An LMI approach to design robust fault detection filter for uncertain LTI systems.

*(English)*Zbl 1036.93061The robust fault detection filter design problem for uncertain linear time-invariant (LTI) systems with both unknown inputs and modelling errors is studied. The basic idea is to use an optimal residual generator (assuming no modelling errors) as the reference residual model of the robust fault detection filter design for uncertain LTI systems with modelling errors and, based on it, to formulate the robust fault detection filter design as an \(H_\infty\) model-matching problem. A solution of the optimization problem is presented. The main results include the development of an optimal reference residual model, the formulation of the robust fault detection filter design problem, the derivation of a sufficient condition for the existence of a robust fault detection filter and a construction of it based on the linear matrix inequality solution parameters, and the determination of an adaptive threshold for fault detection. An illustrative numerical example is given.

Reviewer: Vjatscheslav Vasiliev (Tomsk)

##### MSC:

93E11 | Filtering in stochastic control theory |

93B25 | Algebraic methods |

93B36 | \(H^\infty\)-control |

93B51 | Design techniques (robust design, computer-aided design, etc.) |

Full Text:
DOI

**OpenURL**

##### References:

[1] | Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in systems and control theory, (1994), SIAM Philadelphia, PA · Zbl 0816.93004 |

[2] | Chen, J.; Patton, P.R., Robust model-based fault diagnosis for dynamic systems, (1999), Kluwer Academic Publishers Boston · Zbl 0920.93001 |

[3] | Chen, J., & Patton, R. J. (2000). Standard H∞ filtering formulation of robust fault detection. In Proceedings of SAFEPROCESS’2000, Budapest, Hungary (pp. 256-261). |

[4] | Ding, S. X., Ding, E. L., & Jeinsch, T. (2000). A new optimization approach to the design of fault detection filters. In Proceedings of SAFEPROCESS’2000, Budapest, Hungary (pp. 250-255). |

[5] | Ding, S. X., Zhong, M. -Y., & Tang, B. Y. (2001). An LMI approach to the design of fault detection filter for time-delay LTI systems with unknown inputs. In Proceedings of the American control conference, Arlington, VA (pp. 2137-2142). |

[6] | Frank, P.M., Enhancement of robustness in observer-based fault detection, International journal of control, 59, 4, 955-981, (1994) · Zbl 0813.93003 |

[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) |

[8] | Frank, P. M., Ding, S. X., & Koppen-Seliger, B. (2000). Current developments in the theory of FDI. In Proceedings of SAFEPROCESS, Budapest, Hungary (pp. 16-27). |

[9] | Frisk, E. (1998). Residual generation for fault diagnosis: Nominal and robust design. Technical Report 739, Department of Electrical Engineering, Linköpings Universitet, Linköpings, Sweden. |

[10] | Frisk, E., & Nielsen, L. (1999). Robust residual generation for diagnosis including a reference model for residual behavior. In Proceedings of the 14th IFAC world congress, Beijing, China (pp. 55-60). · Zbl 1123.93050 |

[11] | Nobrega, E. G., Abdalla, M. O., & Grigoriadis, K. M. (2000). LMI-based filter design for fault detection and isolation. In Proceedings of the 39th conference on decision control, Sydney, Australia (pp. 4329-4334). |

[12] | Patton, R. J., & Hou, M. (1999). On sensitivity of robust fault detection observers. In Proceedings of the 14th IFAC world congress, Beijing, China (pp. 67-72). |

[13] | Rambeaux, F., Hamelin, F., & Sauter, D. (1999). Robust residual generation via LMI. In Proceedings of the 14th IFAC world congress, Beijing, China (pp. 241-246). |

[14] | Zhong, M., Ding, S. X., & Tang, B. (2001). An LMI approach to robust fault detection filter design for discrete-time systems with model uncertainty. In Proceedings of the 40th conference on decision control, Orlando, Florida, USA (pp. 3613-3618). |

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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.