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A robust deconvolution scheme for fault detection and isolation of uncertain linear systems: an LMI approach. (English) Zbl 1086.93014
Summary: Optimal $\Cal H_{\infty}$ deconvolution filter theory is exploited for the design of robust fault detection and isolation (FDI) units for uncertain polytopic linear systems. Such a filter is synthesized under frequency domain conditions which ensure guaranteed levels of disturbance attenuation, residual decoupling and deconvolution performance in prescribed frequency ranges. By means of the Projection Lemma, a quasi-convex formulation of the problem is obtained via LMIs. A FDI logic based on adaptive thresholds is also proposed for reducing the generation of false alarms. The effectiveness of the design technique is illustrated via a numerical example.

93C05Linear control systems
93E10Estimation and detection in stochastic control
Full Text: DOI
[1] Boyd, S.; Barratt, C.: Linear controller design. Limits of performance. (1991) · Zbl 0748.93003
[2] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in system and control theory. SIAM studies in applied mathematics 15 (1994) · Zbl 0816.93004
[3] Casavola, A., Famularo, D., & Franzè, G. (2005). A robust deconvolution scheme for fault detection and isolation of uncertain linear systems: An LMI approach. DEIS-University of Calabria, Technical report, DEIS-10/05.
[4] Chen, J.; Patton, R.: Robust model-based fault diagnosis for dynamic systems. (1999) · Zbl 0920.93001
[5] De Souza, C.E., & Trofino, A. (2000). A linear matrix inequality approach to the design of robust H2 filters. In: El Ghaoui, L., & Nivulescu, L. (Eds.), Advances in linear matrix inequality methods in Control (pp. 175-185). Philadephia: Siam · Zbl 0942.93040
[6] Frank, P. M.: Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy--a survey and some new results. Automatica 26, 459-474 (1990) · Zbl 0713.93052
[7] Frank, P. M.; Ding, X.: Frequency domain approach to optimally robust residual generation and evaluation for model-based fault diagnosis. Automatica 30, 789-804 (1994) · Zbl 0799.93018
[8] Frank, P. M.; Ding, X.: Survey of robust residual generation and evaluation methods in observer-based fault detection systems. Journal of process control 7, 403-424 (1997)
[9] Geromel, J. C.: Optimal linear filtering under parameter uncertainty. IEEE transactions on signal processing 47, 168-175 (1999) · Zbl 0988.93082
[10] Geromel, J. C.; De Oliveira, C.: H2 and H$\infty $Robust filtering for convex bounded uncertain systems. IEEE transactions on automatic control 46, 100-107 (2001) · Zbl 1056.93628
[11] Patton, R.; Frank, P.; Clark, R.: Fault diagnosis in dynamic systemstheory and applications. (1989)
[12] Rambeaux, F.; Hamelin, F.; Sauter, D.: Optimal thresholding for robust fault detection of uncertain systems. International journal of robust and nonlinear control 10, 1155-1173 (2000) · Zbl 0965.93059
[13] Rank, M. R. (1998). Robust and optimal control: Robust sampled dataH2and fault detection and isolation. Ph.D. thesis, Department of Automation, Technical University of Denmark, Lyngby, DK.
[14] Saberi, A.; Sannuti, P.; Stoorvogel, A. A.: Inverse filtering and deconcolution. International journal of robust and nonlinear control 11, 131-156 (2001) · Zbl 0972.93067
[15] Scherer, C. W.: An efficient solution to multi-objective control problems with LMI objectives. Systems and control letters 40, 43-57 (2000) · Zbl 0977.93031
[16] Stoorvogel, A. A.; Niemann, H. H.; Saberi, A.; Sannuti, P.: Optimal fault signal estimation. International journal of robust and nonlinear control 12, 697-727 (2002) · Zbl 0996.93039
[17] Stoustrup, J.; Niemann, H. H.: Fault estimation--a standard problem approach. International journal of robust and nonlinear control 12, 649-673 (2002) · Zbl 1011.93049
[18] Tuan, H. D.; Apkarian, P.; Nguyen, T. Q.: Robust filtering for uncertain nonlinearly parametrized plants. IEEE transactions on signal processing 51, 1806-1815 (2003)
[19] Zhong, M.; Ding, S. X.; Lam, J.; Haibo, W.: An LMI approach to design robust fault detection filter for uncertain LTI systems. Automatica 39, 543-550 (2003) · Zbl 1036.93061