##
**LMI-based sliding mode observers for incipient faults detection in nonlinear system.**
*(English)*
Zbl 1300.93052

Summary: This paper presents a diagnosis scheme based on a Linear Matrix Inequality (LMI) algorithm for incipient faults in a nonlinear system class with unknown input disturbances. First, the nonlinear system is transformed into two subsystems, one of which is unrelated to the disturbances. Second, for the subsystem that is free from disturbances, a Luenberger observer is constructed. A sliding mode observer is then constructed for the subsystem which is subjected to disturbances, so that the effect of the unknown input disturbances is eliminated. Together, the entire system achieves both robustness to disturbances and sensitivity to incipient faults. Finally, the effectiveness and feasibility of the proposed method are verified through a numerical example using a single-link robotic arm.

### MSC:

93B12 | Variable structure systems |

93B07 | Observability |

94C12 | Fault detection; testing in circuits and networks |

PDFBibTeX
XMLCite

\textit{C.-F. Zhang} et al., J. Appl. Math. 2012, Article ID 528932, 13 p. (2012; Zbl 1300.93052)

Full Text:
DOI

### References:

[1] | H. H. Choi and K. S. Ro, “LMI-based sliding-mode observer design method,” IEE Proceedings: Control Theory and Applications, vol. 152, no. 1, pp. 113-115, 2005. · doi:10.1049/ip-cta:20041123 |

[2] | W. T. Chen and M. Saif, “Actuator fault diagnosis for uncertain linear systems using a high-order sliding-mode robust differentiator (HOSMRD),” International Journal of Robust and Nonlinear Control, vol. 18, no. 4-5, pp. 413-426, 2008. · Zbl 1284.93054 · doi:10.1002/rnc.1201 |

[3] | W. T. Chen and M. Saif, “Actuator fault isolation and estimation for uncertain nonlinear systems,” in Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, vol. 3, pp. 2560-2565, Waikoloa, Hawaii, USA, October 2005. |

[4] | B. Jiang, M. Staroswiecki, and V. Cocquempot, “Fault accommodation for nonlinear dynamic systems,” IEEE Transactions on Automatic Control, vol. 51, no. 9, pp. 1578-1583, 2006. · Zbl 1366.93694 · doi:10.1109/TAC.2006.878732 |

[5] | K. Zhang, B. Jiang, and V. Cocquempot, “Adaptive observer-based fast fault estimation,” International Journal of Control, Automation and Systems, vol. 6, no. 3, pp. 320-326, 2008. |

[6] | R. Sreedhar, B. Ferandez, and G. Y. Masada, “Robust fault detection in nonlinear systems using sliding mode observers,” in Proceedings of the IEEE Conference on Control Applications, pp. 715-721, Vancouver, Canada, September 1993. |

[7] | B. Jiang, M. Staroswiecki, and V. Cocquempot, “Fault estimation in nonlinear uncertain systems using robust sliding-mode observers,” IEE Proceedings: Control Theory and Applications, vol. 151, no. 1, pp. 29-37, 2004. · doi:10.1049/ip-cta:20040074 |

[8] | X. G. Yan and C. Edwards, “Robust sliding mode observer-based actuator fault detection and isolation for a class of nonlinear systems,” in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference (CDC-ECC’05), pp. 987-992, Seville, Spain, December 2005. · doi:10.1109/CDC.2005.1582286 |

[9] | W. Chen and F. N. Chowdhury, “Design of sliding mode observers with sensitivity to incipient faults,” in Proceedings of the 16th IEEE International Conference on Control Applications (CCA’07), pp. 795-800, Singapore, October 2007. · doi:10.1109/CCA.2007.4389330 |

[10] | X. G. Yan, S. K. Spurgeon, and Y. Orlov, “Sliding mode observer based control for a class of nonlinear time delay systems with delayed uncertainties,” in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC’11), pp. 7611-7616, Orlando, Fla, USA, December 2011. |

[11] | X. R. Li, L. Y. Zhao, and G. Z. Zhao, “Adaptive synchronization of parameter uncertain chaotic systems,” Journal of Zhejiang University (Engineering Science), vol. 39, no. 12, pp. 1993-1997, 2005. · Zbl 1168.37326 |

[12] | L. Yu, Robust Control-Linear Matrix Inequality Processing Method, TsingHua University Press, Beijing, China, 2002. |

[13] | X. D. Zhang, T. Parisini, and M. M. Polycarpou, “Sensor bias fault isolation in a class of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 50, no. 3, pp. 370-376, 2005. · Zbl 1365.93535 · doi:10.1109/TAC.2005.843875 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.