Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2011, Article ID 146038, 17 pages
http://dx.doi.org/10.1155/2011/146038
Research Article

Robust Sensor Fault Reconstruction for Lipschitz Nonlinear Systems

Department of Electrical Engineering, Sahand University of Technology, P.O. Box 51336-1996, Sahand, Tabriz, Iran

Received 29 December 2010; Revised 27 January 2011; Accepted 3 February 2011

Academic Editor: Oleg V. Gendelman

Copyright © 2011 M. J. Khosrowjerdi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. Y. Chen and R. J. Patton, Robust Model-Based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.
  2. Y. Zhang and J. Jiang, “Bibliographical review on reconfigurable fault-tolerant control systems,” Annual Reviews in Control, vol. 32, no. 2, pp. 229–252, 2008. View at Publisher · View at Google Scholar · View at Scopus
  3. I. Hwang, S. Kim, Y. Kim, and C. E. Seah, “A survey of fault detection, isolation, and reconfiguration methods,” IEEE Transactions on Control Systems Technology, vol. 18, no. 3, Article ID 5282515, pp. 636–653, 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. R. Nikoukhah, “Innovations generation in the presence of unknown inputs: application to robust failure detection,” Automatica, vol. 30, no. 12, pp. 1851–1867, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. M. J. Khosrowjerdi, R. Nikoukhah, and N. Safari-Shad, “Fault detection in a mixed 2/ setting,” IEEE Transactions on Automatic Control, vol. 50, no. 7, pp. 1063–1068, 2005. View at Publisher · View at Google Scholar
  6. N. Liu and K. Zhou, “Optimal solutions to multi-objective robust fault detection problems,” in Proceedings of the 46th IEEE Conference on Decision and Control (CDC '07), pp. 981–988, December 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. C. P. Tan and C. Edwards, “Robust sensor fault tolerant control scheme implemented on a crane,” Asian Journal of Control, vol. 9, no. 3, pp. 340–344, 2007. View at Google Scholar · View at Scopus
  8. C. Edwards and C. P. Tan, “Sensor fault tolerant control using sliding mode observers,” Control Engineering Practice, vol. 14, no. 8, pp. 897–908, 2006. View at Publisher · View at Google Scholar
  9. C. P. Tan and M. K. Habib, “Tolerance towards sensor faults: an application to a flexible arm manipulator,” International Journal of Advanced Robotic Systems, vol. 3, no. 4, pp. 343–350, 2006. View at Google Scholar
  10. Z. Gao and S. X. Ding, “Sensor fault reconstruction and sensor compensation for a class of nonlinear state-space systems via a descriptor system approach,” IET Control Theory and Applications, vol. 1, no. 3, pp. 578–585, 2007. View at Publisher · View at Google Scholar
  11. R. H. Chen and J. L. Speyer, “Sensor and actuator fault reconstruction,” Journal of Guidance, Control, and Dynamics, vol. 27, no. 2, pp. 186–196, 2004. View at Google Scholar · View at Scopus
  12. C. Kwan and R. Xu, “A note on simultaneous isolation of sensor and actuator faults,” IEEE Transactions on Control Systems Technology, vol. 12, no. 1, pp. 183–192, 2004. View at Publisher · View at Google Scholar
  13. C. P. Tan and C. Edwards, “Sliding mode observers for detection and reconstruction of sensor faults,” Automatica, vol. 38, no. 10, pp. 1815–1821, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. C. P. Tan and C. Edwards, “Robust fault reconstruction in uncertain linear systems using multiple sliding mode observers in cascade,” IEEE Transactions on Automatic Control, vol. 55, no. 4, pp. 855–867, 2010. View at Publisher · View at Google Scholar
  15. K. Y. Ng, C. P. Tan, Z. Man, and R. Akmeliawati, “New results in disturbance decoupled fault reconstruction in linear uncertain systems using two sliding mode observers in cascade,” International Journal of Control, Automation and Systems, vol. 8, no. 3, pp. 506–518, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. H. Alwi, C. Edwards, and C. P. Tan, “Sliding mode estimation schemes for incipient sensor faults,” Automatica, vol. 45, no. 7, pp. 1679–1685, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. C. P. Tan, F. Crusca, and M. Aldeen, “Extended results on robust state estimation and fault detection,” Automatica, vol. 44, no. 8, pp. 2027–2033, 2008. View at Publisher · View at Google Scholar
  18. K. Y. Ng, C. P. Tan, C. Edwards, and Y. C. Kuang, “New results in robust actuator fault reconstruction for linear uncertain systems using sliding mode observers,” International Journal of Robust and Nonlinear Control, vol. 17, no. 14, pp. 1294–1319, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. C. P. Tan and M. K. Habib, “Robust sensor fault reconstruction applied in real-time to an inverted pendulum,” Mechatronics, vol. 17, no. 7, pp. 368–380, 2007. View at Publisher · View at Google Scholar · View at Scopus
  20. S. Dhahri, F. B. Hmida, A. Sellami, and M. Gossa, “LMI-based sliding mode observer design method for reconstruction of actuator and sensor faults,” International Journal on Sciences and Techniquess, vol. 1, no. 1, pp. 91–101, 2007. View at Google Scholar
  21. C. P. Tan, F. Crusca, and M. Aldeen, “A frequency weighted approach to robust fault reconstruction,” in Proceedings of the 6th Asian Control Conference (ASCC '06), pp. 355–360, Bali, Indonesia, 2006.
  22. Y. Y. Wang, L. Xie, and C. E. de Souza, “Robust control of a class of uncertain nonlinear systems,” Systems & Control Letters, vol. 19, no. 2, pp. 139–149, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. 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. View at Google Scholar · View at Scopus
  24. Z. Gao and H. Wang, “Descriptor observer approaches for multivariable systems with measurement noises and application in fault detection and diagnosis,” Systems & Control Letters, vol. 55, no. 4, pp. 304–313, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. M. J. Khosrowjerdi, “Mixed 2/ approach to fault-tolerant controller design for lipschitz non-linear systems,” Control Theory and Applications, IET, vol. 5, no. 2, pp. 299–307, 2011. View at Publisher · View at Google Scholar
  26. K. Adjallah, D. Maquin, and J. Ragot, “Non-linear observer-based fault detection,” in Proceedings of IEEE Conference on Control Applications, pp. 1115–1120, August 1994. View at Scopus
  27. G. Schreier, J. Ragot, R. J. Patton, and P. M. Frank, “Observer design for a class of nonlinear systems,” in IFAC Fault Detection, Supervision and Safety for Technical Processes, pp. 498–503, Kingston Upon Hull, UK, 1997.
  28. E. A. García and P. M. Frank, “Deterministic nonlinear observer-based approaches to fault diagnosis: a survey,” Control Engineering Practice, vol. 5, no. 5, pp. 663–670, 1997. View at Publisher · View at Google Scholar · View at Scopus
  29. H. Hammouri, M. Kinnaert, and E. H. El Yaagoubi, “Observer-based approach to fault detection and isolation for nonlinear systems,” IEEE Transactions on Automatic Control, vol. 44, no. 10, pp. 1879–1884, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  30. P. Kabore and H. Wang, “Design of fault diagnosis filters and fault-tolerant control for a class of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 46, no. 11, pp. 1805–1810, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  31. X. Zhang, M. M. Polycarpou, and T. Parisini, “Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation,” Automatica, vol. 46, no. 2, pp. 290–299, 2010. View at Publisher · View at Google Scholar · View at Scopus
  32. X.-G. Yan and C. Edwards, “Adaptive sliding-mode-observer-based fault reconstruction for nonlinear systems with parametric uncertainties,” IEEE Transactions on Industrial Electronics, vol. 55, no. 11, pp. 4029–4036, 2008. View at Publisher · View at Google Scholar
  33. A. T. Vemuri, “Sensor bias fault diagnosis in a class of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 46, no. 6, pp. 949–954, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  34. X.-G. Yan and C. Edwards, “Nonlinear robust fault reconstruction and estimation using a sliding mode observer,” Automatica, vol. 43, no. 9, pp. 1605–1614, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  35. M. Aldeen and R. Sharma, “Estimation of states, faults and unknown disturbances in non-linear systems,” International Journal of Control, vol. 81, no. 8, pp. 1195–1201, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  36. X. 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. View at Publisher · View at Google Scholar
  37. X. Zhang, M. M. Polycarpou, and T. Parisini, “Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation,” Automatica, vol. 46, no. 2, pp. 290–299, 2010. View at Publisher · View at Google Scholar · View at Scopus
  38. A. M. Pertew, H. J. Marquez, and Q. Zhao, “LMI-based sensor fault diagnosis for nonlinear Lipschitz systems,” Automatica, vol. 43, no. 8, pp. 1464–1469, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  39. G. Besançon, “High-gain observation with disturbance attenuation and application to robust fault detection,” Automatica, vol. 39, no. 6, pp. 1095–1102, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  40. H. J. Marquez, Nonlinear Control Systems: Analysis and Design, John Wiley & sons, New York, NY, USA, 2003.
  41. M. Abbaszadeh and H. J. Marquez, “A robust observer design method for continuous-time Lipschitz nonlinear systems,” in Proceedings of the 45th IEEE Conference on Decision and Control (CDC '06), pp. 3795–3800, December 2006. View at Scopus
  42. L. El Ghaoui, R. Nikoukhah, F. Delebecque, and J. L. Commeau, “LMITOOL-2.0 Package: An Interface to Solve LMI Problems,” Optimization and Control Group, ENSTA, France, 1998.
  43. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox, The Math Works, Natick, Mass, USA, 1995.
  44. F. E. Thau, “Observing the state of non-linear dynamic systems,” International Journal of Control, vol. 17, no. 3, pp. 471–479, 1973. View at Google Scholar · View at Scopus
  45. R. Patel and M. Toda, “Quantitative measures of robustness for multivariable systems,” in Proceedings of American Control Conference (ACC '80), San Francisco, Calif, USA, 1980.
  46. Z. Mao, B. Jiang, and P. Shi, “Observer based fault-tolerant control for a class of nonlinear networked control systems,” Journal of the Franklin Institute, vol. 347, no. 6, pp. 940–956, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  47. H. R. Karimi, M. Zapateiro, and N. Luo, “A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed time-varying delays and nonlinear perturbations,” Journal of the Franklin Institute, vol. 347, no. 6, pp. 957–973, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  48. M. Abbaszadeh and H. J. Marquez, “Nonlinear observer design for one-sided Lipschitz systems,” in Proceedings of the American Control Conference (ACC '10), pp. 5284–5289, July 2010.
  49. M. Abbaszadeh and H. J. Marquez, “Robust observer design for a class of nonlinear uncertain systems via convex optimization,” in Proceedings of the American Control Conference (ACC '07), pp. 1699–1704, July 2007. View at Publisher · View at Google Scholar · View at Scopus