Amatrix factorization solution to the H − / H ∞ fault detection problem

In this paper we give a matrix factorization solution to the H−/H∞ fault detection (FD) problem for linear time invariant dynamic systems. An H−/H∞ FD filter minimizes the sensitivity of the residual signal to disturbances while maintaining a minimum level of sensitivity to faults. More specifically, it minimizes the largest singular value, over the extended imaginary axis, of the transfer matrix from the disturbance to the residual signal vectors subject to the constraint that the singular values of the transfer matrix from the fault to the residual vectors are larger than or equal to 1. We show, through the use of matrix function factorizations and completions, that the problem reduces to a nonstandard model matching problem which is then solved under a mild assumption concerning the rank of a matrix function. We also give an illustrative example. 2006 Elsevier Ltd. All rights reserved.

[1]  D. Youla,et al.  On the factorization of rational matrices , 1961, IRE Trans. Inf. Theory.

[2]  C. Desoer,et al.  Linear System Theory , 1963 .

[3]  V. Walton,et al.  Detecting Instrument Malfunctions in Control Systems , 1975, IEEE Transactions on Aerospace and Electronic Systems.

[4]  Ron J. Patton,et al.  Robust fault diagnosis using the model-based approach , 1988 .

[5]  Keith Glover,et al.  Spectral factorization via Hermitian pencils , 1989 .

[6]  P. Frank,et al.  Fault detection via optimally robust detection filters , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[7]  B. Francis,et al.  Spectral and inner-outer factorizations of rational matrices , 1989 .

[8]  Paul M. Frank,et al.  Fault diagnosis in dynamic systems: theory and application , 1989 .

[9]  P. Frank,et al.  Fault detection via factorization approach , 1990 .

[10]  Paul M. Frank,et al.  Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy: A survey and some new results , 1990, Autom..

[11]  Paul M. Frank,et al.  An approach to robust residual generation and evaluation , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[12]  M. Tsai,et al.  A numerical algorithm for inner-outer factorizations of real-rational matrices , 1993 .

[13]  Paul M. Frank,et al.  An Approach to Residual Generator and Evaluator Design and Synthesis , 1993 .

[14]  Paul M. Frank,et al.  A frequency domain approach to fault detection of uncertain dynamic systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[15]  Steven X. Ding,et al.  Frequency domain approach to optimally robust residual generation and evaluation for model-based fault diagnosis , 1994, Autom..

[16]  Paul M. Frank,et al.  Analysis of a class of dedicated observer schemes to sensor fault isolation , 1996 .

[17]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[18]  R. J. Patton,et al.  An LMI approach to H - /H∞ fault detection observers , 2002 .

[19]  Brian D. O. Anderson,et al.  Spectral factorization with imaginary-axis zeros☆ , 1997 .

[20]  P. Frank,et al.  Survey of robust residual generation and evaluation methods in observer-based fault detection systems , 1997 .

[21]  Jie Chen,et al.  Robust Model-Based Fault Diagnosis for Dynamic Systems , 1998, The International Series on Asian Studies in Computer and Information Science.

[22]  R. J. Patton,et al.  On Sensitivity of Robust Fault Detection Observers , 1999 .

[23]  Paul M. Frank,et al.  Issues of Fault Diagnosis for Dynamic Systems , 2010, Springer London.

[24]  X. Steven Ding,et al.  Current Developments in the Theory of FDI , 2000 .

[25]  Dominique Sauter,et al.  Optimal thresholding for robust fault detection of uncertain systems , 2000 .

[26]  Jason L. Speyer,et al.  Robust multiple-fault detection filter , 2002 .

[27]  James Lam,et al.  An LMI approach to design robust fault detection filter for uncertain LTI systems , 2003, Autom..