Skip to main content

2018 | OriginalPaper | Buchkapitel

\(H_{-}/H_{\infty }\) Fault Detection Observer Design for Discrete-Time Polytopic LPV System Based on Relative Degree of Output

verfasst von : Meng Zhou, Mickael Rodrigues, Yi Shen, Didier Theilliol

Erschienen in: Advanced Solutions in Diagnostics and Fault Tolerant Control

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This paper proposes an \( H_{-}/H_{\infty } \) fault detection observer for discrete-time polytopic linear parameter-varying (LPV) system based on relative degree of output. First, a new output is generated by gathering the original output and its time shifted value. Then an \( H_{-}/H_{\infty } \) fault detection observer is designed for the new system such that the generated residual is robust against unknown disturbances and sensitive to actuator faults, simultaneously. In order to reduce some conservativeness, the observer is solved by an iterative LMIs algorithm. Simulations results are given to illustrate the effectiveness of the proposed method.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Varrier, S., Koenig, D., Martinez, J.: Robust fault detection for uncertain unknown inputs LPV system. Control Eng. Pract. 22, 125–134 (2014)CrossRef Varrier, S., Koenig, D., Martinez, J.: Robust fault detection for uncertain unknown inputs LPV system. Control Eng. Pract. 22, 125–134 (2014)CrossRef
2.
Zurück zum Zitat Rodrigues, M., Hamdi, H., Theilliol, D., Mechmeche, C., Braiek, N.B.: Actuator fault estimation based adaptive polytopic observer for a class of LPV descriptor systems. Int. J. Robust Nonlinear Control 25, 1–15 (2014)MathSciNetMATH Rodrigues, M., Hamdi, H., Theilliol, D., Mechmeche, C., Braiek, N.B.: Actuator fault estimation based adaptive polytopic observer for a class of LPV descriptor systems. Int. J. Robust Nonlinear Control 25, 1–15 (2014)MathSciNetMATH
3.
Zurück zum Zitat Hou, M., Patton, R.J.: An LMI approach to \({H}_{-}/{H}_{\infty }\) fault detection observers. In: Proceedins of the UKACC International Conference on Control, pp. 305–310, Exeter, UK (1996) Hou, M., Patton, R.J.: An LMI approach to \({H}_{-}/{H}_{\infty }\) fault detection observers. In: Proceedins of the UKACC International Conference on Control, pp. 305–310, Exeter, UK (1996)
4.
Zurück zum Zitat Liu, J., Wang, J.L., Yang, G.H.: An LMI approach to minimum sensitivity analysis with application to fault detection. Automatica 41, 1995–2004 (2005)MathSciNetCrossRefMATH Liu, J., Wang, J.L., Yang, G.H.: An LMI approach to minimum sensitivity analysis with application to fault detection. Automatica 41, 1995–2004 (2005)MathSciNetCrossRefMATH
5.
Zurück zum Zitat Wang, J.L., Yang, G.H., Liu, J.: An LMI approach to \( {H}_- \) index and mixed \( {H}_-/{H}_{\infty } \) fault detection observer design. Automatica 43, 1656–1665 (2007)CrossRefMATH Wang, J.L., Yang, G.H., Liu, J.: An LMI approach to \( {H}_- \) index and mixed \( {H}_-/{H}_{\infty } \) fault detection observer design. Automatica 43, 1656–1665 (2007)CrossRefMATH
6.
Zurück zum Zitat Ding, D.W., Wang, H., Li, X.L.: \({H}_{-}/{H}_{\infty }\) fault detection observer design for two-dimensional Rosser systems. Syst. Control Lett. 82, 115–120 (2015)CrossRefMATH Ding, D.W., Wang, H., Li, X.L.: \({H}_{-}/{H}_{\infty }\) fault detection observer design for two-dimensional Rosser systems. Syst. Control Lett. 82, 115–120 (2015)CrossRefMATH
7.
Zurück zum Zitat Wei, X., Verhaegen, M.: LMI solutions to the mixed \( {H}_{-}/{H}_{\infty } \) fault detection observer design for linear parameter-varying systems. Int. J. Adapt. Control Signal Process. 25, 114–136 (2011)MathSciNetCrossRefMATH Wei, X., Verhaegen, M.: LMI solutions to the mixed \( {H}_{-}/{H}_{\infty } \) fault detection observer design for linear parameter-varying systems. Int. J. Adapt. Control Signal Process. 25, 114–136 (2011)MathSciNetCrossRefMATH
8.
Zurück zum Zitat Estrada, F.R.L., Ponsart, J.C., Theilliol, D., Zaragoza, C.M.A.: Robust \( {H}_{-}/{H}_{\infty } \) fault detection observer for descriptor-LPV systems with unmeasurable gain scheduling functions. Int. J. Control 88, 2380–2391 (2015)CrossRefMATH Estrada, F.R.L., Ponsart, J.C., Theilliol, D., Zaragoza, C.M.A.: Robust \( {H}_{-}/{H}_{\infty } \) fault detection observer for descriptor-LPV systems with unmeasurable gain scheduling functions. Int. J. Control 88, 2380–2391 (2015)CrossRefMATH
9.
Zurück zum Zitat Jee, S.C., Lee, H.J.: \( {H}_{-}/{H}_{\infty } \) fault detection and isolation for nonlinear systems with state delay in T-S form. J. Franklin Inst. 88, 2030–2056 (2016)MathSciNetCrossRefMATH Jee, S.C., Lee, H.J.: \( {H}_{-}/{H}_{\infty } \) fault detection and isolation for nonlinear systems with state delay in T-S form. J. Franklin Inst. 88, 2030–2056 (2016)MathSciNetCrossRefMATH
10.
Zurück zum Zitat Ichalal, D., Marx, B., Maquin, D., Ragot, J.: Actuator fault diagnosis: \( {H}_{\infty } \) framework with relative degree notion. In: 4th IFAC International Conference on Intelligent Control and Automation Science, pp. 327–332. Reims, France (2016) Ichalal, D., Marx, B., Maquin, D., Ragot, J.: Actuator fault diagnosis: \( {H}_{\infty } \) framework with relative degree notion. In: 4th IFAC International Conference on Intelligent Control and Automation Science, pp. 327–332. Reims, France (2016)
11.
Zurück zum Zitat Zhou, M., Rodrigues, M., Shen, Y., Theilliol, D.: \( {H}_{-}/{H}_{\infty } \) fault detection observer design based on generalized output for linear parameter-varying system. In: 13th European Workshop on Advanced Control and Diagnosis, Lille, France (2016) Zhou, M., Rodrigues, M., Shen, Y., Theilliol, D.: \( {H}_{-}/{H}_{\infty } \) fault detection observer design based on generalized output for linear parameter-varying system. In: 13th European Workshop on Advanced Control and Diagnosis, Lille, France (2016)
12.
Zurück zum Zitat Varrier, S., Koenig, D., Matinez, J.J.: Robust fault detection for uncertain unknown inputs LPV system. Control Eng. Practice 22, 125–134 (2014)CrossRef Varrier, S., Koenig, D., Matinez, J.J.: Robust fault detection for uncertain unknown inputs LPV system. Control Eng. Practice 22, 125–134 (2014)CrossRef
13.
Zurück zum Zitat Isidori, A.: Nonlinear control systems. In: Communications and Control Engineering. Springer (1995) Isidori, A.: Nonlinear control systems. In: Communications and Control Engineering. Springer (1995)
14.
Zurück zum Zitat Qi, R.Y., Tao, G., Tan, C., Yao, X.L.: Adptive control of discrete-time state-space T-S fuzzy systems with general relative degree. Fuzzy Sets Syst. 217, 22–40 (2013)CrossRefMATH Qi, R.Y., Tao, G., Tan, C., Yao, X.L.: Adptive control of discrete-time state-space T-S fuzzy systems with general relative degree. Fuzzy Sets Syst. 217, 22–40 (2013)CrossRefMATH
15.
Zurück zum Zitat Wang, H., Yang, G.H.: A finite frequency domain approach to fault detection observer design for linear continuous-time systems. Asian J. Control 10, 1–10 (2008)MathSciNetCrossRef Wang, H., Yang, G.H.: A finite frequency domain approach to fault detection observer design for linear continuous-time systems. Asian J. Control 10, 1–10 (2008)MathSciNetCrossRef
16.
Zurück zum Zitat Wang, Z.H., Rodrigues, M., Theilliol, D., Shen, Y.: Fault estimation filter design for discrete-time descriptor systems. IET Control Theory Appl. 9, 1587–1594 (2015)MathSciNetCrossRefMATH Wang, Z.H., Rodrigues, M., Theilliol, D., Shen, Y.: Fault estimation filter design for discrete-time descriptor systems. IET Control Theory Appl. 9, 1587–1594 (2015)MathSciNetCrossRefMATH
17.
Zurück zum Zitat Huang, D., Duan, Z.S.: A new iterative approach for multi-objective fault detection observer design and its application to a hypersonic vehicle. Int. J. Control (2017). Published online Huang, D., Duan, Z.S.: A new iterative approach for multi-objective fault detection observer design and its application to a hypersonic vehicle. Int. J. Control (2017). Published online
18.
Zurück zum Zitat Rotondo, D., Estrada, F.R.L., Nejjari, F., Ponsart, J.C., Theilliol, D., Puig, V.: Actuator multiplicative fault estimation in discrete-time LPV systems using switched observers. J. Franklin Inst. 353, 3176–3191 (2016)MathSciNetCrossRefMATH Rotondo, D., Estrada, F.R.L., Nejjari, F., Ponsart, J.C., Theilliol, D., Puig, V.: Actuator multiplicative fault estimation in discrete-time LPV systems using switched observers. J. Franklin Inst. 353, 3176–3191 (2016)MathSciNetCrossRefMATH
19.
Zurück zum Zitat Chadli, M., Abdo, A., Ding, S.X.: \( {H}_{-}/{H}_{\infty } \) fault detection filter design for discrete-time Takagi-Sugeno fuzzy system. Automatica 49, 1996–2005 (2013)MathSciNetCrossRefMATH Chadli, M., Abdo, A., Ding, S.X.: \( {H}_{-}/{H}_{\infty } \) fault detection filter design for discrete-time Takagi-Sugeno fuzzy system. Automatica 49, 1996–2005 (2013)MathSciNetCrossRefMATH
Metadaten
Titel
Fault Detection Observer Design for Discrete-Time Polytopic LPV System Based on Relative Degree of Output
verfasst von
Meng Zhou
Mickael Rodrigues
Yi Shen
Didier Theilliol
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-64474-5_10