Research On Fault Diagnosis Of Under-measurement System And Overactuated System With Space Geometric Approach

Commonly called fault diagnosis is the process that we use specific mathematical methods and toolsfor fault isolation and complete the fault correcting after determining the occurrence of a failure by faultdetection.Fault diagnosis technology can be divided into a variety of forms based on its different data andmodels. This paper is mainly for dealing fault detection and isolation problem in linear time invariantsystem, using space geometric approach to do fault analysis and research. Geometric methods change thecontrollability and observability of the system into the geometric properties of the state space, which ischaracterized by transforming a complex matrix operation into a simple space projection operation, clearand concise. The use of unobservable subspace can constructed independently residual signal set or residualsignal set under the state of the case related measurement，achieve correspondence between residual signalsand failure features, complete fault detection and isolation when system abnormalities comes.In this paper, a method based on space geometric theory is used for researching fault detection andisolation, first, create the corresponding system fault model, and design related residual generator, and thenget the final residuals through the parameter matrix and simulation experiments, this step is to achieve thedecoupling of residuals for system input and noise and disturbance, but also to achieve the specific failuresensitive, thereby achieve the other fault decoupling and complete fault detection and isolation finally. Onthe base of realizing the actuator fault detection and isolation for control matrix and measurement matrixare full ranks in linear time invariant system with input disturbances and measurement noises, this articledoes many researches on the following two points.1) For the issue that the measurement matrix is not of full rank in the system equation, the sensorfailure mode is directly converted into state, complete the system model for the establishment ofsensor failure. Firstly, design a residual generator according to the linear system theory. Secondly,using the decoupling between the fault features of the extended unobservable subspace to realizethe solution of parameter matrix in residuals generator that based on space geometric method.Ultimately, each sensor fault can be detected and isolated. 2) For the overactuator system, considering the existence of random interference measurements, onaccount of the space geometric theory，residual generator is constructed and solved to achieveobservation for unique residual faults，but to achieve decoupling for other failures. Theoreticalderivation proves that this algorithm can directly realize the decoupling of input andmeasurement interference, so that the fault residuals generated by the input and measurementinterference are not affected, and complete the system’s fault detection and isolation in the end.