Fault detection for linear discrete-time systems with output quantisation

ABSTRACT

This paper is concerned with the problem of fault detection for a class of linear discrete-time quantised feedback systems, and system outputs are, respectively, quantised by a uniform quantiser and a non-uniform quantiser. A novel unified method is proposed to deal with the two different types of quantisation errors, i.e. the quantisation errors are considered as unknown inputs of the residual generator. Then, an optimal residual generator is constructed to guarantee a suitable trade-off between the sensitivity to faults and the robustness against disturbances as well as quantisation errors. In order to detect the occurrence of faults, the generated residual signal is evaluated, and then two different thresholds based on the stochastic properties of quantisation errors are designed for these two quantisers. In addition, the false alarm rate is introduced to evaluate the fault detection performance. Finally, two examples are given to illustrate the feasibility of the proposed approach.

KEYWORDS:

• Fault detection
• output quantisation
• quantisation error
• threshold

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Erratum

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants 61433003, 61273150, 61573024. Beijing Natural Science Foundation under Grant 4142014. Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality under Grant CIT&TCD201304007, the Research Fund for the Doctoral Program of Higher Education of China under Grant 20121101110029.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant number 61433003], [grant number 61273150], [grant number 61573024]. Beijing Natural Science Foundation grant number 4142014]. Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality [grant number CIT&TCD201304007], the Research Fund for the Doctoral Program of Higher Education of China [grant number 20121101110029].