Fault Diagnosis And Fault Tolerant Control For Non-gaussian Stochastic Systems Via Entropy

In the industrial process, chemical, aerospace and other practical applications, it is inevitable there will occur failure. In order to reduce the losses caused by failures, it is urgent to design effective fault diagnosis(FD) and fault-tolerant control(FTC) algorithms. These practical industrial application process are also subjected to a variety of random disturbance, then the study of FD and FTC for stochastic systems has became an integral and important part of industrial control processes.However, these random disturbance appearing in the practical system are not necessarily subjected to Gaussian distribution, therefore, FD and FTC for non-Gaussian stochastic systems is particularly important. The stochastic distribution control(SDC) system is a part of stochastic systems, where the system output is the probability density function(PDF) of the output not the actual output value. The industrial production, such as papermaking process, fiber particle size distribution of control, grinding fineness distributed process control, there can be seen as typical stochastic distribution system. For the research of fault diagnosis and fault tolerant control for SDC systems, it is crucially significant to improve and expand the research of stochastic systems.In this paper, paper making and grinding process as the background, combining the concept of entropy, FD and FTC algorithm, more suitable methods of FD and FTC are proposed for non-Gaussian stochastic systems. In the first part of this thesis, researching FD and FTC for general non-Gaussian stochastic systems is considered. FD and FTC for non-Gaussian random distribution systems is researched further. The specific contents are shown as follows:(1)As the uncertainty of non-Gaussian stochastic variables can not be fully represented by variance, and specific uncertainty and randomness characteristic of random variables can be represented by entropy. In this case, the concept of entropy is introduced to the research of FD and FTC for non-Gaussian stochastic systems. For non-Gaussian stochastic systems, considering when the fault occurs in the system. First, the filter is designed to obtain residual. The square root B-spline model is used to obtain probability density function of the residual. By minimizing the residual entropy performance function, the fault estimation is achieved. That the observation error system is locally and ultimately bounded in the mean-square sense is further proved. Using fault diagnosis information, active fault tolerant control algorithm based on tracking error entropy minimization for the closed-loop system is given. So that the system with fault still has a good output target value. Finally, computer simulation results verify the effectiveness of the minimum entropy FDD and FTC algorithm.(2)For the non-Gaussian singular stochastic distribution system based on rational square root B-spline approximation, in aspect of fault diagnosis, constructing the adaptive fault diagnosis observer, the fault diagnosis observer gain matrix can be obtained by solving linear matrix inequality(LMI). In aspect of fault-tolerant control, the situation that the target system output PDF is unknown, the fault tolerant controller should be designed to make the output variable uncertainty be minimized, thus the minimum Shannon entropy fault-tolerant control method is adopted. Constructing the performance function with regard to the entropy subjected to mean constraint, the purpose of fault-tolerant control is to seek a control input so that the performance functions minimized, enabling the post-fault system output have minimum uncertainty. Finally, computer simulation verifies the effectiveness of the above mentioned algorithm.(3) Fault diagnosis and minimum rational entropy FTC algorithm is researched for the non-Gaussian singular stochastic distribution system based on the square root B-spline approximation. Utilizing the nature of iterative learning observer, that the current input is updated by the previous time residuals and previous time. The fault diagnosis algorithm can be obtained. Observer gain matrix can be obtained by solving LMI. Using to the results of fault diagnosis, the fault tolerant controller can be designed. When the target system output PDF is unknown, the minimum Shannon entropy method can be used to design controller. But the use of Shannon entropy performance index may cause that non-negative of PDF can not be guaranteed, then the whole performance index maybe an indeterminate performance index. In order to overcome the limitations of Shannon entropy, the performance function with regard to the rational entropy subjected to mean constraint is used to design fault-tolerant controller, so that the output of the post-fault SDC system still have minimum uncertainty. Finally, computer simulation verifies the effectiveness of the fault diagnosis and minimum entropy algorithm.