Abstract
Fault detection observer and fault estimation filter are the main tools for the model based fault diagnosis approach. The dimension of the observer gain normally depends on the system order and the system output dimension. The fault estimation filter traditionally has the same order as the monitored system. For high order systems, these methods have the potential problems such as parameter optimization and the real time implementation on-board for applications. In this paper, the system dynamical model is first decomposed into two subsystems. The first subsystem has a low order which is the same as the fault dimension. The other subsystem is not affected by the fault directly. With the new model structure, a fault detection approach is proposed where only the residual of the first subsystem is designed to be sensitive to the faults. The residual of the second subsystem is totally decoupled from the faults. Moreover, a lower order fault estimation filter (with the same dimension of the fault) design algorithm is investigated. In addition, the design of a static fault estimation matrix is presented for further improving the fault estimation precision. The effectiveness of the proposed method is demonstrated by a simulation example.
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J. Chen and R. Patton, Robust Model-Based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers, London, Great Britain, 1999.
B. Jiang, J. Wang, and Y. C. Soh, “Robust fault diagnosis for a class of linear systems with uncertainty,” Proc. of the American Control Conference, Taipei, Taiwan, pp. 1900–1904, 1999.
X. Zhang, M. M. Polycarpou, and T. Parisini, “A robust detection and isolation scheme for abrupt and incipient faults in nonlinear systems,” IEEE Trans. on Automatic and Control, vol. 47, no. 4, pp. 576–593, 2002.
M. Y. Zhong, S. X. Ding, J. Lam, and H. Wang, “An LMI approach to design robust fault detection filter for uncertain LTI system,” Automatica, vol. 39, no. 3, pp. 543–550, 2003.
B. Jiang, M. Staroswiechi, and V. Cocquempot, “Fault diagnosis based on adaptive observer for a class of nonlinear systems with unknown parameters,” International Journal of Control, vol. 77, no. 4, pp. 415–426, 2004.
B. Jiang and F. N. Chowdhury, “Fault estimation and accommodation for linear MIMO discrete-time systems,” IEEE Trans. on Control System Technology, vol. 13, no. 3, pp. 493–499, 2005.
X. Zhang, T. Parisini, and M. M. Polycarpou, “Sensor bias fault isolation in a class of nonlinear systems,” IEEE Trans. on Automatic and Control, vol. 50, no. 3, pp. 370–376, 2005.
J. L. Wang, G. H. Yang, and J. Liu, “An LMI approach H_ index and mixed H_/H∞ fault detection observer,” Automatica, vol. 43, no. 9, pp. 1656–1665, 2007.
S. X. Ding, Model-Based Fault Diagnosis Tehniques-Design Schemes, Algorithms and Tools, Springer-Verlag, Berlin Heidelberg, 2008.
X. Wei and M. Verhaegen, “Robust fault detection observer design for linear uncertain systems,” International Journal of Control, vol. 84, no. 1, pp. 197–215, 2011.
X. Wei and M. Verhaegen, “LMI solutions to the mixed H_/H∞ infinity fault detection observer design for linear parameter varying systems,” International Journal of Adaptive Control and Signal Processing, vol. 25, no. 5, pp. 114–136, 2011.
X. Zhang, “Sensor bias fault detection and isolation in a class of nonlinear uncertain systems using adaptive estimation,” IEEE Trans. on Automatic and Control, vol. 56, no. 5, pp. 1220–1226, 2011.
N. Liu and K. Zhou, “Optimal robust fault detection for linear discrete time-systems,” Journal of Control Science and Engineering, vol. 2008, pp. 1–16, 2008.
H. Wang and G.-H. Yang, “Fault detection observer design in low frequency domain,” Proc. of the 16th IEEE International Conference on Control Application, pp. 976–981, 2007.
M. Corless and J. Tu, “State and input estimation for a class of uncertain system,” Automatica, vol. 34, no. 6, pp. 757–764, 1998.
C. Edwards and S. K. Spurgeon, Sliding Mode Control-Theory and Applications, Taylor and Francis, London, UK, 1998.
J. Liu, J. L. Wang, and G. H. Yang, “An LMI approach to minimum sensitivity analysis with application to fault detection,” Automatica, vol. 41, no. 11, pp. 1995–2004, 2005.
T. Iwasaki and S. Hara, “Dynamic output feedback synthesis with general frequency domain specification,” Proc. of IFAC World Congress, Prague, Czech Republic, 2005.
T. Iwasaki and S. Hara, “Robust control synthesis with general frequency domain specifications: static gain feedback case,” Proc. of American Control Conference, Massachusetts, USA, pp. 4613–4618, 2004.
R. E. Skelton, T. Iwasaki, and K. M. Grigoriadis, A Unified Algebraic Approach to Linear Control Design, Taylor and Francis, London, UK, 1998.
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Recommended by Editorial Board member Bin Jiang under the direction of Editor Myotaeg Lim.
This work is partly supported by Ph.D. Programs Foundation of Ministry of Education of China (Grant number: 2011000912 0037), Chinese 863 program (Contract No. 2011AA110503-6) and State Key Laboratory of Rail Traffic Control and Safety (Contract No.RCS2011ZZ005).
Xiukun Wei received his Ph.D. degree from Johannes Kepler University, Linz, Austria. Currently he is an associate professor at the State Key Lab of Rail Traffic Control and Safety, Beijing Jiaotong University, China. From 2006 to 2009, he was a PostDoc Researcher at Delft Center for System and Control, Delft University of Technology, Delft, The Netherlands. From 2002 to 2006, he held a Research Assistant position at the Institute of Design and Control of Mechatronical Systems, Johannes Kepler University. His research interests include fault diagnosis and its applications, Intelligent Transportation System, Control theory applications in a variety of fields such as Rail Traffic Control and Safety, Transportation.
Lihua Liu is an associate professor at Beijing Information and Technology university. Her research interests include control theory, fault diagnosis and their applications.
Limin Jia is a professor at the State Key Lab of Rail Traffic Control and Safety, Beijing Jiaotong University, China. His research interests include Intelligent Control, System Safety, Fault Diagnosis and their applications in a variety of fields such as Rail Traffic Control and Safety, Transportation and etc.
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Wei, X., Liu, L. & Jia, L. Fault diagnosis for high order systems based on model decomposition. Int. J. Control Autom. Syst. 11, 75–83 (2013). https://doi.org/10.1007/s12555-012-0009-1
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DOI: https://doi.org/10.1007/s12555-012-0009-1