Fault Diagnosis And Minimum Entropy Fault Tolerant Control Of Non-gaussian Stochastic Distribution Systems

Fault diagnosis and fault tolerant control is one of the important ways to improve reliability and safety for dynamic systems. Over the past decades, fault diagnosis and fault tolerant control for stochastic dynamic systems have always been one of the important areas of research in control theory and applications. In these existing approaches, it is supposed that system fault, stochastic input or disturbance signal obeys Gaussian distribution. However, this assumption is not completely applicable to the practical application process. For many practical systems, the system representation has to be made between the input and the output probability density function, rather than the output itself. It is called the stochastic distribution control system (SDCs). Sometimes the target probability density function can’t be determined in advance and as a result, fault tolerant control can be converted to control the output variable, and make it have the smallest uncertainty. Traditional statistics such as variance can be used to represent the randomness of the system output. However, for non-Gaussian systems, the variance cannot fully represent the randomness of the system output. Therefore entropy concept is proposed to measure the uncertainty of the stochastic system. At present for non-Gaussian stochastic distribution system, there is no literature reported the fault tolerant control when the target probability density function cannot be determined in advance.In this thesis, for the non-Gaussian stochastic distribution control system, fault diagnosis algorithm based on the observer is proposed to estimate the size of the fault. When target probability density function cannot be determined in advance, the concept of entropy is introduced to the fault tolerant control of the stochastic distribution system. Based on the fault estimation information, fault tolerant control scheme is presented to make the system entropy minimized. The main contents of this thesis include following issues:(1) The linear B-spline model is used to approximate the output PDF. Considering the linear and nonlinear dynamics respectively, the fault diagnosis methods are proposed based on the adaptive observer. When the objective probability density function can’t be determined in advance, control target of the SDC system can be translated into controlling the entropy of the output PDF. Because entropy is a concave function, the minimum entropy of the output variables is generally difficult to be determined in practice. Therefore, control target subjected to mean constraint will be suitable for the solution of the minimum entropy controller. Finally, on the basis of fault diagnosis information, the minimum entropy fault tolerant controller is designed by minimizing the entropy performance index, which is subjected to mean constraints. Simulation results are given to illustrate the effectiveness of the proposed algorithms.(2) The rational square-root B-spline model is given to approximate the output PDF. The fault diagnosis method based on the iterative learning observer is proposed. Using the Lyapunov stability theorem, the stability analysis of the observation error system is carried out to determine the parameter of the iterative learning observer. Based on the fault estimation information and observer state information, through the controller reconfiguration, the system entropy can still be minimized, leading to the minimum entropy fault tolerant control subjected to mean constraint. Computer simulations are given to show the effectiveness of the proposed fault diagnosis algorithm, whether the abrupt fault, the slow-varying fault or the fast-varying fault occurs.(3) For either the linear B-spline model or the rational square-root B-spline model, the expression of the minimum entropy fault tolerant controller is implicit. For a class of discrete stochastic distribution systems, based on the optimal control principle, the control input can be designed to make the performance index function about the entropy be minimized. This goal can be achieved by making the partial derivative of the performance index function about the entropy to control input equal zero. Thus the explicit expression of the minimum entropy fault tolerant controller is obtained.