Sensor fault estimation for hydraulic servo actuator based on sliding mode observer

Vladimir Djordjevic; Ljubisa Dubonjic; Marcelo Menezes Morato; Dragan Prsic; Vladimir Stojanovic; Vladimir Djordjevic; Ljubisa Dubonjic; Marcelo Menezes Morato; Dragan Prsic; Vladimir Stojanovic

doi:10.3934/mmc.2022005

Mathematical Modelling and Control

2022, Volume 2, Issue 1: 34-43. doi: 10.3934/mmc.2022005

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Research article

Sensor fault estimation for hydraulic servo actuator based on sliding mode observer

1.
Faculty of Mechanical and Civil Engineering, University of Kragujevac, 36000 Kraljevo, Serbia
2.
Departamento de Automação e Sistemas, Universidade Federal de Santa Catarina, Florianópolis, Brazil
3.
Univ. Grenoble-Alpes, CNRS, Grenoble INP^T, GIPSA-Lab, 38000 Grenoble, France

Received: 10 January 2022 Revised: 26 January 2022 Accepted: 28 January 2022 Published: 08 March 2022

In this paper, the mechanism for the fault estimation (FE) problem for a hydraulic servo actuator (HSA) with sensor faults is investigated. To deal with the design issues, we transformed the nonlinear model of HSA into a new coordinate system to estimate the sensor faults. In the new coordinate system, the Lipschitz conditions and system uncertainties are also considered. Then, we implement a sliding mode observer (SMO) approach to introduce the transformation scheme to make the system rational. The proposed fault estimation scheme essentially transforms the original system into two subsystems where the first one includes system uncertainties, but is free from sensor faults and the second one has sensor faults but without uncertainties. The effects of system uncertainties on the estimation errors of states and faults are minimized by integrating an $ H_\infty $ uncertainty attenuation level into the observer. The sufficient conditions for the state estimation error to be bounded and satisfy a prescribed $ H_\infty $ performance are derived and expressed as a linear matrix inequality (LMI) optimization problem. Finally, the numerical example with simulation results is provided to validate the practicability and efficacy of the developed control strategy.
- fault estimation,
- sensor faults,
- hydraulic servo actuator,
- sliding-mode observer,
- system uncertainties
Citation: Vladimir Djordjevic, Ljubisa Dubonjic, Marcelo Menezes Morato, Dragan Prsic, Vladimir Stojanovic. Sensor fault estimation for hydraulic servo actuator based on sliding mode observer[J]. Mathematical Modelling and Control, 2022, 2(1): 34-43. doi: 10.3934/mmc.2022005

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Abstract

In this paper, the mechanism for the fault estimation (FE) problem for a hydraulic servo actuator (HSA) with sensor faults is investigated. To deal with the design issues, we transformed the nonlinear model of HSA into a new coordinate system to estimate the sensor faults. In the new coordinate system, the Lipschitz conditions and system uncertainties are also considered. Then, we implement a sliding mode observer (SMO) approach to introduce the transformation scheme to make the system rational. The proposed fault estimation scheme essentially transforms the original system into two subsystems where the first one includes system uncertainties, but is free from sensor faults and the second one has sensor faults but without uncertainties. The effects of system uncertainties on the estimation errors of states and faults are minimized by integrating an $ H_\infty $ uncertainty attenuation level into the observer. The sufficient conditions for the state estimation error to be bounded and satisfy a prescribed $ H_\infty $ performance are derived and expressed as a linear matrix inequality (LMI) optimization problem. Finally, the numerical example with simulation results is provided to validate the practicability and efficacy of the developed control strategy.

References

[1]	J. Vyas, B. Gopalsamy, H. Joshi, Electro-Hydraulic Actuation Systems: Design, Testing, Identification and Validation, 1st Eds., Singapore: Springer, 2019. https://doi.org/10.1007/978-981-13-2547-2
[2]	A. Vacca, G. Franzoni, Hydraulic Fluid Power: Fundamentals, Applications, and Circuit Design, 1st Eds., New Jersey: Wiley, 2021. https://doi.org/10.1002/9781119569145
[3]	N. Manring, Fluid Power Pumps and Motors: Analysis, Design and Control, 1st Eds., New York: McGraw-Hill Education, 2013.
[4]	J. Zhang, A. Swain, S. Nguang, Detection and isolation of incipient sensor faults for a class of uncertain nonlinear systems, IET Contr. Theory Appl., 6 (2012), 1870–1880. https://doi.org/10.1049/iet-cta.2011.0440 doi: 10.1049/iet-cta.2011.0440
[5]	P. Zhang, J. Zou, Observer-based fault diagnosis and self-restore control for systems with measurement delays, Asian J. Control, 14 (2012), 1717–1723. https://doi.org/10.1002/asjc.458 doi: 10.1002/asjc.458
[6]	D. Jayamaha, N. Lidula, A. Rajapakse, Wavelet-multi resolution analysis based ANN architecture for fault detection and localization in DC microgrids, IEEE Access, 3 (2019), 145371–145384. https://doi.org/10.1109/ACCESS.2019.2945397 doi: 10.1109/ACCESS.2019.2945397
[7]	Z. Wang, Y. Shen, X. Zhang, Actuator fault estimation for a class of nonlinear descriptor systems, Int. J. Syst. Sci., 45 (2014), 487–496. https://doi.org/10.1080/00207721.2012.724100 doi: 10.1080/00207721.2012.724100
[8]	J. Yang, Y. Guo, W. Zhao, Long short-term memory neural network based fault detection and isolation for electro-mechanical actuators, Neurocomputing, 360 (2019), 85–96. https://doi.org/10.1016/j.neucom.2019.06.029 doi: 10.1016/j.neucom.2019.06.029
[9]	X. Li, J. Shen, H. Akca, R. Rakkiyappan, LMI-based stability for singularly perturbed nonlinear impulsive differential systems with delays of small parameter, Appl. Math. Comput., 250 (2015), 798–804. https://doi.org/10.1016/j.amc.2014.10.113 doi: 10.1016/j.amc.2014.10.113
[10]	X. Lv and X. Li, Finite time stability and controller design for nonlinear impulsive sampled-data systems with applications, ISA T., 70 (2017), 30–36. https://doi.org/10.1016/j.isatra.2017.07.025 doi: 10.1016/j.isatra.2017.07.025
[11]	X. Zhang, X. Li, Input-to-state stability of non-linear systems with distributed-delayed impulses, IET Control Theory A., 11 (2017), 81–89. https://doi.org/10.1049/iet-cta.2016.0469 doi: 10.1049/iet-cta.2016.0469
[12]	H. Zhang, R. Ye, S. Liu, J. Cao, A. Alsaedi, X. Li, LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays, Int. J. Syst. Sci., 49 (2018), 537–545. https://doi.org/10.1080/00207721.2017.1412534 doi: 10.1080/00207721.2017.1412534
[13]	X. Li, X. Yang, S. Song, Lyapunov conditions for finite-time stability of time-varying time-delay systems, Automatica, 103 (2019), 135–140. https://doi.org/10.1016/j.automatica.2019.01.031 doi: 10.1016/j.automatica.2019.01.031
[14]	F. Ferracuti, V. Artists, A. Monteriù, Algorithms for Fault Detection and Diagnosis, 1st Eds., Basel: MDPI, 2021.
[15]	S. Gómez-Peñate, G. Valencia-Palomo, F. R. López-Estrada, C. M. Astorga-Zaragoza, R. A. Osornio-Rios, I. Santos-Ruiz, Sensor fault diagnosis based on a sliding mode and unknown input observer for Takagi-Sugeno systems with uncertain premise variables, Asian J. Control, 21(1) (2019), 339–353. https://doi.org/10.1002/asjc.1913 doi: 10.1002/asjc.1913
[16]	D. Henry, J. Cieslak, A. Zolghadri, D. Efimov, $H_\infty$/ $H_{\rm{LPV}}$ solutions for fault detection of aircraft actuator faults: Bridging the gap between theory and practice, Int. J. Robust Nonlin., 25 (2015), 649–672. https://doi.org/10.1002/rnc.3157 doi: 10.1002/rnc.3157
[17]	Q. Jia, W. Chen, Y. Zhang, X. Chen, Robust fault reconstruction via learning observers in linear parameter-varying systems subject to loss of actuator effectiveness, IET Control Theory A., 8 (2014), 42–50. https://doi.org/10.1049/iet-cta.2013.0417 doi: 10.1049/iet-cta.2013.0417
[18]	D. Rotondo, A. Cristofaro, T. Johansen, F. Nejjari, V. Puig, Robust fault and icing diagnosis in unmanned aerial vehicles using LPV interval observers, Int. J. Robust Nonlin., 29 (2019), 5456–5480. https://doi.org/10.1002/rnc.4381 doi: 10.1002/rnc.4381
[19]	S. Li, H. Wang, A. Aitouche, N. Christov, Unknown input observer design for faults estimation using linear parameter varying model: application to wind turbine systems, Proceedings of the 7th International Conference on Systems and Control, (2018), 45–50. https://doi.org/10.1109/ICoSC.2018.8587778
[20]	J. Zhang, A. Swain, S. Nguang, Robust sliding mode observer based fault estimation for certain class of uncertain nonlinear systems, Asian J. Control, 17 (2015), 1296–1309. https://doi.org/10.1002/asjc.987 doi: 10.1002/asjc.987
[21]	C. Bonivento, A. Isidoria, L. Marconia, A. Paolia, Implicitfault-tolerant control: application to induction motors, Automatica, 40 (2004), 355–371. https://doi.org/10.1016/j.automatica.2003.9.003 doi: 10.1016/j.automatica.2003.9.003
[22]	Z. Gao, S. Ding, Sensor fault reconstruction and sensor compensation for a class of nonlinear state-space systems via a descriptor system approach, IET Control Theory A., 1 (2007), 578–585. https://doi.org/10.1049/iet-cta:20050509 doi: 10.1049/iet-cta:20050509
[23]	C. Tan, C. Edwards, An LMI approach for designing sliding mode observers, Int. J. Control, 74 (2001), 1559–1568. https://doi.org/10.1080/00207170110081723 doi: 10.1080/00207170110081723
[24]	V. Utkin, Sliding Modes in Control and Optimization, 1st Eds., Berlin: Springer Science & Business Media, 2013.
[25]	C. Tan, C. Edwards, Sliding mode observers for detection and reconstruction of sensor faults, Automatica, 38 (2002), 1815–1821. https://doi.org/10.1016/S0005-1098(02)00098-5 doi: 10.1016/S0005-1098(02)00098-5
[26]	B. Jiang, M. Staroswiecki, V. Cocquempot, Fault estimation in nonlinear uncertain systems using robust/slidingmode observers, IEE Proceedings-Control Theory and Applications, 151 (2004), 29–37. https://doi.org/10.1049/ip-cta:20040074 doi: 10.1049/ip-cta:20040074
[27]	I. Castillo, T. Edgar, B. Fernández, Robust model-based fault detection and isolation for nonlinear processes using sliding modes, Int. J. Robust Nonlin., 22 (2012), 89–104. https://doi.org/10.1002/rnc.1807 doi: 10.1002/rnc.1807
[28]	C. Edwards, S. Spurgeon, R. Patton, Sliding mode observers for fault detection and isolation, Automatica, 36 (2000), 541–553. https://doi.org/10.1016/S0005-1098(99)00177-6 doi: 10.1016/S0005-1098(99)00177-6
[29]	C. Tan, C. Edwards, A robust sensor fault tolerant control scheme implemented on a crane, Asian J. Control, 9 (2007), 340–344. https://doi.org/10.1111/j.1934-6093.1907.tb00420.x doi: 10.1111/j.1934-6093.1907.tb00420.x
[30]	H. Alwi, C. Edwards, C. Tan, Sliding mode estimation schemes for incipient sensor faults, Automatica, 45 (2009), 1679–1685. https://doi.org/10.1016/j.automatica.2009.02.031 doi: 10.1016/j.automatica.2009.02.031
[31]	K. Zhang, B. Jiang, V. Cocquempot, Adaptive observer-based fast fault estimation, Int. J. Control Autom. Syst., 6 (2008), 320–326.
[32]	K. Zhang, B. Jiang, P. Shi, Fast fault estimation and accommodation for dynamical systems, IET Control Theory Appl., 3 (2009), 189–199. https://doi.org/10.1049/iet-cta:20070283 doi: 10.1049/iet-cta:20070283
[33]	X. Yan, C. Edwards, Nonlinear robust fault reconstruction and estimation using a sliding mode observer, Automatica, 43 (2007), 1605–1614. https://doi.org/10.1016/j.automatica.2007.02.008 doi: 10.1016/j.automatica.2007.02.008
[34]	B. Jiang, M. Staroswiecki, V. Cocquempot, Fault accommodation for nonlinear dynamic systems, IEEE T. Automat. Contr., 51 (2006), 1578–1583. https://doi.org/10.1109/TAC.2006.878732 doi: 10.1109/TAC.2006.878732
[35]	M. Jelali, A. Kroll, Hydraulic Servo-systems: Modelling, Identification and Control, 1st Eds., London: Springer-Verlag, 2003. https://doi.org/10.1007/978-1-4471-0099-7
[36]	R. Raoufi, H. Marquez, A. Zinober, $H_\infty$ sliding mode observer for uncertain nonlinear Lipschitz systems with fault estimation synthesis, Int. J. Robust Nonlin., 20 (2010), 1785–1801. https://doi.org/10.1002/rnc.1545 doi: 10.1002/rnc.1545
[37]	M. Corless, J. Tu, State and input estimation for a class of uncertain systems, Automatica, 34 (1998), 757–764. https://doi.org/10.1016/S0005-1098(98)00013-2 doi: 10.1016/S0005-1098(98)00013-2
[38]	S. Hui, S. Zak, Observer design for system with unknown inputs, Int. J. Appl. Math. Comput. Sci, 15 (2005), 431–446.
[39]	J. Zhang, A. Swain, S. Nguang, Robust Observer-Based Fault Diagnosis for Nonlinear Systems Using MATLAB®, 1st Eds., Cham: Springer, 2016. https://doi.org/10.1007/978-3-319-32324-4_1
[40]	C. Gao, Q. Zhao, G. Duan, Robust actuator fault diagnosis scheme for satellite attitude control systems, J. Franklin I., 350 (2013), 2560–2580. https://doi.org/10.1016/j.jfranklin.2013.02.021 doi: 10.1016/j.jfranklin.2013.02.021
[41]	F. Zhu, Z. Han, A note on observers for lipschitz nonlinear systems, IEEE T. Automat. Contr., 47 (2002), 1751–1754. https://doi.org/10.1109/TAC.2002.803552 doi: 10.1109/TAC.2002.803552

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