Fault Diagnosis And Fault Tolerant Control For Non-Gaussian Uncertain Stochastic Distribution Control Systems

With the development of modern industry,the complexity of industrial and engineering control system increased rapidly,and the requirement of reliability and security of practical industrial process control system increased day by day.Once fault occurred in the process of system operation,if the fault can not be detected and diagnosed timely and the right way is taken to eliminate the impact,there will be very serious consequences.It makes the research of fault diagnosis and fault tolerant control received more and more attentions.The practical industrial applications are subjected to a variety of unknown stochastic disturbances,then the study of stochastic system control becomes an important part of control theory and applications.The traditional research of stochastic systems is based on the assumption that stochastic variables obey Gaussian distribution.However,in practical applications,this assumption is not always true.As a branch of stochastic systems,the shape of output probability density function(PDF)is controlled directly for stochastic distribution control(SDC)systems,avoiding the restriction of the distribution of stochastic variables.The study of SDC systems has a wide range of applications on some practical industrial processes,such as the process control of papermanufacturing,the distribution control of ore particle size in the process of grinding,the high polymer polymerization control and the flame distribution control.Besides,because of the complexity of practice systems,the difference between the model and the practical objects caused by simplified system modeling,environmental changes or parameter drift is called model uncertainty.These uncertainties are different from the external uncertain factors such as external disturbances and noise,making the application of fault diagnosis and fault tolerant control technique more difficult,and reducing the sensitivity and accuracy of fault diagnosis and tolerant control.It is necessary for us to study the fault diagnosis and fault tolerant control of non-Gaussian uncertain SDC systems.Based on the background of paper-manufacturing and coal-layer-fired boiler,fault diagnosis and fault tolerant control of non-Gaussian uncertain SDC systems is researched systematically in this paper.The specific contents are shown as follows:(1)For the non-Gaussian uncertain SDC systems,the linear B-spline model is adopted to approximate the system output PDF,and the weights system model is established.First a tracking controller is designed based on the weights tracking error when fault does not occur,in order to make the output PDF tracking the desired one.The boundedness of the weight vector is proved.When fault occurred,an adaptive observer is designed to diagnose the fault.Then the system input and desired weight vector are augmented as a new control input,and the augmented input is constructed based on the integral of the output PDF tracking error and the fault estimation.Thus the reconstructed fault tolerant controller is designed to make the post-fault output PDF track the desired PDF.Finally,simulation results show the effectiveness of the fault diagnosis and fault tolerant control algorithm for a constant fault.(2)For the non-Gaussian uncertain SDC system with PDF approximation error,the linear B-spline model is adopted to approximate the system output PDF.An integral fault diagnosis and sliding mode fault tolerant control algorithm is proposed.Based on the thought of unknown input observer,an augmented adaptive observer is designed by regarding the uncertain input and PDF approximation error as unknown external disturbances,and the stability of the augmented observation error dynamic system and?H performance index is proved.Based on the weight tracking error dynamic system,the integral switch function is designed,and using the information of fault diagnosis,the sliding mode fault tolerant controller is designed to make the post-fault output PDF still track the desired PDF.The stability of both the closed-loop control system and the tracking error dynamic system is proved.Two different illustrated examples are given to demonstrate the effectiveness of the proposed algorithm for complex time-varying fault.(3)For the non-Gaussian uncertain singular SDC system with PDF approximation error,the square-root B-spline model is adopted to approximate the PDF of the system output.A PDF tracking controller is constructed to make the output PDF track the desired one before fault occurring based on the feedback of integral of the PDF tracking error,the impact of uncertainty and PDF approximationerror is eliminated,and the boundedness of the state vector is proved.An adaptive fault diagnosis observer is designed to estimate the fault information.When fault occurred,the tracking controller is reconfigured to ensure that the post-fault output probability density function still track the desired one using the fault information.The Lyapunov stability theory is used to analyse the stability of the observation error dynamic system,the closed-loop system and the tracking error dynamic system,and the gain matrices are solved by linear matrix inequalities(LMIs).An illustrated example is given to demonstrate the effectiveness of the proposed algorithm for time-varying fault.