Multi-Objective Integrated Robust Optimal Control for Wastewater Treatment Processes

Multi-objective optimal control is widely applied in wastewater treatment processes (WWTPs) to ensure the security and stability of the operation processes. However, for the existing stepwise multi-objective optimal control (SMOC) algorithms, the unknown disturbances will further influence the obtain of set-points and the design of control laws, which may degrade the control performance and operation performance of WWTPs. Aim at the above-mentioned problem, this study presents a multi-objective integrated robust optimal control (MIROC) method for WWTPs. The merits of MIROC are three folds. First, a model approximator is designed to capture the nonlinear dynamics of WWTPs. Second, a disturbance observer is utilized to describe the disturbances of WWTPs. Then, based on the model approximator and disturbance observer, a more accurate prediction model of WWTPs with disturbances is established. Third, under the framework of multi-objective model predictive control (MMPC), a MIROC structure with a cooperative cost function (CCF) and a gradient-based multi-objective optimization algorithm (GMOA) is developed to coordinate optimization and control solution of WWTPs with unknown disturbances. Finally, the stability analysis of MIROC is provided in theory. Meanwhile, the results on the benchmark simulation platform demonstrate that MIROC can improve the performance of WWTPs. Note to Practitioners —The SMOC algorithms may degrade the performance of WWTPs with the unknown disturbances. In the paper, a MIROC scheme is presented for WWTPs with the unknown disturbances. Three key parts are contained, the model approximator, the disturbance observer and the MIROC structure. A prediction model of WWTPs with disturbances is established with the model approximator and the disturbance observer. Then, the model approximator and the disturbance observer are applied to improve modeling accuracy of MIROC. Based on the prediction model of WWTPs, a MIROC structure is designed to comprehensively analyze the optimization process and control process of WWTPs with the unknown disturbances. Then, MIROC structure is composed of a CCF and a GMOA. Finally, the results on an industrial application of WWTPs demonstrate that MIROC can achieve optimal operation of WWTPs.