Fixed-Time Fault-Tolerant Control for Wastewater Treatment Processes With Asymmetric State Constraints

In wastewater treatment processes (WWTPs), the presence of aeration equipment faults (actuator faults) prevents the desired tracking control effect of the state-constrained dissolved oxygen concentration (DOC). To solve this problem, an adaptive fixed-time fault-tolerant control (AFTFTC) strategy based on the asymmetric integral barrier Lyapunov function (AIBLF) is developed in this article. First, in order to directly consider asymmetric state constraints in the controller design process, an AIBLF is constructed. Second, a fixed-time FTC method is proposed to compensate for the effects of actuator faults on DOC regulation and achieve fast tracking of the DOC setpoint. Specifically, the adaptive compensation term with DOC asymmetric constraint boundaries is used to estimate the unknown boundary of the actuator bias fault (BF). Furthermore, it is proven that the designed controller can ensure the fixed-time stability of the closed-loop system. Finally, the validity of the control strategy is validated on the benchmark simulation model 1 (BSM1).