Fault Diagnosis And Fault Tolerant Control For Non-Gaussian Stochastic Distribution Control Systems Using T-S Fuzzy Model

With the development of modern industrial technology, industrial control engineering becomes more and more complex. The non-linearity, uncertainty, multivariable, time delay and external disturbance makes it difficult for the researchers to build precise mathematical models for controlled objects. Only using traditional control theories and methods is difficult to meet the design requirements of complex control systems.In 1985, the Takagi-Sugeno fuzzy model was put forward by Japanese scholars T. Takagi and M. Sugeno. T-S fuzzy model, without needing to know the precise mathematical models of controlled objects, for the different regions of nonlinear systems, the locally linear models were built, and then the locally linear models were linked by fuzzy membership function to approximate global nonlinear systems, solving the problem of analysis and control of the nonlinear systems, which breaks a new path for the research of nonlinear systems.Most research of stochastic distribution systems is based on the assumption that stochastic variables obey Gaussian distribution. However, in practical application, the stochastic variables not always obey Gaussian distribution. For example, controlling of pulp uniformity in the process of paper-manufacturing, controlling of ore particle size in the process of grinding, the high polymer polymerization and the flame distribution control are all required to control the system output PDF shape. Based on these practical application background, Professor Hong Wang put forward new stochastic distribution control theory, in which the crisp control input is directly designed to make the output PDF track the given distribution. Stochastic distribution systems include Gaussian systems and non-Gaussian systems. After more than ten years of research, there are many literatures about modeling, control algorithm design and fault diagnosis. Most research of fault diagnosis (FD) and fault tolerant control (FTC) of stochastic distribution systems is based on linear stochastic distribution systems. Few published papers have discussed the nonlinear stochastic distribution systems. T-S fuzzy model breaks a new path for the research of nonlinear system. Based on the above background, this paper launched a study on the non-Gaussian stochastic distribution control system using T-S fuzzy model.The specific contents of this paper are as follows:(1) For the non-Gaussian nonlinear stochastic distribution control system using the Takagi-Sugeno fuzzy model, the linear B-spline is adopted to approximate the PDF of the system output. In order to diagnose the fault that occurred in the system, the residual signal is used to construct the adaptive fault diagnosis observer. And the relevant parameters can be obtained by solving linear matrix inequality (LMI). Then the weight error dynamic system can be obtained and the integral switching function is designed. According to the sliding mode control theory, the equivalent control law can be obtained. Integral switching surface and sliding mode control law can ensure that the system is asymptotically stable. By designing the sliding mode control law, the moving point that starts from any position can reach the switching surface in limited time. Finally, simulation results show the effectiveness of the fault diagnosis algorithm and the sliding mode fault tolerant control algorithm in our study.(2) For the non-Gaussian nonlinear stochastic distribution control system using Takagi-Sugeno fuzzy model, the adaptive fault diagnosis observer is designed to diagnose the fault that occurred in the system. A reference model with perfect dynamics features is given. According to the bounded real lemma and the regional pole assignment theory, the relevant parameters can be obtained and the H∞ performance index is satisfied. The fault tolerant tracking controller can be designed based on the fault information, the desired state and the residual signal, which makes the post-fault output PDF still track the desired PDF. Finally, simulation results show the effectiveness of the fault diagnosis algorithm and the model reference fault tolerant control algorithm in our study.(3) For the non-Gaussian nonlinear singular stochastic distribution control system using Takagi-Sugeno fuzzy model, the square root B-spline is adopted to approximate the PDF of the system output. The adaptive fault diagnosis observer is designed to diagnose the fault that occurred in the system, and the relevant parameters can be obtained by solving linear matrix inequality (LMI). Based on the fault information, the desired state and the residual signal, the fault tolerant tracking controller can be designed to make the post-fault output PDF still track the desired PDF. Finally, simulation results show the effectiveness of the fault diagnosis algorithm and the model reference fault tolerant control algorithm in our study.