# Input reconstruction by means of system inversion: A geometric approach to fault detection and isolation in nonlinear systems

András Edelmayer; József Bokor; Zoltán Szabó; Ferenc Szigeti

International Journal of Applied Mathematics and Computer Science (2004)

- Volume: 14, Issue: 2, page 189-199
- ISSN: 1641-876X

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topEdelmayer, András, et al. "Input reconstruction by means of system inversion: A geometric approach to fault detection and isolation in nonlinear systems." International Journal of Applied Mathematics and Computer Science 14.2 (2004): 189-199. <http://eudml.org/doc/207690>.

@article{Edelmayer2004,

abstract = {In this paper the classical detection filter design problem is considered as an input reconstruction problem. Input reconstruction is viewed as a dynamic inversion problem. This approach is based on the existence of the left inverse and arrives at detector architectures whose outputs are the fault signals while the inputs are the measured system inputs and outputs and possibly their time derivatives. The paper gives a brief summary of the properties and existence of the inverse for linear and nonlinear multivariable systems. A view of the inversion-based input reconstruction with special emphasis on the aspects of fault detection and isolation by using invariant subspaces and the results of classical geometrical systems theory is provided. The applicability of the idea to fault reconstruction is demonstrated through examples.},

author = {Edelmayer, András, Bokor, József, Szabó, Zoltán, Szigeti, Ferenc},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {system inversion; input reconstruction; fault detection and isolation; nonlinear systems; linear systems; nonlinear system},

language = {eng},

number = {2},

pages = {189-199},

title = {Input reconstruction by means of system inversion: A geometric approach to fault detection and isolation in nonlinear systems},

url = {http://eudml.org/doc/207690},

volume = {14},

year = {2004},

}

TY - JOUR

AU - Edelmayer, András

AU - Bokor, József

AU - Szabó, Zoltán

AU - Szigeti, Ferenc

TI - Input reconstruction by means of system inversion: A geometric approach to fault detection and isolation in nonlinear systems

JO - International Journal of Applied Mathematics and Computer Science

PY - 2004

VL - 14

IS - 2

SP - 189

EP - 199

AB - In this paper the classical detection filter design problem is considered as an input reconstruction problem. Input reconstruction is viewed as a dynamic inversion problem. This approach is based on the existence of the left inverse and arrives at detector architectures whose outputs are the fault signals while the inputs are the measured system inputs and outputs and possibly their time derivatives. The paper gives a brief summary of the properties and existence of the inverse for linear and nonlinear multivariable systems. A view of the inversion-based input reconstruction with special emphasis on the aspects of fault detection and isolation by using invariant subspaces and the results of classical geometrical systems theory is provided. The applicability of the idea to fault reconstruction is demonstrated through examples.

LA - eng

KW - system inversion; input reconstruction; fault detection and isolation; nonlinear systems; linear systems; nonlinear system

UR - http://eudml.org/doc/207690

ER -

## References

top- Balas G., Bokor J. and Szabó Z. (2003): Invariant subspaces for LPV systems and their applications. - IEEE Trans. Automat. Cont., Vol. 48, No. 11, pp. 2065-2069.
- Basile G. and Marro G. (1973): A new characterization of some structural properties of linear systems: Unknown-input observability, invertability and functional controllability. - Int. J. Contr., Vol. 17, No. 5, pp. 931-943. Zbl0255.93009
- Basseville M. and Nikiforov I.V. (1993): Detection of Abrupt Changes. Theory and Application. - Englewood Cliffs: Prentice Hall.
- Bokor J. and Balas G. (2004): Detection filter design for LPV systems - A geometric approach. - Automatica, Vol. 40, No. 3, pp. 511-518. Zbl1042.93018
- Chen J. and Patton R.J. (1998): Robust Model-Based Fault Diagnosis for Dynamic Systems. - Boston: Kluwer.
- De Persis C. and Isidori A. (2001): A geometric approach to nonlinear fault detection and isolation. - IEEE Trans. Automat. Contr., Vol. 46, No. 6, pp. 853-865. Zbl1009.93003
- Edelmayer A., Bokor J., Szigeti F. and Keviczky L. (1997): Robust detection filter design in the presence of time varying system perturbations. - Automatica, Vol. 33, No. 3, pp. 471-475. Zbl0872.93077
- Fliess M. (1986): A note on the invertibility of nonlinear input-output differential systems. - Syst. Contr. Lett., Vol. 8, No. 2, pp. 147-151. Zbl0634.93035
- Gertler J.J.(1998): Fault Detection and Diagnosis in Engineering Systems. - New York: Marcel Dekker.
- Goodwin G.C.(2002): Inverse problems with constraints. - Proc. 15th IFAC World Congress, Barcelona, Spain, (published on CD-ROM).
- Hammouri H., Kinnaert M. and El, Yaagoubi E.H. (1999): Observer-based approach to fault detection and isolation for nonlinear systems. - IEEE Trans. Automat. Contr., Vol. 44, No. 10, pp. 1879-1884. Zbl0956.93005
- Hirschorn R.M. (1979): Invertibility of multivariable nonlinear control systems. - IEEE Trans. Automat. Contr., Vol. AC-24, No. 6, pp. 855-865. Zbl0427.93020
- Hou M. and Patton R.J. (1998): Input observability and input reconstruction. - Automatica, Vol. 34, No. 6, pp. 789-794. Zbl0959.93006
- Isidori A.(1995): Nonlinear Control Systems, 3rd Ed.. -London: Springer Verlag. Zbl0878.93001
- Krupadanam A.S., Annaswamy A.M. and Mangoubi R.S. (2002): Multivariable adaptive control design with applications to autonomous helicopters. - AIAA J. Guid. Contr. Dynam., Vol. 25, No. 5, pp. 843-851.
- MangoubiR.S. (1998): Robust Estimation and Failure Detection - A Concise Treatment. - London: Springer Verlag.
- Mangoubi R.S. and Edelmayer A.(2000): Model based fault detection: The optimal past, the robust present and a few thoughts on the future. - Proc. 4th IFAC Symp. Fault Det. Sup. Safety for Tech. Sys., Safeprocess'00 (A. Edelmayer, Ed.), pp. 65-76, London: Pergamon Press.
- Massoumnia M.A. (1986): A geometric approach to the synthesis of failure detection filters. - IEEE Trans. Automat. Contr., Vol. AC-31, No. 3, pp. 839-846. Zbl0599.93017
- Massoumnia M.A., Verghese G.C. and Willsky A.S. (1989): Fault detection and identification. - IEEE Trans. Automat. Contr., Vol. AC-34, No. 3, pp. 316-321. Zbl0682.93061
- Morse A.S. and Wonham W.M. (1971): Status of noninteracting control. - IEEE Trans. Automat. Contr., Vol. AC-16, No. 6, pp. 568-581.
- Nijmeijer H. and van der Schaft A.J. (1991): Nonlinear Dynamical Control Systems. - London: Springer Verlag. Zbl0701.93001
- Silverman L.M. (1969): Inversion of multivariable linear systems. - IEEE Trans. Automat. Contr., Vol. AC-14, No. 3, pp. 270-276.
- Szabó Z., Bokor J. and Balas G. (2003): Computational issues in fault detection filter design. - Proc. Mediterranean Conf. Contr. Automat., MED'03, Rhodes, Greece, (published on CD-ROM).
- Szigeti F., Riós-Bolivar A. andRennola L. (2000): Fault detection and isolation in the presence of unmeasured disturbance: application to binary distillation columns. - Proc. 4th IFAC Symp. Fault Det. Sup. Safety for Techn. Sys., Safeprocess (A. Edelmayer, Ed.), pp. 989-992, London: Pergamon Press.
- Szigeti F., Vera C.E., Bokor J. and Edelmayer A. (2001): Inversion based fault detection and isolation. - Proc. 40th IEEE Conf. Dec. Cont., Orlando, FL, pp. 1005-1010.
- Szigeti F., Bokor J. and Edelmayer A. (2002): Input reconstruction by means of system inversion: Application to fault detection and isolation. - Proc. 15th IFAC World Congress, Barcelona, Spain, (published on CD-ROM). Zbl1083.93008
- Varga A. (2002): Computational issues in fault detection filter design. -Proc. 41st IEEE Conf. Dec. Contr., Las Vegas, NV, pp. 4760-4765.
- White J.E. and Speyer J.L. (1987): Detection filter design: Spectral theory and algorithms. - IEEE Trans. Automat. Contr., Vol. AC-32, No. 7, pp. 593-603. Zbl0625.93071
- Wonham W.M.(1992): Linear Multivariable Control. A Geometric Approach, 3rd Ed.. - New York: Springer. Zbl0314.93007

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