Observer-based Fault Detection and Isolation for 2D State-space Models

In this paper, the fault detection and isolation problems for two-dimensional (2D) state-space models are investigated, both when no disturbances affect the system and when they actually do. Basing on some old results about dead-beat observers [Bisiacco, M. (1986) IEEE Transactions on Automatic Control, AC-31, 676–680] and on some recent results about dead-beat unknown input observers (UIOs) (for 2D systems affected by disturbances) [Bisiacco, M. & Valcher, M. E. (2004) International Journal of Control 77(9), 861–876], we develop a complete theory of dead-beat (possibly unknown input) observer-based fault detectors and isolators (FDIs). Necessary and sufficient conditions for the existence of a dead-beat observer-based FDI or for the existence of a dead-beat UIO-based FDI are derived, and constructive procedures for obtaining such FDIs are described in detail.

[1]  M. Bisiacco.  State and output feedback stabilizability of 2-D systems , 1985 .

[2]  H. Rosenbrock,et al.  State-space and multivariable theory, , 1970 .

[3]  Thomas Kailath,et al.  Linear Systems , 1980 .

[4]  R. Suárez,et al.  Global stabilization of a certain class of nonlinear systems , 1991 .

[5]  M. Bisiacco.  On the state reconstruction of 2D systems , 1985 .

[6]  Christian Commault,et al.  Observer-based fault detection and isolation for structured systems , 2002, IEEE Trans. Autom. Control..

[7]  Michel Kinnaert,et al.  Fault detection and isolation for unstable linear systems , 1995, IEEE Trans. Autom. Control..

[8]  Ettore Fornasini,et al.  A note on the state space realization of 2D FIR transfer functions , 1991 .

[9]  Robert M. Pap,et al.  Fault Diagnosis , 1990, Bayesian Networks in Fault Diagnosis.

[10]  C. Byrnes,et al.  Frequency domain and state space methods for linear systems , 1986 .

[11]  M. Morf,et al.  New results in 2-D systems theory, part II: 2-D state-space models—Realization and the notions of controllability, observability, and minimality , 1977, Proceedings of the IEEE.

[12]  Guang-Ren Duan,et al.  Robust fault detection in descriptor linear systems via generalized unknown input observers , 2002, Int. J. Syst. Sci..

[13]  Maria Paula Macedo Rocha.  Structure and representation of 2-D systems , 1990 .

[14]  Sandro Zampieri.  2D residual generation and dead-beat observers , 1991 .

[15]  T. Kaczorek.  Positive 1D and 2D Systems , 2001 .

[16]  R. Patton,et al.  Optimal filtering and robust fault diagnosis of stochastic systems with unknown disturbances , 1996 .

[17]  T. Kaczorek.  Two-Dimensional Linear Systems , 1985 .

[18]  Dante C. Youla,et al.  Notes on n-Dimensional System Theory , 1979 .

[19]  J.-Y. Keller.  Fault isolation filter design for linear stochastic systems , 1999, Autom..

[20]  Ettore Fornasini,et al.  Doubly-indexed dynamical systems: State-space models and structural properties , 1978, Mathematical systems theory.

[21]  W. Cholewa,et al.  Fault Diagnosis: Models, Artificial Intelligence, Applications , 2004 .

[22]  Ramine Nikoukhah,et al.  Innovations generation in the presence of unknown inputs: Application to robust failure detection , 1994, Autom..

[23]  P. Müller,et al.  Fault detection and isolation observers , 1994 .

[24]  Osami Saito,et al.  Design and Parameterization of 2D State Observer , 1997 .

[25]  Sun-Yuan Kung,et al.  New results in 2-D systems theory, part I: 2-D polynomial matrices, factorization, and coprimeness , 1977, Proceedings of the IEEE.

[26]  Michael A. Demetriou,et al.  UIO for fault detection in vector second order systems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[27]  Ettore Fornasini,et al.  Matrix Pairs in Two-Dimensional Systems: An Approach Based on Trace Series and Hankel Matrices , 1995 .

[28]  T. Kaczorek.  Perfect Observers for Singular 2D Linear Systems , 2001 .

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

[30]  Mauro Bisiacco,et al.  Unknown input observers for 2D state-space models , 2004 .

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

[32]  Ettore Fornasini,et al.  nD Polynomial Matrices with Applications to Multidimensional Signal Analysis , 1997, Multidimens. Syst. Signal Process..

[33]  M. Bisiacco.  On the structure of 2-D observers , 1986 .