Comparative Analysis of Canonical Forms in Fault Diagnosis and Estimation Problems

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.

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