Virtual Sensors in the Fault Diagnosis Problem

Abstract

The paper is devoted to the problem of fault diagnosis (isolation and identification) in linear dynamic systems under disturbances. The performances of fault diagnosis depend on the sensors which are in the system under diagnosis. To improve the performances, additional sensors can be applied. But sometimes it is impossible to use such sensors; besides they have low reliability. In this paper, we suggest to use so-called virtual sensors instead of additional ones. To obtain such sensors,Luenberger observers can be used. Such an observer is designed in two steps. On the first step, the model of minimal dimension invariant with respect to the disturbances and estimating a predetermined component of the system state vector and some other components of the system state vector is designed. The second components are necessary to provide stability of the observer by means of generating residual and using feedback. Such components are determined during t  he process of the problem solution which is based on the canonical form of matrices describing the model. On the second step, the feedback matrix is found based on the required quality of transient. To obtain this matrix, eigenvalues are selected and coefficients of the characteristic equation are calculated. The rule to find the predetermined component of the system state vector to be estimated by vir tual obser ver is suggested. Theoretical results are illustrated by practical example of well known three tank system.