechanism is preferably combined with the gradient-sign-based ES that was also proposed by the authors to mitigate the sudden change in the curvature of the performance index caused by the switching functions. Some numerical simulations of the proposed ES with a simple model are performed to illustrate the principle of the proposed idea at first, and then the effectiveness of the proposed ES to WWTPs is demonstrated by using a complex nonlinear biological model.