Fault diagnosis in discrete time hybrid systems - A case study

  • Authors:

  • Prodip Bhowal;Dipankar Sarkar;Siddhartha Mukhopadhyay;Anupam Basu

  • Affiliations:

  • Investment Projects (Corporate Expert Group, Process Automation) Mittal Steel, Poland SA, Poland;Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur 721 302, India;Department of Electrical Engineering, Indian Institute of Technology, Kharagpur 721 302, India;Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur 721 302, India

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2007

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Abstract

A method of analysing diagnosability of discrete time hybrid systems (DTHS), which are similar to the simple n-rate timed automata [R. Alur, C. Courcoubetis, T.A. Henzinger, P. Ho, Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems, in: Hybrid Systems, LNCS 736, Springer Verlag, 1993, pp. 209-229], has been proposed. A state based fault modeling formalism is used. The properties of the DTHS model, under measurement limitations due to inadequacy or non-availability of sensors, are discussed. A definition of diagnosability for DTHS models has been adopted from the one proposed in [M. Sampath, R. Sengupta, S. Lafortune, K. Sinnamohideen, D. Teneketzis, Diagnosability of discrete-event systems, IEEE Transactions on Automatic Control 40 (9) (1995) 1555-1575] for discrete-event system (DES) models. Based on the measurement limited DTHS models, an algorithm for construction of a diagnoser is presented. It is next demonstrated through an example of a chemical reaction chamber that the diagnosability condition (over the diagnoser), which has been shown to be necessary and sufficient for DES diagnosability, fails to hold for many systems. This is so because the abstraction employed in DES modeling obliterates an important feature of the transitions namely fairness. Exploiting the explicit continuous dynamics of the DTHS models, the fairness of transitions is identified and used to demonstrate diagnosability. The diagnosability condition over the diagnoser is suitably modified to encompass the situations typified by the example.