Nonlinear robust fault reconstruction and estimation using a sliding mode observer. (English) Zbl 1128.93389

Yan, Xing-Gang; Edwards, Christopher

Automatica 43, No. 9, 1605-1614 (2007).

Summary: This paper considers fault detection and estimation issues for a class of nonlinear systems with uncertainty, using an equivalent output error injection approach. A particular design of sliding mode observer is presented for which the parameters can be obtained using LMI techniques. A fault estimation approach is presented to estimate the fault and the estimation error is dependent on the bounds on the uncertainty. For a special class of uncertainty, a fault reconstruction scheme is presented where the reconstructed signal can approximate the fault signal to any accuracy. The proposed fault estimation/reconstruction signals are only based on the available plant input/ouput information and can be calculated on-line. Finally, a simulation study on a robotic arm system is presented to show the effectiveness of the scheme.

MSC:

93E10	Estimation and detection in stochastic control theory
93C41	Control/observation systems with incomplete information
93C10	Nonlinear systems in control theory
93B07	Observability

Keywords:

nonlinear systems; sliding mode observer; fault reconstruction/estimation; equivalent output injection

Software:

LMI toolbox

References:

[1]	Chen, J.; Patton, R. J., Robust model-based fault diagnosis for dynamic systems (1999), Kluwer: Kluwer Boston, MA · Zbl 0920.93001
[2]	Edwards, C.; Spurgeon, S. K., Sliding mode control: theory and applications (1998), Taylor and Francis Ltd: Taylor and Francis Ltd London
[3]	Edwards, C.; Spurgeon, S. K.; Patton, R. J., Sliding mode observers for fault detection and isolation, Automatica, 36, 4, 541-553 (2000) · Zbl 0968.93502
[4]	Fan, X.; Arcak, M., Observer design for systems with multivariable monotone nonlinearities, Systems & Control Letters, 50, 319-330 (2003) · Zbl 1157.93330
[5]	Floquet, T.; Barbot, J. P.; Perruquetti, W.; Djemai, M., On the robust fault detection via a sliding mode disturbance observer, International Journal of Control, 77, 7, 622-629 (2004) · Zbl 1062.93006
[6]	Frank, P. M., Fault diagnosis in dynamic system via state estimation—a survey, (Tzafestas; Singh; Schmidt, System fault diagnostic, reliability & related knowledge-based approaches (1987), D. Reidel Press: D. Reidel Press Dordrecht), 35-98
[7]	Frank, P. M.; Ding, X., Survey of robust residual generation and evaluation methods in observer-based fault detection systems, Journal of Process Control, 7, 6, 403-424 (1997)
[9]	Jiang, B.; Staroswiecki, M.; Cocquempot, V., Fault estimation in nonlinear uncertain systems using robust sliding-mode observers, IEE Proceedings, Part D: Control Theory and Applications, 151, 1, 29-37 (2004)
[10]	Kwan, C. M., On variable structure output feedback controllers, IEEE Transactions on Automatic Control, 41, 11, 1691-1693 (1996) · Zbl 0875.93056
[11]	Persis, D. C.; Isidori, A., A geometric approach to nonlinear fault detection and isolation, IEEE Transactions on Automatic Control, 46, 6, 853-865 (2001) · Zbl 1009.93003
[12]	Shields, D. N., Observer-based residual generation for fault diagnosis for non-affine non-linear polynomial systems, International Journal of Control, 78, 5, 363-384 (2005) · Zbl 1088.93005
[14]	Tan, C. P.; Edwards, C., Sliding mode observers for detection and reconstruction of sensor faults, Automatica, 38, 5, 1815-1821 (2002) · Zbl 1011.93505
[15]	Tan, C. P.; Edwards, C., Sliding mode observers for robust detection and reconstruction of actuator sensor faults, International Journal of Robust Nonlinear Control, 13, 5, 443-463 (2003) · Zbl 1036.93025
[16]	Utkin, V. I., Sliding modes in control optimization (1992), Springer: Springer Berlin · Zbl 0748.93044
[17]	Xu, A.; Zhang, Q., Nonlinear system fault diagnosis based on adaptive estimation, Automatica, 40, 7, 1181-1193 (2004) · Zbl 1056.93034
[18]	Yan, X. G.; Edwards, C.; Spurgeon, S. K., Decentralised robust sliding mode control for a class of nonlinear interconnected systems by static output feedback, Automatica, 40, 4, 613-620 (2004) · Zbl 1060.93026
[19]	Yan, X. G.; Wang, J. J.; Lü, X. Y.; Zhang, S. Y., Decentralized output feedback robust stabilization for a class of nonlinear interconnected systems with similarity, IEEE Transactions on Automatic Control, 43, 2, 294-299 (1998) · Zbl 0906.93003
[20]	Zhang, X.; Polycarpou, M. M.; Parisini, T., A robust detection and isolation scheme for abrupt and incipient faults in nonlinear systems, IEEE Transactions on Automatic Control, 47, 4, 576-593 (2002) · Zbl 1125.93358
[21]	Zhou, K.; Doyle, J. C.; Glover, K., Robust and optimal control (1995), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ