Neural network and integer programming-based Model Predictive Control for a wastewater treatment process

The wastewater treatment process (WWTP) plays a crucial role in treating large volumes of wastewater, making it essential for both environmental protection and human health. Control of WWTP is challenging. In this work, a neural network (NN) model with rectified linear unit (ReLU) activation function-based Model Predictive Control (MPC) is designed and deployed to the WWTP Benchmark Simulation Model No. 1 (BSM1). The ReLU-based NN model helps obtain the MPC optimal control problem (OCP) as a mixed-integer quadratic programming (MIQP) problem, which guarantees feasibility and can be solved to global optimality. The ReLU-based NN model is trained from the BSM1 model, and closed-loop numerical simulations are performed without and under disturbance in the influent flow. For the case without disturbance, the conventional linear state-space model-based MPC yields good tracking performance. However, for the case under disturbance, the conventional MPC controller fails to track the set points satisfactorily. In contrast, the ReLU-based NN MPC controller helps maintain the output variables close to the set points. The controller can be deployed in real-world WWTPs to achieve good control performance even under strong disturbances in influent flow.