A reference model based robust H∞ filtering approach to fault detection in uncertain systems
Fault Detection, Supervision and Safety of Technical Processes, Volume # 6 | Part# 1
Zhenhai Li; Imad M. Jaimoukha; Emmanuel Mazars
Digital Object Identifier (DOI)
fault detection,robust estimation,uncertain linear systems,model reference,matrix inequality
Model-based robust fault diagnosis aims to attenuate influence from model uncertainties on the residual while maintaining fault detection and isolation performance. In this paper, we consider robust residual generation for integral quadratic constrained (IQC) uncertain systems. The design consists of two steps. A reference model, incorporated into a robust H∞ filtering framework, is set up to represent desired detection performance such as disturbance attenuation. Then, the extended robust H∞ filtering problem is solved by constructing a nonlinear matrix inequality (NLMI). Linearization of the NLMI results in an tractable LMI solution, where an illustrative example follows to verify the algorithm.
 Casavola, A., D. Famularo and G. Franze (2005). A robust deconvolution scheme for fault detection and isolation of uncertain linear systems: An lmi approach. Automatica 41(8), 1463-1472.  Chen, J. and P.R. Patton (1999). Robust model-based fault diagnosis for dynamic systems. Boston: Kluwer Academic Publishers.  Fliess, M., C. Join and H. Sira-Ramirez (2004). Robust residual generation for linear fault diagnosis: an algebraic setting with examples. Int. J. Control 77(14), 1223-1242.  Frank, P. M. and X. Ding (1997). Survey of robust residual generation and evaluation methods in observer-based fault detection systems. J. Proc. Cont. 7(6), 403-424.  Frank, P.M. and X. Ding (1994). Frequency domain approach to optimally robust residual generation and evaluation for model-based fault diagnosis. Automatica 30(5), 789-804.  Frisk, E. and L. Nielsen (1999). Robust residual generation for diagnosis including a reference model for residual behavior. In: Proceedings of the 14th IFAC World Congress. Beijing, China. pp. 55-60.  Henry, D. and A. Zolghadri (2005). Design of fault diagnosis filters: A multi-objective approach. J. The Franklin Institute 342(4), 421-446.  Li, H. and M. Fu (1997). A linear matrix inequality approach to robust H
∞filtering. IEEE Trans. Signal Processing 45(9), 2338-2350.  Palhares, R. M. and P. L. D. Peres (2001). Lmi approach to the mixed H 2/H ∞filtering design for discrete-time uncertain systems. IEEE Trans. Aerospace and Electronic Systems 37(1), 292-296.  Patton, R. J. and J. Chen (1997). Observer-based fault detection and isolation: Robustness and applications. Control Engineering Practice 5(5), 671-682.  Rank, M. L. and H. Niemann (1999). Norm based design of fault detectors. Int. J. Control 72(9), 773-783.  Rantzer, A. and A. Megretski (1994). System analysis via integral quadratic constraints. In: Proc. IEEE Conf. Dec. & Control. Lake Buena Vista, FL. pp. 3062-3067. Also Tech. Report TFRT-7531, Dept. of Automatic Control, Lund Inst. of Tech., April 1994.  Saberi, A., A.A. Stoorvogel, P. Sannuti and H. Niemann (2000). Fundamental problems in fault detection and identification. Int. J. Robust & Nonlinear Control 10(14), 1209-1236.  Yaesh, I. and U. Shaked (2000). Robust H ∞deconvolution and its application to fault detection. J. Guidance, Control, and Dynamics 23(6), 1101-1112.  Zhong, M., S.X. Ding, J. Lam and H. Wang (2003). An LMI approach to design robust fault detection filter for uncertain LTI systems. Automatica 39(3), 543-550.