Parity Relation Based Fault Estimation for Nonlinear Systems: An LMI Approach

Sing Kiong Nguang; Ping Zhang; Steven X. Ding

doi:10.1007/s11633-007-0164-7

April 2007

Article Contents

Sing Kiong Nguang, Ping Zhang and Steven X. Ding. Parity Relation Based Fault Estimation for Nonlinear Systems: An LMI Approach. International Journal of Automation and Computing, vol. 4, no. 2, pp. 164-168, 2007. doi: 10.1007/s11633-007-0164-7

Cite as: Sing Kiong Nguang, Ping Zhang and Steven X. Ding. Parity Relation Based Fault Estimation for Nonlinear Systems: An LMI Approach. International Journal of Automation and Computing, vol. 4, no. 2, pp. 164-168, 2007. doi: 10.1007/s11633-007-0164-7

Parity Relation Based Fault Estimation for Nonlinear Systems: An LMI Approach

1.
The Department of Electrical and Computer Engineering, the University of Auckland, Auckland, New Zealand;
2.
AKS, Faculty of Engineering, University of Duisburg-Essen, Duisburg, Germany

Received: 2006-01-10

Fund Project:

This work was supported by the Alexander von Humboldt Foundation.

Abstract

This paper proposes a parity relation based fault estimation for a class of nonlinear systems which can be modelled by Takagi-Sugeno (TS) fuzzy models. The design of a parity relation based residual generator is formulated in terms of a family of linear matrix inequalities (LMIs). A numerical example is provided to illustrate the effectiveness of the proposed design techniques.
- Fuzzy systems,
- nonlinear systems,
- fault identification,
- fault detection,
- fault diagnosis

References

[1]	M.Basseville.Detecting Changes in Signals and Systems -A Survey.Automatica,vol.24,no.3,pp.309-326,1988.
[2]	R.Isermann.Process Fault Detection Based on Modeling and Estimation Methods-A Survey.Automatica,vol.20,no.4,pp.387-404,1984.
[3]	P.M.Frank.Fault Diagnosis in Dynamic Systems Using Analytical and Knowledge Based Redundancy-A Survey of Some New Results.Automatica,vol.26,no.3,pp.459-474,1990.
[4]	R.J.Patton,J.Chen.A Review of Parity Space Approaches to Fault Diagnosis.In Proceedings of IFAC Symposium on Safeprocess'91,Hull,UK,vol.1,pp.239-255,1991.
[5]	J.E.Potter,M.C.Suman.Threshold Redundancy Management with Arrays of Skewed Instruments.Integrity in Electronic Flight Control Systems,vol.Agardograph 224,no.15,pp.11-25,1977.
[6]	E.Y.Chow,A.S.Willsky.Analytical Redundancy and the Design of Robust Failure Detection Systems,IEEE Transactions on Automatic Control,vol.29,no.7,pp.603-614,1984.
[7]	J.J.Gertler.Survey of Model-based Failure Detection and Isolation in Complex Plants,IEEE Control Systems Magazine,vol.3,no.6,pp.3-11,1988.
[8]	X.C.Lou,A.S.Willsky,G.C.Verghese.Optimally Robust Redundancy Relations for Failure Detection in Uncertain Systems.Automatica,vol.22,no.3,pp.333-344,1986.
[9]	J.J.Gertler.Analytical Redundancy Methods in Fault Detection and Isolation,In Proceedings of IFAC/IMACS Symposium on Safeproeess,Baden-Baden,Germany,vol.1,pp.9-21,1991.
[10]	F.Hamelin,D.Sauter,D.Theilliol.Some Extensions to the Parity Space Method for FDI Using Alternated Projection Subspaces.In Proceedings of 34th IEEE Conference on Decision and Control,New Orleans,LA,vol.3,pp.2407-2412,1995.
[11]	X.Ding,L.Guo,T.Jeinsch.A Characterization of Parity Space and Its Application to Robust Fault Detection.IEEE Transactions on Automatic Control,vol.44,no.2,pp.337-343,1999.
[12]	D.L.Yu,D.Williams,D.N.Shields,J.B.Gomm.An Extended Parity Space Method for Bilinear Systems.In Proceedings of American Control Conference,Seattle,WA,pp.1132-1133,1995.
[13]	M.Staroswiecki,G.Comtet-Varga.Analytical Redundancy Relations for Fault Detection and Isolation in Algebraic Dynamic Systems.Automatica,vol.37,no.5,pp.687-699,2001.
[14]	V.Krishnaswami,G.Rizzoni.A Survey of Observerbased Residual Generation for FDI.In Proceedings of the IFAC Symposium on SafeProcess,Espoo,Finland,vol.1,pp.34-37,1994
[15]	T.Takagi,M.Sugeno.Fuzzy Identification of Systems and Its Applications to Modelling and Control.IEEE Transactions on Systems,Man,and Cybernetics,vol.15,no.1,pp.116-132,1985.
[16]	B.S.Chen,C.S.Tseng,H.J.Uang.Mixed H2/H∞ Fuzzy Output Feedback Control Design for Nonlinear Dynamic Systems:An LMI Approach.IEEE Transactions on Fuzzy Systems,vol.8,no.2,pp.249-265,2000.
[17]	S.K.Nguang,P.Shi.Fuzzy Output Feedback Control Design for Nonlinear Systems:An LMI Approach.IEEE Transactions on Fuzzy Systems,vol.11,no.3,pp.331-340,2003.
[18]	S.K.Nguang,P.Shi.H∞ Output Feedback Control of Fuzzy System Models Under Sampled Measurements.Automatica,vol.39,no.12,pp.2169-2174,2003.
[19]	S.K.Nguang,W.Assawinchaichote.H∞ Filtering for Fuzzy Dynamical Systems with Pole Placement Constraints.IEEE Transactions on Circuits and Systems,Part 1,vol.50,no.11,pp.1503-1508,2003.
[20]	W.Assawinchaichote,S.K.Nguang.H∞ Fuzzy Control Design for Nonlinear Singularly Perturbed Systems with Pole Placement Constraints:An LMI Approach.IEEE Transactions on Systems,Man,and Cybernetics,Part B,vol.36,no.4,pp.579-588,2004.
[21]	W.Assawinchaichote,S.K.Nguang.H∞ Filtering for Nonlinear Singularly Perturbed Systems with Pole Placement Constraints:An LMI Approach,IEEE Transactions on Signal Processing,vol.52,no.6,pp.1659-1667,2004.
[22]	S.P.Boyd,L.El Ghaoui,E.Feron,V.Balakrishnan.Linear Matrix Inequalities in System and Control,SIAM,Philadelphia,PA,1994.
[23]	L.X.Wang.A Course in Fuzzy Systems and Control,Prentice-Hall,Englewood Cliffs,NJ,1997.
[24]	L.Wang,R.Langari.Building Sugeno-type Models Using Fuzzy Discretization and Orthogonal Parameter Estimation Techniques.IEEE Transactions on Fuzzy Systems,vol.3,no.4,pp.454-458,1995.
[25]	H.O.Wang,K.Tanaka,M.F.Griffin.An Approach to Fuzzy Control of Nonlinear Systems:Stability and Design Issues,IEEE Transaction on Fuzzy Systems,vol.4,no.2,pp.14-23,1996.
[26]	T.Taniguchi,K.Tanaka,H.Ohtake,H.W.Wang.Model Construction,Rule Reduction,and Robust Compensation for Generalized Form of Takagi-Sugeno Fuzzy Systems.IEEE Transactions on Fuzzy Systems,vol.9,no.4,pp.525-538,2001.
[27]	K.Tanaka,T.Ikeda,H.O.Wang.Fuzzy Regulators and Fuzzy Observers:Relaxed Stability Conditions and LMI-based Design,IEEE Transactions on Fuzzy Systems,vol.6,no.2,pp.250-265,1998.

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1.
沈阳化工大学材料科学与工程学院沈阳 110142

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Parity Relation Based Fault Estimation for Nonlinear Systems: An LMI Approach

1. The Department of Electrical and Computer Engineering, the University of Auckland, Auckland, New Zealand;

2. AKS, Faculty of Engineering, University of Duisburg-Essen, Duisburg, Germany

Received: 2006-01-10

Fund Project:

This work was supported by the Alexander von Humboldt Foundation.

Key words:

Abstract: This paper proposes a parity relation based fault estimation for a class of nonlinear systems which can be modelled by Takagi-Sugeno (TS) fuzzy models. The design of a parity relation based residual generator is formulated in terms of a family of linear matrix inequalities (LMIs). A numerical example is provided to illustrate the effectiveness of the proposed design techniques.

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Reference (27)

[1]	M.Basseville.Detecting Changes in Signals and Systems -A Survey.Automatica,vol.24,no.3,pp.309-326,1988.
[2]	R.Isermann.Process Fault Detection Based on Modeling and Estimation Methods-A Survey.Automatica,vol.20,no.4,pp.387-404,1984.
[3]	P.M.Frank.Fault Diagnosis in Dynamic Systems Using Analytical and Knowledge Based Redundancy-A Survey of Some New Results.Automatica,vol.26,no.3,pp.459-474,1990.
[4]	R.J.Patton,J.Chen.A Review of Parity Space Approaches to Fault Diagnosis.In Proceedings of IFAC Symposium on Safeprocess'91,Hull,UK,vol.1,pp.239-255,1991.
[5]	J.E.Potter,M.C.Suman.Threshold Redundancy Management with Arrays of Skewed Instruments.Integrity in Electronic Flight Control Systems,vol.Agardograph 224,no.15,pp.11-25,1977.
[6]	E.Y.Chow,A.S.Willsky.Analytical Redundancy and the Design of Robust Failure Detection Systems,IEEE Transactions on Automatic Control,vol.29,no.7,pp.603-614,1984.
[7]	J.J.Gertler.Survey of Model-based Failure Detection and Isolation in Complex Plants,IEEE Control Systems Magazine,vol.3,no.6,pp.3-11,1988.
[8]	X.C.Lou,A.S.Willsky,G.C.Verghese.Optimally Robust Redundancy Relations for Failure Detection in Uncertain Systems.Automatica,vol.22,no.3,pp.333-344,1986.
[9]	J.J.Gertler.Analytical Redundancy Methods in Fault Detection and Isolation,In Proceedings of IFAC/IMACS Symposium on Safeproeess,Baden-Baden,Germany,vol.1,pp.9-21,1991.
[10]	F.Hamelin,D.Sauter,D.Theilliol.Some Extensions to the Parity Space Method for FDI Using Alternated Projection Subspaces.In Proceedings of 34th IEEE Conference on Decision and Control,New Orleans,LA,vol.3,pp.2407-2412,1995.
[11]	X.Ding,L.Guo,T.Jeinsch.A Characterization of Parity Space and Its Application to Robust Fault Detection.IEEE Transactions on Automatic Control,vol.44,no.2,pp.337-343,1999.
[12]	D.L.Yu,D.Williams,D.N.Shields,J.B.Gomm.An Extended Parity Space Method for Bilinear Systems.In Proceedings of American Control Conference,Seattle,WA,pp.1132-1133,1995.
[13]	M.Staroswiecki,G.Comtet-Varga.Analytical Redundancy Relations for Fault Detection and Isolation in Algebraic Dynamic Systems.Automatica,vol.37,no.5,pp.687-699,2001.
[14]	V.Krishnaswami,G.Rizzoni.A Survey of Observerbased Residual Generation for FDI.In Proceedings of the IFAC Symposium on SafeProcess,Espoo,Finland,vol.1,pp.34-37,1994
[15]	T.Takagi,M.Sugeno.Fuzzy Identification of Systems and Its Applications to Modelling and Control.IEEE Transactions on Systems,Man,and Cybernetics,vol.15,no.1,pp.116-132,1985.
[16]	B.S.Chen,C.S.Tseng,H.J.Uang.Mixed H2/H∞ Fuzzy Output Feedback Control Design for Nonlinear Dynamic Systems:An LMI Approach.IEEE Transactions on Fuzzy Systems,vol.8,no.2,pp.249-265,2000.
[17]	S.K.Nguang,P.Shi.Fuzzy Output Feedback Control Design for Nonlinear Systems:An LMI Approach.IEEE Transactions on Fuzzy Systems,vol.11,no.3,pp.331-340,2003.
[18]	S.K.Nguang,P.Shi.H∞ Output Feedback Control of Fuzzy System Models Under Sampled Measurements.Automatica,vol.39,no.12,pp.2169-2174,2003.
[19]	S.K.Nguang,W.Assawinchaichote.H∞ Filtering for Fuzzy Dynamical Systems with Pole Placement Constraints.IEEE Transactions on Circuits and Systems,Part 1,vol.50,no.11,pp.1503-1508,2003.
[20]	W.Assawinchaichote,S.K.Nguang.H∞ Fuzzy Control Design for Nonlinear Singularly Perturbed Systems with Pole Placement Constraints:An LMI Approach.IEEE Transactions on Systems,Man,and Cybernetics,Part B,vol.36,no.4,pp.579-588,2004.
[21]	W.Assawinchaichote,S.K.Nguang.H∞ Filtering for Nonlinear Singularly Perturbed Systems with Pole Placement Constraints:An LMI Approach,IEEE Transactions on Signal Processing,vol.52,no.6,pp.1659-1667,2004.
[22]	S.P.Boyd,L.El Ghaoui,E.Feron,V.Balakrishnan.Linear Matrix Inequalities in System and Control,SIAM,Philadelphia,PA,1994.
[23]	L.X.Wang.A Course in Fuzzy Systems and Control,Prentice-Hall,Englewood Cliffs,NJ,1997.
[24]	L.Wang,R.Langari.Building Sugeno-type Models Using Fuzzy Discretization and Orthogonal Parameter Estimation Techniques.IEEE Transactions on Fuzzy Systems,vol.3,no.4,pp.454-458,1995.
[25]	H.O.Wang,K.Tanaka,M.F.Griffin.An Approach to Fuzzy Control of Nonlinear Systems:Stability and Design Issues,IEEE Transaction on Fuzzy Systems,vol.4,no.2,pp.14-23,1996.
[26]	T.Taniguchi,K.Tanaka,H.Ohtake,H.W.Wang.Model Construction,Rule Reduction,and Robust Compensation for Generalized Form of Takagi-Sugeno Fuzzy Systems.IEEE Transactions on Fuzzy Systems,vol.9,no.4,pp.525-538,2001.
[27]	K.Tanaka,T.Ikeda,H.O.Wang.Fuzzy Regulators and Fuzzy Observers:Relaxed Stability Conditions and LMI-based Design,IEEE Transactions on Fuzzy Systems,vol.6,no.2,pp.250-265,1998.

Parity Relation Based Fault Estimation for Nonlinear Systems: An LMI Approach

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