Comparative Analysis of Canonical Forms in Fault Diagnosis and Estimation Problems

Abstract

The paper considers the methods of different canonical forms application to the problems of fault diagnosis and estimation in technical systems described by linear dynamic models under disturbances. Identification and Jordan canonical forms are investigated. The main relations describing fault diagnosis and estimation problems for different canonical forms are given, and comparative analysis of possibility of their application is performed. An analysis shows that the identification canonical form produces relations enable developing algorithms for the diagnostic observer and estimator design while Jordan canonical form assumes using some heuristic methods. It was shown that Jordan canonical form is more preferable to guarantee full disturbance decoupling, that is invariance with respect to the disturbance. On the other hand, when full decoupling is impossible, the identification canonical form enables developing algorithm of partial decoupling while Jordan canonical form assumes using some heuristic methods. The advantage of Jordan canonical form is that it ensures stability of the designed system based on properties of the matrix describing this form while the identification canonical form assumes using feedback based on the residual which must be generated. This allows for Jordan canonical form to reduce the dimension of the designed diagnostic observer and estimator. The new method to guarantee sensitivity of the diagnostic observer to the faults is developed. The method is based on analysis of the observability matrix and new rules to calculate matrices describing the diagnostic observer. Theoretical results are illustrated by practical example of well known three tank system.