Modeling and control of wastewater treatment process with time delay based on event-triggered recursive least squares

Abstract

Accurate control of dissolved oxygen (DO) concentration is the key to ensuring the quality of effluent from the wastewater treatment process (WWTP). However, the delay disturbance caused by the hydraulic retention time (HRT) hinders the accurate control of DO concentration. To solve this problem, an event-triggered recursive least squares-based sliding mode control (ETRLS-SMC) is proposed to overcome the obstacles caused by the delay disturbance for accurate control of DO concentration. First, a differential equation with a delay disturbance term is established to describe the dynamic process of the system. Then, the delay disturbance is explicitly depicted to lay the foundation for the controller design considering delay disturbance variables. Second, an RLS identification algorithm is used to online obtain the model parameters of the system. In particular, an event-triggered mechanism is designed to reduce the number of model updates with guaranteed accuracy. Third, combined with the ETRLS identification algorithm, an SMC method is introduced to control the DO concentration with delay disturbance variables. Then, the control law is computed to achieve stable control of the system. Finally, the performance of ETRLS-SMC is verified on the benchmark simulation model 1 (BSM1). The results show that the proposed method can reduce ISE by 0.0014 and 0.0128 when the threshold is 2.5% in two cases, including the reference value being fixed and changed, compared with the case without considering the delay disturbance. The results of trigger mechanism test further demonstrate the effectiveness of event-triggered mechanism.