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Multiplicative fault estimation-based adaptive sliding mode fault-tolerant control design for nonlinear systems. (English) Zbl 1398.93055

Summary: This article deals with the sliding mode Fault-Tolerant Control (FTC) problem for a nonlinear system described under Takagi-Sugeno (T-S) fuzzy representation. In particular, the nonlinear system is corrupted with multiplicative actuator faults, process faults, and uncertainties. We start by constructing the separated FTC design to ensure robust stability of the closed-loop nonlinear system. First, we propose to conceive an adaptive observer in order to estimate nonlinear system states, as well as robust multiplicative fault estimation. The novelty of the proposed approach is that the observer gains are obtained by solving the multiobjective Linear Matrix Inequality (LMI) optimization problem. Second, an adaptive sliding mode controller is suggested to offer a solution to stabilize the closed-loop system despite the occurrence of real fault effects. Compared with the separated FTC, this paper provides an integrated sliding mode FTC in order to achieve an optimal robustness interaction between observer and controller models. Thus, in a single-step LMI formulation, sufficient conditions are developed with multiobjective optimization performances to guarantee the stability of the closed-loop system. At last, nonlinear simulation results are given to illustrate the effectiveness of the proposed FTC to treat multiplicative faults.

MSC:

93B12 Variable structure systems
93B35 Sensitivity (robustness)
93D09 Robust stability
93C10 Nonlinear systems in control theory
93C42 Fuzzy control/observation systems
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[1] Wang, L.; Cai, M.; Zhang, H.; Alsaadi, F.; Chen, L., Active fault-tolerant control for wind turbine with simultaneous actuator and sensor faults, Complexity, 2017, (2017) · Zbl 1380.93096 · doi:10.1155/2017/6164841
[2] Van, M.; Franciosa, P.; Ceglarek, D., Fault diagnosis and fault-tolerant control of uncertain robot manipulators using high-order sliding mode, Mathematical Problems in Engineering, 2016, (2016) · Zbl 1400.93214 · doi:10.1155/2016/7926280
[3] Isermann, R., Fault-Diagnosis Applications : Model-Based Condition Monitoring: Actuators, Drives, Machinery, Plants, Sensors, and Fault-Tolerant Systems, (2011), Springer, Science and Business Media · Zbl 1304.94001
[4] Alwi, H.; Edwards, C.; Tan, C. P., Fault Detection and Fault-Tolerant Control Using Sliding Modes, (2011), Springer, Science and Business Media · Zbl 1237.93002
[5] Wang, J., H_{∞} fault-tolerant controller design for networked control systems with time-varying actuator faults, International Journal of Innovative Computing Information and Control, 11, 4, 1471-1481, (2015)
[6] Li, F.; Zhenggao, H.; Zhao, G., Fault estimation and adaptive fault tolerant control for dynamic systems based on the second-order sliding mode observer, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 230, 3, 222-230, (2016) · doi:10.1177/0959651815621674
[7] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems, Man, and Cybernetics, SMC-15, 1, 116-132, (1985) · Zbl 0576.93021 · doi:10.1109/TSMC.1985.6313399
[8] Aouaouda, S.; Chadli, M.; Cocquempot, V.; Tarek Khadir, M., Multi-objective H_{−} ∕ H_{∞} fault detection observer design for Takagi-Sugeno fuzzy systems with unmeasurable premise variables: descriptor approach, International Journal of Adaptive Control and Signal Processing, 27, 12, 1031-1047, (2013) · Zbl 1282.93153 · doi:10.1002/acs.2374
[9] Wang, H.; Ye, D.; Yang, G. H., Actuator fault diagnosis for uncertain T–S fuzzy systems with local nonlinear models, Nonlinear Dynamics, 76, 4, 1977-1988, (2014) · Zbl 1314.93025 · doi:10.1007/s11071-014-1262-z
[10] Ichalal, D.; Marx, B.; Ragot, J.; Maquin, D., Fault detection, isolation and estimation for Takagi–Sugeno nonlinear systems, Journal of the Franklin Institute, 351, 7, 3651-3676, (2014) · Zbl 1290.93107 · doi:10.1016/j.jfranklin.2013.04.012
[11] Yang, G. H.; Wang, H., Fault detection and isolation for a class of uncertain state-feedback fuzzy control systems, IEEE Transactions on Fuzzy Systems, 23, 1, 139-151, (2015) · doi:10.1109/TFUZZ.2014.2308920
[12] Brahim, A. B.; Dhahri, S.; Hmida, F. B.; Sellami, A., An H_{∞} sliding mode observer for Takagi–Sugeno nonlinear systems with simultaneous actuator and sensor faults An, International Journal of Applied Mathematics and Computer Science, 25, 3, 547-559, (2015) · Zbl 1322.93027 · doi:10.1515/amcs-2015-0041
[13] Ben Brahim, A.; Dhahri, S.; Ben Hmida, F.; Sellami, A., Simultaneous actuator and sensor faults reconstruction based on robust sliding mode observer for a class of nonlinear systems, Asian Journal of Control, 19, 1, 362-371, (2017) · Zbl 1357.93019 · doi:10.1002/asjc.1359
[14] Raoufi, R.; Marquez, H. J.; Zinober, A. S. I., ℋ_{∞} sliding mode observers for uncertain nonlinear Lipschitz systems with fault estimation synthesis, International Journal of Robust and Nonlinear Control, 20, 1785-1801, (2010) · Zbl 1202.93027 · doi:10.1002/rnc.1545
[15] Dhahri, S.; Sellami, A.; Hmida, F. B., Robust H_{∞} sliding mode observer design for fault estimation in a class of uncertain nonlinear systems with LMI optimization approach, International Journal of Control, Automation and Systems, 10, 5, 1032-1041, (2012) · doi:10.1007/s12555-012-0521-3
[16] Zhang, J.; Nguang, S. K.; Swain, A. K., Detection and isolation of incipient sensor faults for a class of uncertain non-linear systems, IET Control Theory and Applications, 6, 12, 1870-1880, (2012) · doi:10.1049/iet-cta.2011.0440
[17] Valibeygi, A.; Toudeshki, A.; Vijayaraghavan, K., Observer-based sensor fault estimation in nonlinear systems, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 230, 8, 759-777, (2016)
[18] Lan, J.; Patton, R. J., Integrated fault estimation and fault-tolerant control for uncertain Lipschitz nonlinear systems, International Journal of Robust and Nonlinear Control, 27, 5, 761-780, (2017) · Zbl 1359.93127 · doi:10.1002/rnc.3597
[19] Lu, C.; Cheng, Y.; Liu, H.; Wang, Z., An approach to fault detection and isolation for control components in the aircraft environmental control system, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 228, 7, 1202-1214, (2014) · doi:10.1177/0954410013487614
[20] Yin, S.; Luo, H.; Ding, S. X., Real-time implementation of fault-tolerant control systems with performance optimization, IEEE Transactions on Industrial Electronics, 61, 5, 2402-2411, (2014) · doi:10.1109/TIE.2013.2273477
[21] Ding, S. X.; Frank, P. M.; Ding, E. L., An approach to the detection of multiplicative faults in uncertain dynamic systems, Proceedings of the 41st IEEE Conference on Decision and Control, 2002 · doi:10.1109/CDC.2002.1185060
[22] Tan, C. P.; Edwards, C., Multiplicative fault reconstruction using sliding mode observers, 2004 5th Asian Control Conference (IEEE Cat. No.04EX904)
[23] Zhang, K.; Jiang, B.; Shi, P., Fast fault estimation and accommodation for dynamical systems, IET Control Theory & Applications, 3, 2, 189-199, (2009) · doi:10.1049/iet-cta:20070283
[24] Lan, J.; Patton, R. J., A new strategy for integration of fault estimation within fault-tolerant control, Automatica, 69, 48-59, (2016) · Zbl 1338.93129 · doi:10.1016/j.automatica.2016.02.014
[25] Zhang, X.; Polycarpou, M. M.; Parisini, T., Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation, Automatica, 46, 2, 290-299, (2010) · Zbl 1205.93066 · doi:10.1016/j.automatica.2009.11.014
[26] Gao, C.; Duan, G., Robust adaptive fault estimation for a class of nonlinear systems subject to multiplicative faults, Circuits, Systems, and Signal Processing, 31, 6, 2035-2046, (2012) · Zbl 1269.93111 · doi:10.1007/s00034-012-9434-x
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