Data-driven soft constrained model predictive control for sludge bulking in wastewater treatment process

The complex causes of sludge bulking, strict system constraints, and dynamic operating conditions increase the challenges of controlling wastewater treatment process. To address this issue, a data-driven soft constrained model predictive control (DD-SCMPC) strategy is proposed, which can adaptively adjust the control law in response to the identified fault cause. First, an intelligent diagnosis algorithm is utilized to identify the key cause variable according to the relative reconstruction contribution of process variables. Consequently, the priority control order of the controlled variables can be determined based on the correlation between the cause variable and output variables. Second, a soft constrained MPC strategy is designed to regulate the concentrations of dissolved oxygen and nitrate nitrogen in accordance with the predetermined control order, thereby avoid sludge bulking caused by abnormal process variables. The incorporation of soft constraints alleviates the strict constraints on system outputs, enhancing the adaptability of the controller. Third, a predictive control barrier function is designed to obtain an enlarged attractive domain, ensuring the stability of the system under soft constraints. Then, the feasibility and stability analysis provide theoretical support for the application of DD-SCMPC. Finally, the effectiveness of the proposed DD-SCMPC strategy is verified on the benchmark simulation model 1.