Stochastic fuzzy predictive fault‐tolerant control for time‐delay nonlinear system with actuator fault under a certain probability

Abstract

AbstractOwing to the characteristics of time‐delay, fault randomness, uncertainty, nonlinearity and unknown interference in industrial production processes, a stochastic fuzzy predictive fault‐tolerant control algorithm is put forward based on the traditional fault‐tolerant control algorithm. The main idea of this algorithm is to integrate actuator fault into the established Takagi‐Sugeno (T‐S) model to solve actuator fault under a certain probability for the nonlinear industrial processes with time‐varying delays by combining stochastic control theory and relevant theorems. First, the actuator fault under a certain probability is considered as a T‐S model, which can be used as a description of the fault situation in the nonlinear industrial processes. Afterwards, the augmented state space model is established through integrating state deviation and output tracking error. Second, the stochastic fuzzy predictive fault‐tolerant control law can be designed on the basis of the augmented model. Meanwhile, the actuator control mode for different faults is given. If the actuator fault is under a small probability, the control mode is switched to normal control; if the actuator fault is under a large probability, the control mode is switched to fault‐tolerant control. To this end, this control algorithm can reduce energy consumption and raw material consumption. On this basis, the designed control law can be solved by using the given stochastic stability conditions in terms of linear matrix inequality. Finally, the temperature control process of a strongly nonlinear continuous stirred tank reactor is selected as a simulation object to prove the feasibility and effectivity of this algorithm.