Novel optimal recursive filter for state and fault estimation of linear stochastic systems with unknown disturbances

• Autorzy: Khémiri K. , Ben Hmida F. , Ragot J. , Gossa M.
• Języki publikacji: EN

Abstrakty

EN

This paper studies recursive optimal filtering as well as robust fault and state estimation for linear stochastic systems with unknown disturbances. It proposes a new recursive optimal filter structure with transformation of the original system. This transformation is based on the singular value decomposition of the direct feedthrough matrix distribution of the fault which is assumed to be of arbitrary rank. The resulting filter is optimal in the sense of the unbiased minimum-variance criteria. Two numerical examples are given in order to illustrate the proposed method, in particular to solve the estimation of the simultaneous actuator and sensor fault problem and to make a comparison with the existing literature results.

Słowa kluczowe

EN

Kalman filtering; minimum variance estimation; state estimation; fault estimation; unknown disturbances; linear discrete time systems

PL

filtracja Kalmana; estymacja stanu; zakłócenie nieznane; system liniowy; system dyskretno-czasowy

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2011
• Tom: Vol. 21, no 4
• Strony: 629--637
• Opis fizyczny: Bibliogr. 19 poz., tab., wykr.

Twórcy

autor

Khémiri K.

autor

Ben Hmida F.

autor

Ragot J.

autor

Gossa M.

• Research Unit on Control, Monitoring and Safety of Systems (C3S), High School of Sciences and Techniques of Tunis (ESSTT), 5 av. Taha Hussein, BP 56-1008 Tunis, Tunisia,

Bibliografia

• [1] Ben Hmida, F., Khémiri, K., Ragot, J. and Gossa, M. (2010). Unbiased minimum-variance filter for state and fault estimation of linear time-varying systems with unknown disturbances, Mathematical Problems in Engineering, Vol. 2010, Article ID 343586, 17 pages.
• [2] Blanke, M., Kinnaert, M., Lunze, J. and Staroswiecki, M. (2006). Diagnosis and Fault-Tolerant Control, Springer-Verlag, Berlin/Heidelberg.
• [3] Chen, J. and Patton, R. (1996). Optimal filtering and robust fault diagnosis of stochastic system with unknown disturbances, IEE Proceedings: Control Theory Application 143(1): 31-36.
• [4] Chen, J. and Patton, R. (1999). Robust Model-based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers, Norwell, MA.
• [5] Cheng, Y., Ye, H., Wang, Y. and Zhou, D. (2009). Unbiased minimum-variance state estimation for linear systems with unknown input, Automatica 45(2): 485-491.
• [6] Darouach, M. and Zasadzinski, M. (1997). Unbiased minimum variance estimation for system with unknown exogenous inputs, Automatica 33(4): 717-719.
• [7] Darouach, M., Zasadzinski, M. and Boutayeb, M. (2003). Extension of minimum variance estimation for systems with unknown inputs, Automatica 39(5): 867-876.
• [8] Gillijns, S. and Moor, B. (2007a). Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough, Automatica 43(5): 934-937.
• [9] Gillijns, S. and Moor, B. (2007b). Unbiased minimum-variance input and state estimation for linear discrete-time systems, Automatica 43(1): 111-116.
• [10] Hou, M. and Patton, R. J. (1998). Optimal filtering for system with unknown inputs, IEEE Transactions on Automatic Control 43(3): 445-449.
• [11] Hsieh, C. (2009). Extension of unbiased minimum-variance input and state estimation for systems with unknown inputs, Automatica 45(9): 2149-2153.
• [12] Hsieh, C. S. (2000). Robust two-stage Kalman filters for systems with unknown inputs, IEEE Transactions on Automatic Control 45(12): 2374-2378.
• [13] Jamouli, H., Keller, J. and Sauter, D. (2003). Fault isolation filter with unknown inputs in stochastic systems, Proceedings of Safeprocess, Washington, DC, USA, pp. 531-536.
• [14] Kailath, T., Sayed, A. and Hassibi, B. (2000). Linear Estimation, Prentice Hall, Englewood Cliffs, NJ.
• [15] Keller, J. (1998). Fault isolation filter design for linear stochastic systems with unknown inputs, 37th IEEE Conference on Decision and Control, Tampa, FL, USA, pp. 598-603.
• [16] Keller, J. (1999). Fault isolation filter design for linear stochastic systems, Automatica 35(10): 1701-1706.
• [17] Keller, J. and Sauter, D. (2011). Restricted diagonal detection filter and updating strategy for multiple fault detection and isolation, International Journal of Adaptive Control and Signal Processing 25(1): 68-87.
• [18] Kitanidis, P. (1987). Unbiased minimum-variance linear state estimation, Automatica 23(6): 775-778.
• [19] Nikoukhah, R. (1994). Innovation generation in the presence of unknown inputs: Application to robust failure detection, Automatica 30(12): 1851-1867.