Abstract
This paper considers the problem of identifying (estimating) faults in systems described by linear models under exogenous disturbances. It is solved using optimal control methods; in comparison with sliding mode observers, they avoid high-frequency switching. The solution method proposed below involves a reduced model of the original system that is sensitive to faults and insensitive to disturbances. The corresponding theory is illustrated by an example.
REFERENCES
Edwards, C., Spurgeon, S., and Patton, R., Sliding Mode Observers for Fault Detection and Isolation, Automatica, 2000, vol. 36, pp. 541–553.
Floquet, T., Barbot, J., Perruquetti, W., and Djemai, M., On the Robust Fault Detection via a Sliding Mode Disturbance Observer, Int. J. Control, 2004, vol. 77, pp. 622–629.
Yan, X. and Edwards, C., Nonlinear Robust Fault Reconstruction and Estimation Using a Sliding Modes Observer, Automatica, 2007, vol. 43, pp. 1605–1614.
Rios, H., Efimov, D., Davila, J., Raissi, T., Fridman, L., and Zolghadri, A., Non-minimum Phase Switched Systems: HOSM Based Fault Detection and Fault Identification via Volterra Integral Equation, Int. J. Adapt. Contr. and Signal Proc., 2014, vol. 28, pp. 1372–1397.
Zhirabok, A.N., Zuev, A.V., Filaretov, V.F., et al., Fault Identification in Nonlinear Systems Based on Sliding Mode Observers with Weakened Existence Conditions, J. Comput. Syst. Sci. Int., 2022, vol. 61, no. 3, pp. 313–321.
Zhirabok, A., Zuev, A., Sergiyenko, O., and Shumsky, A., Identification of Faults in Nonlinear Dynamical Systems and Their Sensors Based on Sliding Mode Observers, Autom. Remote Control, 2022, vol. 83, pp. 214–236.
Zhirabok, A.N., Zuev, A.V., and Shumskii, A.E., Diagnosis of Linear Systems Based on Sliding Mode Observers, J. Comput. Syst. Sci. Int., 2019, vol. 58, no. 6, pp. 898–914.
Mironovskii, L.A., Funktsional’noe diagnostirovanie dinamicheskikh sistem (Functional Diagnosis of Dynamic Systems), Moscow–St. Petersburg: MGU-GRIF, 1998.
Hautus, M., Strong Detectability and Observers, Linear Algebra and Its Applications, 1983, vol. 50, pp. 353–368.
Korn, G.A. and Korn, Th.M., Manual of Mathematics, McGraw-Hill, 1967.
Mufti, I.H., Chow, C.K., and Stock, F.T., Solution of Ill-Conditioned Linear Two-Point Boundary Value Problems by the Riccati Transformation, SIAM Rev., 1969, vol. 11, no. 4, pp. 616–619.
Naidu, D.S., Optimal Control Systems, Electrical Engineering Handbook, Florida, Boca Raton: CRC Press, 2003.
Bryson, A.E. and Ho, Y.-C., Applied Optimal Control, Routledge, 1975.
Kwakernaak, H. and Sivan, R., Linear Optimal Control Systems, Wiley-Interscience, 1972.
Kim, S. and Kwon, S.J., Nonlinear Optimal Control Design for Underactuated Two-Wheeled Inverted endulum Mobile Platform, IEEE/ASME Transactions on Mechatronics, 2017, vol. 22, no. 6, pp. 2803–2808.
Funding
This work was supported by the Russian Science Foundation, project no. 22-19-00392; https://rscf.ru/project/22-19-00392/.
Author information
Authors and Affiliations
Corresponding authors
Additional information
This paper was recommended for publication by L.B. Rapoport, a member of the Editorial Board
Publisher’s Note.
Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kabanov, A.A., Zuev, A.V., Zhirabok, A.N. et al. Fault Identification: An Approach Based on Optimal Control Methods. Autom Remote Control 84, 956–965 (2023). https://doi.org/10.1134/S0005117923090059
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117923090059