Research On Fault Diagnosis Of A Class Of Variable Coefficient Wave Equation

With the development of science and technology,control theory has been widely used in various industries,and in modern control theory,system failure is always a problem that has to be considered.In order to avoid the property loss caused by system failure as much as possible,it is necessary to detect the occurrence of faults and understand the nature of these faults as soon as possible.In the existing research,the fault diagnosis problem of ordinary differential system has a relatively perfect system,while the research on the fault diagnosis of partial differential system is relatively less.The fault diagnosis of partial differential equations has attracted more and more attention.This paper will study the fault diagnosis of a class of variable coefficient wave equations,as follows:1.We study the fault detection problem of the perturbed variable coefficient wave equation.Firstly,an observer is designed.And we construct the error system by this observer.After that we use the Lyapunov method to analyze the stability of the error system,design the appropriate residual and threshold according to the system output,give the fault detection logic: when the residual is greater than the threshold,the fault is detected;when the residual is less than the threshold,the system is considered to be in a healthy state.Finally,numerical simulations are given to verify the validity of the theoretical results.2.We discuss the boundary actuator fault diagnosis problem of variable coefficient cascade wave PDE-ODE equations.First we design a fault diagnosis scheme,identify actuator fault types off-line.Next,we design an observer for fault estimation and give the error system.Then we design the adaptive update law of fault estimation by Lyapunov method.Finally,we complete the well-posedness analysis of the system and give numerical simulation to verify the effectiveness of the above research.