Self-Organizing Fuzzy Terminal Sliding Mode Control for Wastewater Treatment Processes

Wastewater treatment process is a complex industrial process with disturbance and strong nonlinearity, and it is difficult to accurately track the pre-designed dissolved oxygen (DO) concentration in finite time. In this paper, a self-organizing fuzzy terminal sliding mode (SOFTSM) control strategy is proposed to solve this problem. First, a terminal sliding mode controller (TSMC) is designed to obtain a control law and achieve the finite time tracking of the pre-designed DO concentration. Second, a self-organizing fuzzy neural network (SOFNN) is utilized to estimate the nonlinear term. Then, the pruning strategy without pre-setting pruning threshold is designed to improve the approximation accuracy and further ensure the accuracy of control performance. Third, an adaptive law and robust control term are designed to reduce the influence of uncertainty and approximation error. Moreover, the stability of SOFTSM and the characteristic of finite time convergence are proved. Finally, the proposed method is tested on the benchmark simulation model no. 1 (BSM1). In contrast to other existing methods, SOFTSM can realize accurate control of DO concentration in finite time.
Note to Practitioners
—The nonlinear and strong disturbance characteristics of wastewater treatment process will reduce the control accuracy of dissolved oxygen (DO) concentration in infinite time. To realize the finite time precise control of DO concentration, a self-organizing fuzzy terminal sliding mode (SOFTSM) control strategy is designed in this paper. The strategy mainly includes three parts: First, a terminal sliding mode controller (TSMC) is designed to obtain the specific expression of control law and realize the finite time tracking of pre-designed DO concentration. Second, the self-organizing fuzzy neural network (SOFNN) without pre-setting pruning threshold is used to estimate the nonlinear term. The pruning strategy without pre-setting pruning threshold is designed to improve the approximation accuracy. Third, adaptive law and robust control term are designed to reduce the influence of uncertainty and approximation error. Finally, the effectiveness of SOFTSM is verified by industrial applications of wastewater treatment processes. The simulation results show that SOFTSM can achieve precise control of DO concentration in finite time.