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Wastewater treatment process (WWTP), consisting of a class of physical, chemical, and biological phenomena, is an important means to reduce environmental pollution and improve recycling efficiency of water resources. Considering characteristics of the complexities, uncertainties, nonlinearities, and multitime delays in WWTPs, an adaptive neural controller is presented to achieve the satisfying control performance for WWTPs. With the advantages of radial basis function neural networks (RBF NNs), the unknown dynamics in WWTPs are identified. Based on the mechanistic analysis, the time-varying delayed models of the denitrification and aeration processes are established. Based on the established delayed models, the Lyapunov–Krasovskii functional (LKF) is used to compensate for the time-varying delays caused by the push-flow and recycle flow phenomenon. The barrier Lyapunov function (BLF) is used to ensure that the dissolved oxygen (DO) and nitrate concentrations are always kept within the specified ranges though the time-varying delays and disturbances exist. Using Lyapunov theorem, the stability of the closed-loop system is proven. Finally, the proposed control method is carried out on the benchmark simulation model 1 (BSM1) to verify the effectiveness and practicability.
Qiao et al. (Wed,) studied this question.