An Interval Observer-Based Method to Diagnose Discrete-Time Systems

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

This paper proposes a method for diagnosing linear dynamic systems described by discrete-time models with exogenous disturbances based on interval observers. Formulas are derived to construct an interval observer producing two values of the residual as follows: if zero is between these values, then the system has no faults to be detected by the observer. The case where zero does not belong to the interval between these values is qualified as the occurrence
of a fault. The theoretical results are illustrated by an example.

About the authors

A. N. Zhirabok

Far Eastern Federal University; Institute of Marine Technology Problems, Far Eastern Branch, Russian Academy of Sciences

Email: zhirabok@mail.ru
Vladivostok, Russia; Vladivostok, Russia

A. V. Zuev

Far Eastern Federal University; Institute of Marine Technology Problems, Far Eastern Branch, Russian Academy of Sciences

Author for correspondence.
Email: alvzuev@yandex.com
Vladivostok, Russia; Vladivostok, Russia

References

  1. Жирабок А.Н., Зуев А.В., Ким Чхун Ир. Метод построения интервальных наблюдателей для стационарных линейных систем // Известия РАН. Теория и системы управления. 2022. № 4. С. 22-32.
  2. Жирабок А.Н., Зуев А.В., Филаретов В.Ф., Шумский А.Е., Ким Чхун Ир. Каноническая форма Жордана в задачах диагностирования и оценивания // АиТ. 2022. № 9. С. 49-67.
  3. Ефимов Д.В., Раисси Т. Построение интервальных наблюдателей для динамических систем с неопределенностями // АиТ. 2016. № 2. С. 5-49.
  4. Khan A., Xie W., Zhang L., Liu L. Design and applications of interval observers for uncertain dynamical systems // IET Circuits Devices Syst. 2020. V. 14. P. 721-740.
  5. Кремлев А.С., Чеботарев С.Г. Синтез интервального наблюдателя для линейной системы с переменными параметрами // Изв. вузов. Приборостроение. 2013. Т. 56. № 4. C. 42-46.
  6. Efimov D., Raissi T., Perruquetti W., Zolghadri A. Estimation and control of discrete-time LPV systems using interval observers // 52nd IEEE Conf. On Decision and Control. Florence, Italy. 2013. P. 5036-5041.
  7. Chebotarev S., Efimov D., Raissi T., Zolghadri A. Interval observers for continuoustime LPV systems with L1/L2 performance // Automatica. 2015. V. 51. P. 82-89.
  8. Mazenc F., Bernard O. Asymptotically stable interval observers for planar systems with complex poles // IEEE Trans. Automatic Control. 2010. V. 55. No. 2. P. 523-527.
  9. Zheng G., Efimov D., Perruquetti W. Interval state estimation for uncertain nonlinear systems // IFAC Nolcos 2013. Toulouse, France, 2013.
  10. Zhang K., Jiang B., Yan X., Edwards C. Interval sliding mode based fault accommodation for non-minimal phase LPV systems with online control application // Int. J. Control. 2019. https://doi.org/10.1080/00207179.2019.1687932
  11. Kolesov N., Gruzlikov A., Lukoyanov E. Using fuzzy interacting observers for fault diagnosis in systems with parametric uncertainty // Proc. XII-th Inter. Symp. Intelligent Systems, INTELS'16, 5-7 October 2016, Moscow, Russia. P. 499-504.
  12. Zhang Z., Yang G. Fault detection for discretetime LPV systems using interval observers // Int. J. Syst. Sci. 2017. https://doi.org/10.1080/00207721.2017.1363926
  13. Zhang Z., Yang G. Event-triggered fault detection for a class of discrete-time linear systems using interval observers // ISA Transactions. 2017. https://doi.org/10.1016/j.isatra.2016.11.016
  14. Zhang Z., Yang G. Interval observer-based fault isolation for discrete-time fuzzy interconnected systems with unknown interconnections // IEEE Trans. Cybernetics. 2017. https://doi.org/10.1109/TCYB.2017.2707462
  15. Yi Z., Xie W., Khan A., Xu B. Fault detection and diagnosis for a class of linear time-varying discrete-time uncertain systems using interval observers // Proc. 39th Chinese Control Conf., July 27-29, 2020, Shenyang, China. P. 4124-4128.
  16. Rotondo D., Fernandez-Cantia R., Tornil-Sina S., Blesa J., Puig V. Robust fault diagnosis of proton exchange membrane fuel cells using a Takagi-Sugeno interval observer approach // Int. J. Hydrogen Energy. 2015. P. 2875-2886.
  17. Saijai J., Ding S., Abdo A., Shen B., Damlakhi W. Threshold computation for fault detection in linear discrete-time Markov jump systems // Int. J. Adapt. Control Signal Process. 2014. Vol. 28. P. 1106-1127.
  18. Шумский А.Е., Жирабок А.Н. Принятие решений при диагностировании нелинейных динамических систем непараметрическим методом // АиТ. 2021. № 2. С. 111-131.
  19. Жирабок А.Н., Шумский А.Е., Соляник С.П., Суворов А.Ю. Метод построения нелинейных робастных диагностических наблюдателей // АиТ. 2017. № 9. С. 34-48.
  20. Low X., Willsky A., Verghese G. Optimally robust redundancy relations for failure detection in uncertain systems // Automatica. 1996. Vol. 22. P. 333-344.

Copyright (c) 2023 The Russian Academy of Sciences

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies