Interval parity relations for fault diagnosis in discrete-time stationary dynamic systems

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

The problem of interval parity relations design to solve the problem of fault detection in stationary systems described by linear and nonlinear dynamic models under external disturbances is studied. It is assumed that a solution is based on the model of minimal dimension estimating some linear function of the system state vector and insensitive or having minimal sensitivity to the disturbances. The results obtained allow designing interval parity relations which are basis to solve the problem of fault diagnosis. Theoretical results are illustrated by example.

Full Text

Restricted Access

About the authors

A. Zhirabok

Far Eastern Federal University; Institute of Marine Technology Problems

Author for correspondence.
Email: zhirabok@mail.ru
Russian Federation, Vladivostok; Vladivostok

A. Zuev

Institute of Marine Technology Problems

Email: zhirabok@mail.ru
Russian Federation, Vladivostok

References

  1. Ефимов Д.В. Построение интервальных наблюдателей для динамических систем с неопределенностями // АиТ. 2016. № 2. С. 5–49.
  2. 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.
  3. 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.
  4. Chebotarev S., Efimov D., Raissi T., Zolghadri A. Interval Observers for Continuous-Time LPV Systems with L 1 /L 2 Performance // Automatica. 2015. V. 51. P. 82-89.
  5. Mazenc F., Bernard O. Asymptotically Stable Interval Observers for Planar Systems with Complex Poles // IEEE Trans. Automatic Control. 2010. V. 55. № 2. P. 523–527.
  6. Zheng G., Efimov D., Perruquetti W. Interval State Estimation for Uncertain Nonlinear Systems // IFAC Nolcos 2013. Toulouse, France, 2013.
  7. 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. № 2. https://doi.org/10.1080/00207179.2019.1687932
  8. Жирабок А.Н., Зуев А.В., Ким Чхун Ир. Метод построения интервальных наблюдателей для стационарных линейных систем // Изв. РАН. ТиСУ. 2022. № 5. С. 3-13.
  9. 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. №1. 2016.
  10. Zhang Z., Yang G. Interval Observer-Based Fault Isolation for Discrete-Time Fuzzy Interconnected Systems With Unknown Interconnections // IEEE Trans. on Cybernetics. № 5. 2017. https://doi.org/10.1109/TCYB.2017.2707462
  11. Kravaris C, Venkateswaran S. Functional Observers with Linear Error Dynamics for Nonlinear Systems // Systems Control Lett. 2021. V. 157. P. 105021.
  12. Liu L., Xie W., Khan A., Zhang L. Finite-Time Functional Interval Observer for Linear Systems with Uncertainties // IET Control Theory and Applications. 2020. V. 14. № 18. P. 2868–2878.
  13. Meyer L. Robust Functional Interval Observer for Multivariable Linear Systems // J. Dynamic Systems, Measurement, and Control. 2019. V. 141. № 9. Art. no. 094502.
  14. Venkateswaran S., Liu Q, Kravaris C. Design of linear Residual Generators for Fault Detection and Isolation in Nonlinear Systems // Int. J. Control. 2022. V. 95. P. 804–820.
  15. Venkateswaran S., Wilhite B., Kravaris C. Functional Observers with Linear Error Dynamics for Discrete-Time Nonlinear Systems, with Application to Fault Diagnosis // Preprint 2021. https://www.researchgate.net/publication/352177782
  16. Blanke M., Kinnaert M., Lunze J., Staroswiecki M. Diagnosis and Fault Tolerant Control. Berlin: Springer-Verlag, 2016.
  17. Жирабок А.Н. Диагностические наблюдатели и соотношения паритета: сравнительный анализ // АиТ. 2012. № 5. С. 141–160.
  18. Квакернаак Х., Сиван Р. Линейные оптимальные системы управления. М.: Мир, 1977.
  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. Zhirabok A., Shumsky A., Scherbatyuk A. Nonparametric Methods for Fault Diagnosis in Dynamic Systems // Int. J. Robust and Nonlinear Control. 2018. V. 28. № 17. P. 5424–5436.
  21. Жирабок А.Н., Шумский А.Е. Непараметрический метод диагностирования нелинейных динамических систем // АиТ. 2019. № 2. С. 24–45.
  22. Жирабок А.Н., Зуев А.В., Шумский A.Е., Бобко Е.Ю. Построение интервальных наблюдателей для дискретных нелинейных динамических систем // Мехатроника, автоматизация, управление. 2023. Т. 24. № 6. С. 283–291.
  23. Low X., Willsky A., Verghese G. Optimally Robust Redundancy Relations for Failure Detection in Uncertain Systems // Automatica. 1996. V. 22. P. 333–344.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Fig. 1. Behavior of residuals for the case of absence of defects.

Download (117KB)
Indexing metadata
3. Fig. 2. Behavior of residuals and when a defect appears.

Download (124KB)
Indexing metadata

Copyright (c) 2024 Russian Academy of Sciences