Dynamically multi-objective optimization with state observer for wastewater treatment process

Wastewater treatment plays an important role in alleviating the water shortage and protecting the environment from contamination. Since the wastewater treatment process (WWTP) is a time-varying and highly complex system, it is challenging to design an effective optimization control method to ensure effluent quality (EQ) and reduce energy consumption (EC). To overcome this problem, a dynamically multi-objective optimal control strategy is proposed in this paper. Firstly, a multi-objective gray wolf optimization algorithm based on subpopulation and multi-strategy exploration (MOGWO-SM) is designed to obtain dynamic setpoints that can achieve the tradeoff between EC and EQ. Then, multi-unit nonsingular fast terminal sliding mode controllers based on extended state observer (MNFTSMC-ESO) are used to accurately track these setpoints to keep the dissolved oxygen and nitrate maintained at appropriate concentrations throughout the WWTP. Finally, the effectiveness of the proposed method is verified using the Benchmark Simulation Model No. 1 (BSM1). Simulation results show that the proposed method not only has satisfactory control accuracy, but also can ensure that the effluent quality meets the discharge requirements with a significant reduction in EC. EC values are decreased by 10.14$\text{\%}$ and 21.69$\text{\%}$ compared with traditional PID strategy in dry and storm conditions, respectively. Overall, the proposed method has a certain potential for practical application due to its superior performance, contributing to sustainable wastewater management.