Part of the book series:Advances in Intelligent Systems and Computing ((AISC,volume 1196))
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Abstract
The conditions for observer based residual filter design for linear discrete-time state-multiplicative systems are presented in the paper. With respect to the residual signal’s time evolution, as well as to its robustness, the design problem is stated in terms of linear matrix inequalities (LMI). To expand the standard LMI formulation, norm bounds on disturbance and, in particular, a new characterisation of the norm boundaries of the multiplicative faults are projected into enhanced bounded real lemma structure of LMI. With given restrictions, the design steps are revealed in the example for projecting the state estimation error to fault residuals.
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References
Chiang, L.H., Russell, E.L., Braatz, R.D.: Fault Detection and Diagnosis in Industrial Systems. Springer, London (2001).https://doi.org/10.1007/978-1-4471-0347-9
Ellis, G.: Observers in Control Systems. A Practical Guide. Academic Press, San Diego (2002)
Ferdowsi, H., Jagannathan, S.: Unified model-based fault diagnosis scheme for nonlinear discrete-time systems with additive and multiplicative faults. In: Proceedings 50th IEEE Conference on Decision and Control and European Control Conference CDC-ECC 2011, Orlando, USA, pp. 1570–1575 (2011).https://doi.org/10.1109/CDC.2011.6161292
Filasová, A., Krokavec, D., Liššinský, P.: Conditions with D-stability circle area in design of observer-based fault estimation. Appl. Math. Sci.10(35), 1705–1717 (2016).https://doi.org/10.12988/ams.2016.63112
Gao, Z.: Fault estimation and fault-tolerant control for discrete-time dynamic systems. IEEE Tran. Ind. Electron.62(4), 3874–3884 (2015).https://doi.org/10.1109/TIE.2015.2392720
Gao, C., Duan, G.: Robust adaptive fault estimation for a class of nonlinear systems subject to multiplicative faults. Circuits Syst. Sig. Proces.31(6), 2035–2046 (2012).https://doi.org/10.1007/s00034-012-9434-x
Gershon, E., Shaked, U., Yaesh, I.: H\(_{\infty }\) Control and Estimation of State-Multiplicative Linear Systems. Springer, London (2005).https://doi.org/10.1007/b103068
Gertler, J.: Fault Detection and Diagnosis in Engineering Systems. CRC Press, Boca Raton (1998)
Kim, K.S., Rew, K.H.: Reduced order disturbance observer for discrete-time linear systems. Automatica49(4), 968–975 (2013).https://doi.org/10.1016/j.automatica.2013.01.014
Korovin, S.K., Fomichev, V.V.: State Observers for Linear Systems with Uncertainty. Walter de Gruyter, Berlin (2009)
Krokavec, D., Filasová, A.: H\(_{\infty }\) norm principle in residual filter design for discrete-time linear positive systems. Eur. J. Control45, 17–29 (2019).https://doi.org/10.1016/j.ejcon.2018.10.001
Krokavec, D., Filasová, A.: On fault detection for discrete-time linear state-multiplicative systems with uncorrelated multiplicative faults. In: Proceedings 6th International Conference on Control, Decision and Information Technologies CoDIT 2019, Paris, France, pp. 894–899 (2019).https://doi.org/10.1109/CoDIT.2019.8820338
Lin, Y., Stadtherr, M.A.: Fault detection in continuous-time systems with uncertain parameters. In: Proceedings American Control Conference ACC 2007, New York, USA, pp. 3216–3221 (2007).https://doi.org/10.1109/ACC.2007.4282164
Luenberger, D.G.: Introduction to Dynamic Systems. Theory, Models and Applications. Wiley, New York (1979)
Peaucelle, D., Henrion, D., Labit, Y., Taitz, K.: User’s Guide for SeDuMi Interface 1.04, LAAS-CNRS, Toulouse (2002)
Acknowledgment
The work presented in this paper was supported by VEGA, the Grant Agency of the Ministry of Education and the Academy of Science of Slovak Republic under Grant No. 1/0608/17. This support is very gratefully acknowledged.
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Faculty of Electrical Engineering and Informatics, Department of Cybernetics and Artificial Intelligence, Technical University of Košice, Letná, 04200, Košice, Slovakia
Dušan Krokavec & Anna Filasová
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Correspondence toDušan Krokavec.
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Institute of Automatic Control, Lodz University of Technology, Lodz, Poland
Andrzej Bartoszewicz
Institute of Automatic Control, Lodz University of Technology, Lodz, Poland
Jacek Kabziński
Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland
Janusz Kacprzyk
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Krokavec, D., Filasová, A. (2020). Detection of State-Multiplicative Faults in Discrete-Time Linear Systems. In: Bartoszewicz, A., Kabziński, J., Kacprzyk, J. (eds) Advanced, Contemporary Control. Advances in Intelligent Systems and Computing, vol 1196. Springer, Cham. https://doi.org/10.1007/978-3-030-50936-1_118
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