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Mathematical Problems in Engineering
Volume 2016, Article ID 2740645, 17 pages
http://dx.doi.org/10.1155/2016/2740645
Research Article

Minimal-Order Functional Observer-Based Residual Generators for Fault Detection and Isolation of Dynamical Systems

School of Engineering, Deakin University, Geelong, VIC 3217, Australia

Received 10 January 2016; Revised 22 March 2016; Accepted 5 April 2016

Academic Editor: Zehui Mao

Copyright © 2016 H. M. Tran and H. Trinh. 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. Z. Gao, X. Liu, and M. Z. Q. Chen, “Unknown input observer-based robust fault estimation for systems corrupted by partially decoupled disturbances,” IEEE Transactions on Industrial Electronics, vol. 63, no. 4, pp. 2537–2547, 2016. View at Publisher · View at Google Scholar
  2. A. S. Willsky, “A survey of design methods for failure detection in dynamic systems,” Automatica, vol. 12, no. 6, pp. 601–611, 1976. View at Google Scholar
  3. M. Hou and P. C. Muller, “Design of observers for linear systems with unknown inputs,” IEEE Transactions on Automatic Control, vol. 37, no. 6, pp. 871–875, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. 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 · View at MathSciNet · View at Scopus
  5. Q. P. Ha and H. Trinh, “State and input simultaneous estimation for a class of nonlinear systems,” Automatica, vol. 40, no. 10, pp. 1779–1785, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. 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 MathSciNet · View at Scopus
  7. H. Trinh and Q. P. Ha, “State and input simultaneous estimation for a class of time-delay systems with uncertainties,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 54, no. 6, pp. 527–531, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. S. S. Delshad, A. Johansson, M. Darouach, and T. Gustafsson, “Robust state estimation and unknown inputs reconstruction for a class of nonlinear systems: multiobjective approach,” Automatica, vol. 64, pp. 1–7, 2016. View at Google Scholar · View at MathSciNet
  9. J. Chen and R. J. Patton, Robust Model-Based Fault Diagnosis for Dynamic Systems, Kluwer Academic, Norwell, Mass, USA, 1999.
  10. P. M. Frank, “Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy. a survey and some new results,” Automatica, vol. 26, no. 3, pp. 459–474, 1990. View at Publisher · View at Google Scholar · View at Scopus
  11. J. Yang and F. Zhu, “FDI design for uncertain nonlinear systems with both actuator and sensor faults,” Asian Journal of Control, vol. 17, no. 1, pp. 213–224, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. P. M. Frank and X. Ding, “Survey of robust residual generation and evaluation methods in observer-based fault detection systems,” Journal of Process Control, vol. 7, no. 6, pp. 403–424, 1997. View at Publisher · View at Google Scholar · View at Scopus
  13. R. J. Patton and J. Chen, “Observer-based fault detection and isolation: robustness and applications,” Control Engineering Practice, vol. 5, no. 5, pp. 671–682, 1997. View at Publisher · View at Google Scholar · View at Scopus
  14. G. R. Duan and R. J. Patton, “Robust fault detection using Luenbergertype unknown input observers-a parametric approach,” International Journal of Systems Science, vol. 32, no. 4, pp. 533–540, 2001. View at Publisher · View at Google Scholar
  15. J. Su, W.-H. Chen, and B. Li, “Disturbance observer based fault diagnosis,” in Proceedings of the 33rd Chinese Control Conference (CCC '14), pp. 3024–3029, Nanjing, China, July 2014. View at Publisher · View at Google Scholar · View at Scopus
  16. G. R. Duan and R. J. Patton, “Robust fault detection in linear systems using Luenberger observers,” in Proceedings of the UKACC International Conference on Control, vol. 2, pp. 1468–1473, Swansea, UK, September 1998. View at Publisher · View at Google Scholar
  17. W. Ge and C. Z. Fang, “Detection of faulty components via robust observation,” International Journal of Control, vol. 47, no. 2, pp. 581–599, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  18. H. Liu, D. Liu, C. Lu, and X. Wang, “Fault diagnosis of hydraulic servo system using the unscented Kalman Filter,” Asian Journal of Control, vol. 16, no. 6, pp. 1713–1725, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  19. F. Zhu and F. Cen, “Full-order observer-based actuator fault detection and reduced-order observer-based fault reconstruction for a class of uncertain nonlinear systems,” Journal of Process Control, vol. 20, no. 10, pp. 1141–1149, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. C. Edwards, S. K. Spurgeon, and R. J. Patton, “Sliding mode observers for fault detection and isolation,” Automatica, vol. 36, no. 4, pp. 541–553, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. O. A. Z. Sotomayor and D. Odloak, “Observer-based fault diagnosis in chemical plants,” Chemical Engineering Journal, vol. 112, no. 1–3, pp. 93–108, 2005. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Chen, R. J. Patton, and H.-Y. Zhang, “Design of unknown input observers and robust fault detection filters,” International Journal of Control, vol. 63, no. 1, pp. 85–105, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  23. P. Rosa and C. Silvestre, “Fault detection and isolation of LPV systems using set-valued observers: an application to a fixed-wing aircraft,” Control Engineering Practice, vol. 21, no. 3, pp. 242–252, 2013. View at Publisher · View at Google Scholar · View at Scopus
  24. T.-G. Park, “Designing fault detection observers for linear systems with mismatched unknown inputs,” Journal of Process Control, vol. 23, no. 8, pp. 1185–1196, 2013. View at Publisher · View at Google Scholar · View at Scopus
  25. F. Xu, V. Puig, C. Ocampo-Martinez, F. Stoican, and S. Olaru, “Actuator-fault detection and isolation based on set-theoretic approaches,” Journal of Process Control, vol. 24, no. 6, pp. 947–956, 2014. View at Publisher · View at Google Scholar · View at Scopus
  26. M. Hou and P. C. Muller, “Fault detection and isolation observers,” International Journal of Control, vol. 60, no. 5, pp. 827–846, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  27. J. Gertler, “Fault detection and isolation using parity relations,” Control Engineering Practice, vol. 5, no. 5, pp. 653–661, 1997. View at Publisher · View at Google Scholar · View at Scopus
  28. D. Koenig and S. Mammar, “Design of a class of reduced order unknown inputs nonlinear observer for fault diagnosis,” in Proceedings of the American Control Conference, vol. 3, pp. 2143–2147, Arlington, Va, USA, June 2001. View at Scopus
  29. A. Varga, “On designing least order residual generators for fault detection and isolation,” in Proceedings of the 16th International Conference on Control Systems and Computer Science, pp. 323–330, Bucharest, Romania, May 2007.
  30. Y. Xiong and M. Saif, “Unknown disturbance inputs estimation based on a state function observer design,” Automatica, vol. 39, no. 8, pp. 1389–1398, 2003. View at Google Scholar
  31. Z. Yuan, G. C. Vansteenkiste, and C. Wen, “Improving the observer-based FDI design for efficient fault isolation,” International Journal of Control, vol. 68, no. 1, pp. 197–218, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. P. S. Teh and H. Trinh, “Design of unknown input functional observers for nonlinear systems with application to fault diagnosis,” Journal of Process Control, vol. 23, no. 8, pp. 1169–1184, 2013. View at Publisher · View at Google Scholar · View at Scopus
  33. H. Trinh, T. Fernando, K. Emami, and D. C. Huong, “Fault detection of dynamical systems using first-order functional observers,” in Proceedings of the 8th IEEE International Conference on Industrial and Information Systems (ICIIS '13), pp. 197–200, IEEE, Peradeniya, Sri Lanka, December 2013. View at Publisher · View at Google Scholar · View at Scopus
  34. D. C. Huong, H. Trinh, H. M. Tran, and T. Fernando, “Approach to fault detection of time-delay systems using functional observers,” Electronics Letters, vol. 50, no. 16, pp. 1132–1134, 2014. View at Publisher · View at Google Scholar · View at Scopus
  35. K. Emami, T. Fernando, B. Nener, H. Trinh, and Y. Zhang, “A functional observer based fault detection technique for dynamical systems,” Journal of the Franklin Institute, vol. 352, no. 5, pp. 2113–2128, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  36. M. Darouach, “Existence and design of functional observers for linear systems,” IEEE Transactions on Automatic Control, vol. 45, no. 5, pp. 940–943, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  37. H. Trinh and T. Fernando, “On the existence and design of functional observers for linear systems,” in Proceedings of the IEEE International Conference on Mechatronics and Automation (ICMA '07), pp. 1974–1979, Harbin, China, August 2007. View at Publisher · View at Google Scholar · View at Scopus
  38. H. Trinh and T. Fernando, Functional Observers for Dynamical Systems, Springer, Berlin, Germany, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  39. F. Rotella and I. Zambettakis, “On functional observers for linear time-varying systems,” IEEE Transactions on Automatic Control, vol. 58, no. 5, pp. 1354–1360, 2013. View at Publisher · View at Google Scholar · View at Scopus
  40. T. Fernando and H. Trinh, “A system decomposition approach to the design of functional observers,” International Journal of Control, vol. 87, no. 9, pp. 1846–1860, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  41. T. L. Fernando, H. M. Trinh, and L. Jennings, “Functional observability and the design of minimum order linear functional observers,” IEEE Transactions on Automatic Control, vol. 55, no. 5, pp. 1268–1273, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  42. G.-R. Duan, “Solutions of the equation AV+BW=VF and their application to eigenstructure assignment in linear systems,” IEEE Transactions on Automatic Control, vol. 38, no. 2, pp. 276–280, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  43. J. Su and W. H. Chen, “Fault diagnosis for vehicle lateral dynamics with robust threshold,” in Proceedings of the IEEE International Conference on Industrial Technology, Taipei, Taiwan, March 2016.
  44. A. Termehchy, A. Afshar, and M. Javidsharifi, “A novel design of unknown input observer for fault diagnosis in the Tennessee-Eastman process system to solve non-minimum phase problem,” in Proceedings of the IEEE International Conference on Smart Instrumentation, Measurement and Applications (ICSIMA '13), pp. 1–6, Kuala Lumpur, Malaysia, November 2013. View at Publisher · View at Google Scholar · View at Scopus