Integrated design of observer based fault detection for a class of uncertain nonlinear systems

Wei Chen ; Abdul Q. Khan ; Muhammmad Abid ; Steven X. Ding

International Journal of Applied Mathematics and Computer Science, Tome 21 (2011), p. 423-430 / Harvested from The Polish Digital Mathematics Library

Résumé

Integrated design of observer based Fault Detection (FD) for a class of uncertain nonlinear systems with Lipschitz nonlinearities is studied. In the context of norm based residual evaluation, the residual generator and evaluator are designed together in an integrated form, and, based on it, a trade-off FD system is finally achieved in the sense that, for a given Fault Detection Rate (FDR), the False Alarm Rate (FAR) is minimized. A numerical example is given to illustrate the effectiveness of the proposed design method.

Détail

Publié le : 2011-01-01

Zbl 1234.93036

EUDML-ID : urn:eudml:doc:208057

Bibliographie

[000] Abbaszadeh, M. and Marquez, H. (2008). LMI optimization approach to robust $H_∞$ filtering for discrete-time nonlinear uncertain systems, Proceedings of the American Control Conference, Washington, DC, USA, pp. 1905-1910.

[001] Basseville, M. and Nikiforov, I.V. (1993). Detection of Abrupt Changes-Theory and Application, Prentice-Hall, Englewood Cliffs, NJ.

[002] Blanke, M., Kinnaert, M., Lunze, J. and Staroswiecki, M. (2003). Diagnosis and Fault-Tolerant Control, Springer, New York, NY. | Zbl 1023.93001

[003] Chen, J. and Patton, R.J. (1999). Robust Model-Based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers, Boston, MA. | Zbl 0920.93001

[004] Chen, W. and Saif, M. (2007). Observer-based strategies for actuator fault detection, isolation and estimation for certain class of uncertain nonlinear systems, IET Control Theory & Applications 1(6): 1672-1680.

[005] de Souza, C.E., Xie, L. and Wang, Y. (1993). $H_∞$ filtering for a class of uncertain nonlinear systems, Systems and Control Letters 20(6): 419426.

[006] Ding, S.X. (2008). Model-based Fault Diagnosis Techniques, Springer, Berlin.

[007] Ding, S.X., Frank, P.M., Ding, E.L. and Jeinsch, T. (2000a). A unified approach to the optimization of fault detection systems, International Journal of Adaptive Control and Signal Processing 14(7): 725-745. | Zbl 0983.93016

[008] Ding, S.X., Frank, P.M., Ding, E.L. and Jeinsch, T. (2000b). Fault detection system design based on a new trade-off strategy, Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, pp. 4144-4149.

[009] Ding, S.X., Guo, L. and Frank, P.M. (1993). A frequency domain approach to fault detection of uncertain dynamic systems, Proceedings of the 32th IEEE Conference on Decision and Control, San Antonio, TX, USA, pp. 1722-1727.

[010] Edelmayer, A., Bokor, J., Szab, Z. and Szigeti, F. (2004). Input reconstruction by means of system inversion: A geometric approach to fault detection and isolation in nonlinear systems, International Journal of Applied Mathematics and Computer Science 14(2): 189-199. | Zbl 1083.93008

[011] Ferrari, R., Parisini, T. and Polycarpou, M. (2007). A fault detection and isolation scheme for nonlinear uncertain discretetime systems, Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, USA, pp. 1009-1014.

[012] Frank, P.M. (1994). On-line fault detection in uncertain nonlinear systems using diagnostic observers: A survey, International Journal of Systems Science 25(12): 2129-2154. | Zbl 0822.93046

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

[014] Hammouri, H., Kinnaert, M. and Yaagoubi, E.H.E. (1999). Observer-based approach to fault detection and isolation for nonlinear systems, IEEE Transactions on Automatic Control 44(10): 1879-1884. | Zbl 0956.93005

[015] Henry, D. and Zolghadri, A. (2005). Design and analysis of robust residual generators for systems under feedback control, Automatica 41(2): 251-264. | Zbl 1116.93331

[016] Hou, M. and Patton, R.J. (1996). An LMI approach to $H_/H_{∞}$ fault detection observers, Proceedings of the UKACC International Conference on Control, Exeter, UK, pp. 1710-1715.

[017] Khan, A.Q., Abid, M., Chen, W. and Ding, S.X. (2009). On optimal fault detection of nonlinear systems, Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, China, pp. 1032-1037.

[018] Lai, T.L. and Shan, J.Z. (1999). Efficient recursive algorithms for detection of abrupt changes in signals and control systems, IEEE Transactions on Automatic Control 44(5): 952-966. | Zbl 0956.93060

[019] Narasimhan, S., Vachhani, P. and Rengaswamy, R. (2007). New nonlinear residual feedback observer for fault diagnosis in nonlinear systems, Automatica 44(9): 2222-2229. | Zbl 1153.93331

[020] Patton, R.J., Frank, P.M. and Clark, R.N. (2002). Issues of Fault Diagnosis for Dynamic Systems, Springer, Berlin.

[021] Pertew, A.M., Marquez, H.J. and Zhao, Q. (2007). LMI-based sensor fault diagnosis for nonlinear Lipschitz systems, Automatica 43(8): 1464-1469. | Zbl 1130.93314

[022] Qiu, Z. and Gertler, J. (1993). Robust FDI systems and $H_∞$ optimization, Proceedings of the American Control Conference, San Francisco, CA, USA, pp. 1710-1715.

[023] Rajamani, R. (1998). Observers for Lipschitz nonlinear systems, IEEE Transactions on Automatic Control 43(3): 397-401. | Zbl 0905.93009

[024] Rajamani, R. and Ganguli, A. (2004). Sensor fault diagnostics for a class of non-linear systems using linear matrix inequalities, International Journal of Control 77(10): 920-930. | Zbl 1069.93009

[025] Shumsky, A. (2007). Redundancy relations for fault diagnosis in nonlinear uncertain systems, International Journal of Applied Mathematics and Computer Science 17(4): 477-489, DOI: 10.2478/v10006-007-0040-1. | Zbl 1228.62129

[026] Wang, J.L., Yang, G. and Liu, J. (2007). An LMI approach to H index and mixed $H_/H_{∞}$ fault detection observer design, Automatica 43(9): 1656-1665. | Zbl 1128.93321

[027] Wang, Y., Xie, L. and Souza, C.E. (1992). Robust control of a class of uncertain nonlinear systems, Systems & Control Letters 19(2): 139-149. | Zbl 0765.93015

[028] Xie, L., de Souza, C.E. and Wang, Y. (1996). Robust filtering for a class of discrete-time uncertain nonlinear systems: An $H_∞$ approach, International Journal of Robust and Nonlinear Control 6(4): 297312. | Zbl 0851.93030

[029] Yaz, E. and Azemi, A. (1998). Actuator fault detection and isolation in nonlinear systems using LMIs and LMEs, Proceedings of the American Control Conference, Philadelphia, PA, USA, pp. 1590-1594.

[030] Zhang, P. and Ding, S.X. (2008). An integrated trade-off design of observer based fault detection systems, Automatica 44(7): 1886-1894. | Zbl 1149.93314

[031] Zhang, P., Ding, S.X., Wang, G. and Zhou, D. (2005). Fault detection of linear discrete-time periodic systems, IEEE Transactions on Automatic Control 50(2): 239-244.