Robust Soft Constrained Model Predictive Control and Its Application in Wastewater Treatment Processes

A robust soft constrained model predictive control (RSCMPC) method is proposed to address the effects of unknown disturbances for wastewater treatment processes (WWTPs). The disturbances involving inflow fluctuation and noises from WWTPs may result in the constraints violation of MPC due to its uncertainty of bioprocess, which may degrade the performance of the steady state. First, the artificial steady state is introduced to mimic the nearest feasible steady state when the reference steady state is not feasible. The deviation caused by disturbances between the artificial steady state and the reference steady state is also penalized to ensure that the output of MPC converges to the reference steady state. Second, the soft constraints, incorporating two slack variables and a penalty term, are designed to relax the state constraints of MPC and continuously mitigate the constraint violation, thereby ensuring its stability. Third, the input state stability (ISS) under disturbances is analyzed. Finally, the simulation tested on Benchmark simulation model 1 verifies the effectiveness of the proposed RSCMPC. The results demonstrate that RSCMPC improves the robustness of the system to maintain the stable operation of the WWTPs. Note to Practitioners—The external disturbances of wastewater treatment processes (WWTPs) will result in the constraints violation of model predictive control (MPC) and degrade the steady state performance. To overcome the influence of external disturbances, a robust soft constrained model predictive control (RSCMPC) method is designed. This method mainly includes three contributions: First, the artificial steady state is constructed with the prediction derived from fuzzy neural network, which is to mimic the nearest feasible steady state when the reference steady state is not feasible under disturbances. Second, the soft constrained method relaxes the state constraints of MPC through two slack variables to compensate the effects of disturbances and restore the feasibility of the controller. Third, the input state stability under disturbances is analyzed. Finally, the effectiveness of the proposed RSCMPC method is evaluated on a pilot platform of a real WWTPs. The experimental results show that RSCMPC can improves the control accuracy and robustness of the system under external disturbances. The proposed RSCMPC method can help practitioners improve the reliability of WWTPs operation.