LMI approach to mixed H_/H _∞ fault detection observer design

Abstract

To investigate the robust fault detection (RFD) observer design for linear uncertain systems, the H _{t_} index and H _∞ norm are used to describe this observer design as optimization problems. Conditions for the existence of such a fault detection observer are given in terms of matrix inequalities. The solution is obtained by new iterative linear matrix inequality (ILMI) algorithms. The RFD observer design over finite frequency range in which D _f does not have full column rank for a system is also considered. Numerical example demonstrates that the designed fault detection observer has high sensitivity to the fault and strong robustness to the unknown input.

Keywords

fault detection / observer / robustness / sensitivity / linear matrix inequality (LMI)

References

[1] Frank P. M. Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy: A survey and some new results[J]. Automatica, 1990, 26(3): 459-474.

[2] Hwang I., Kim S., Kim Y., et al. A survey of fault detection, isolation, and reconfiguration methods[J]. IEEE Transactions on Control Systems Technology, 2010, 18(3): 636-653.

[3] Gertler J. J. Survey of model-based failure detection and isolation in complex plants[J]. IEEE Control Systems Magazine, 1988, 8(6): 3-11.

[4] Isermann R., Balle P. Trends in the application of modelbased fault detections and diagnosis of technical processes[J]. Control Engineering Practice, 1997, 5(5): 709-719.

[5] Isermann R. Model-based fault-detection and diagnosisstatus and applications[J]. Annual Reviews in Control, 2005, 29(1): 71-85.

[6] Patton R. J. Robustness in model-based fault diagnosis: The 1995 situation[J]. Annual Reviews in Control, 1997, 21, 103-123.

[7] Frank P. M., Ding X. Survey of robust residual generation and evaluation methods in observer-based fault detection systems[J]. Journal of Process Control, 1997, 7(6): 403-424.

[8] Ma W. J., Sznaier M., Lagoa C. A risk adjusted approach to robust simultaneous fault detection and isolation[J]. Automatica, 2007, 43(3): 499 504

[9] Liu Y. S. Robust adaptive observer for nonlinear systems with unmodeled dynamics[J]. Automatica, 2009, 45(8): 1891 1895

[10] Spurgeon S. K. Sliding mode observers: A survey[J]. International Journal of Systems Science, 2008, 39(8): 751 764

[11] Ibaraki S, Suryanarayanan S, Tomizuka M. H _∞ optimization of Luenberger state observers and its application to fault detection filter design[C]. In: Proceedings of the IEEE Conference on Decision and Control. Orlando, Florida, USA, 2001. 1011–1016.

[12] Chen J, Patton R J. Standard H _∞ filtering formulation of robust fault detection[C]. In: IFAC Fault Detection, Supervision and Safety for Technical Process. Budapest, Hungary, 2000. 261–266.

[13] Li T., Wu L. Y., Wei X. J. Robust fault detection filter design for uncertain LTI systems based on new bounded real lemma[J]. International Journal of Control, Automation, and Systems, 2009, 7(4): 644-650.

[14] Edelmayer A, Bokor J, Szabo Z. Robust detection and estimation of faults by exact fault decoupling and H _∞ disturbance attenuation in linear dynamical systems[C]. In: The 2006 American Control Conference. Minneapolis, Minnesota, USA, 2006. 5716–5721.

[15] Liu J., Wang J. L., Yang G. H. An LMI approach to minimum sensitivity analysis with application to fault detection[J]. Automatica, 2005, 41(11): 1995 2004

[16] Wang J. L., Yang G. H., Liu J. An LMI approach to H ₋ index and mixed H ₋/H _∞ fault detection observer design[J]. Automatica, 2007, 43(9): 1656 1665

[17] Wei X K, Verhaegen M. Robust fault detection observer for LTI systems with additive uncertainties[C]. In: The 7th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes. Barcelona, Spain, 2009. 756–761.

[18] Wei X. K., Verhaegen M. Robust fault detection observer design for linear uncertain systems[J]. International Journal of Control, 2011, 84(1): 197 215

[19] Peng T., Gui W., Steven X. D., et al. An LMI-based H ₋/H _∞ optimal design approach for fault detection observer[J]. Journal of Central South University of Technology (Science and Technology), 2004, 35(4): 628-631.

[20] Zhong M. Y., Ye H., Chen G. Y., et al. An ILMI approach to RFDF for uncertain linear systems with nonlinear perturbations[J]. Acta Automatica Sinica, 2005, 31(2): 297-300.

[21] Wang H. B., Wang J. L., Lam J. Robust fault detection observer design: Iterative LMI approaches[J]. Journal of Dynamic Systems, Measurement, and Control, 2007, 129(1): 77-82.