Fault Tolerant Control For Failure System Via Observer Technique

Fault tolerant control(FTC)is an emerging interdisciplinary.The theoretical basis of FTC includes statistical mathematics,modern control theory,signal processing,pattern recognition,optimization method,decision theory,etc.And related subjects are fault detection and diagnosis,robust control,adaptive control,sliding mode control,intelligent control,etc.FTC studies control problems when the system fails,and it involves a wide range of fields,such as artificial intelligence,computer science,automation science and related production fields.Specifically speaking,before or after the device fails,according to the detected fault information,corresponding fault tolerant control measures are taken for different fault sources and fault features to ensure the normal operation of the device.FTC has the effect that the feedback of the system is insensitive to faults.Its research and application will not only effectively improve the automation level of the related industrial production fields,but also provide new growth points for the combination of control theory and artificial intelligence.Implementing FTC is an effective mean to improve the reliability of dynamic systems.In recent years,the research on FTC concerning dynamic system has been gradually perfected in theory and has been applied in practice.However,there are still many issues to be studied.This paper mainly studies the fault tolerant control problems of Markov jump systems and nonlinear discrete systems,based on observer.(1)The research of Markov jump system(MJS)has always been a hot topic in academic circles.However,most studies on the control problem of MJS assume that the transfer probability is known.This paper discusses the general case of transition probability for MLJs,that is,the case where the transition probability is partially known.At the same time,the MLJs here have actuator failures.Firstly,the conditions of the transition probability are clarified,including completely known,unknown but the upper and lower bound information are available and completely unknown.Secondly,an iterative approach is used to design the learning observer for the system,meanwhile estimate system status and failures.Thirdly,fault tolerance control law is designed based on the designed learning observer to ensure the progressive stability of the system.Finally,a comparative study was conducted to demonstrate the feasibility and effectiveness of the method.(2)The research results of discrete system observer design problems are relatively few.This paper discusses the design of nonlinear discrete-time system observers and fault-tolerant controllers with sensor failures.Firstly,in order to implement the simultaneous estimation of states and faults,the original system is transformed into a generalized system by using transformation,and the observability of the system is judged by the theoretical knowledge of the generalized system.Secondly,based on the sliding mode control theory,the PD sliding mode observer is designed for the generalized system,and the augmented state vector is observed.Thirdly,a fault-tolerant controller is designed.Finally,the effectiveness of the numerical example verification method is given.