Skip to main content
SpringerLink
Log in

Fault-Tolerant Trajectory Tracking Control for Takagi–Sugeno Systems with Unmeasurable Premise Variables: Descriptor Approach

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

This paper discusses the problem of fault-tolerant tracking control (FTTC) for fuzzy nonlinear systems with unmeasurable premise variables. To simultaneously estimate the system states and the sensor faults, a fuzzy descriptor observer is developed. Then, a fault-tolerant controller to track the desired reference trajectories is synthesized. The sufficient stability conditions of the appropriate nonlinear augmented system are derived via the Lyapunov theory and the \(H_\infty \) approach. In order to obtain both the observer and the controller gains the design conditions are formulated in Linear matrix inequality terms which can be solved using a one-step design procedure. Finally, the FTTC strategy is illustrated on a two-tank system to show its effectiveness.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. A. Benzaouia, A. Hmamed, A. El Hajjaji, Stabilization of controlled positive discrete-time T-S fuzzy systems by state feedback control. Int. J. Adapt. Control Signal Process. 24(12), 1091–1106 (2010)

    Google Scholar 

  2. M. Bouattour, M. Chadli, M. Chaabane, A. El Hajjaji, Robust fault tolerant control for Takagi–Sugeno system using singular approach. Int. Rev. Autom. Control. 3(4), 388–395 (2010)

  3. M. Bouattour, M. Chadli, A. El Hajjaji, M. Chaabane, Design of robust fault detection observer for Takagi-Sugeno models using the descriptor approach. Int. J. Control Autom. Syst. 9(5), 973–979 (2011)

    Google Scholar 

  4. H. Ghorbel, A. El Hajjaji, M. Souissi, M. Chaabane, in Sensor Fault Tolerant Control for TS Systems with Unmeasurable Premise Variables Using a Descriptor Approach, International Conference on Sciences and Techniques of Automatic control and computer engineering, Monastir, Tunisia, 2012, pp. 653–665

  5. T. Guerra, A. Kruszewski, L. Vermeiren, H. Tirmant, Conditions of output stabilization for nonlinear models in the Takagi-Sugeno’s form. Fuzzy Sets Syst. 157(9), 1248–1259 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. D. Ichalal, B. Marx, J. Ragot, D. Maquin, in State Estimation of Nonlinear Systems Using Multiple Model Approach, American Control Conference, St. Louis, MO, 2009, pp. 4636–4641

  7. D. Ichalal, B. Marx, D. Maquin, J. Ragot, in New Fault Tolerant Control Strategy for Nonlinear Systems with Multiple Model Approach, Conference on Control and Fault Tolerant Systems, Nice, France, 2010, pp. 606–611

  8. D. Ichalal, B. Marx, J. Ragot, D. Maquin, in Fault Tolerant Control Strategy for Takagi–Sugeno Systems with Unmeasurable Premise Variables by Trajectory Tracking, IEEE International Symposium on Industrial Electronics, Bari, Italy, 2010, pp. 2097–2102

  9. D. Ichalal, B. Marx, J. Ragot, D. Maquin, in Observer Based Actuator Fault Tolerant Control for Nonlinear Takagi–Sugeno systems: An LMI Approach, 18th Mediterranean Conference on Control and Automation, Congress Palace, Marrakech, Morocco 2010, pp. 1278–1283

  10. Z. Lendek, J. Laubert, T.M. Guerra, R. Babuska, B.D. Schutter, Adaptive observers for TS fuzzy systems with unknown polynomial-inputs. Fuzzy Sets Syst. 161(15), 2043–2065 (2010)

    Article  MATH  Google Scholar 

  11. W. Li, D. Jiang, W. Liu, Robust fault tolerant control for networked control system based on Takagi-Sugeno fuzzy model, IEEE International Conference on Measuring Technology and Mechatronics Automation, Hunan-Changsha, China, 2009, pp. 868–873

  12. Y. Li, S. Tong, T. Li, Adaptive fuzzy output feedback control of uncertain nonlinear systems with unknown backlash-like hysteresis. Inform. Sci. 198, 130–146 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  13. S. Luo, Y. Niu, J. Qiu, Y. Yang, W. Lu, R. Liu, in Fault Tolerant Guaranteed Cost Control Based on T–S Fuzzy Systems with the Sensor Fault and Time Delay, IEEE International Conference on Machine Learning and Cybernetics, Guilin, 2011, pp. 1232–1236

  14. B. Mansouri, N. Manamanni, K. Guelton, A. Kruszewski, T.M. Guerra, Output feedback LMI tracking control conditions with \(H_\infty \) criterion for uncertain and disturbed TS models. Inform. Sci. 179, 446–457 (2009)

    MATH  MathSciNet  Google Scholar 

  15. H. Noura, D. Sauter, F. Hamelin, D. Theilliol, Fault-tolerant control in dynamics systems: application to a winding machine. IEEE Control Syst. Mag. 20(1), 33–49 (2000)

    Article  Google Scholar 

  16. H. Noura, D. Theilliol, J. Ponsart, A. Chamseddine, Fault-Tolerant Control Systems Design and Practical Applications (Springer-Verlag, Heidelberg, 2009)

    Book  MATH  Google Scholar 

  17. M. Oudghiri, M. Chadli, A. El Hajjaji, Robust observer-based fault tolerant control for vehicle lateral dynamics. Int. J. Vehicle. Des. 48(3/4), 173–189 (2008)

    Google Scholar 

  18. M. Oudghiri-Bentaie, M. Chadli, A. El Hajjaji, in Observer-Based Fault Tolerant Control for Vehicle Lateral Dynamics, European Control Conference, KOS, Greece, 2007, pp. 632–637

  19. M. Oudghiri-Bentaie, M. Chadli, A. El Hajjaji, Robust Output \(H_\infty \) Fuzzy Control for Active Fault Tolerant Vehicle Stability 17th International Federation of Automatic Control World Congress, Seoul Korea, 2008, pp. 129–134

  20. J. Qiv, N. Ren, D. Xi, Y. Zhao, Y. Guo, X. Zhu, in Fault Tolerant Control Design for a Class of T–S Fuzzy Systems with Time Delays and Sensor Faults, IEEE International Conference on Machine Learning and Cybernetics, Qingdao, 2010, pp. 1–8

  21. M. Sami, R.J. Patton, in A Multiple-Model Approach to Fault Tolerant Tracking Control for Non-Linear Systems, 20th Mediterranean Conference on Control and Automation, Barcelona, Spain, 2012, pp. 498–503

  22. T. Takagi, M. Sugeno, Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 15(11), 116–132 (1985)

    Article  MATH  Google Scholar 

  23. S. Tong, B. Huo, Y. Li, Observer-based adaptive decentralized fuzzy fault-tolerant control of nonlinear large-scale systems with actuator failures. IEEE Trans. Fuzzy Syst. PP(99), 1–13 (2013)

    Google Scholar 

  24. S. Tong, Y. Li, Observer-based fuzzy adaptive control for strict-feedback nonlinear systems. Fuzzy Sets Syst. 160(12), 1749–1764 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  25. C.S. Tseng, B.S. Chen, H.J. Uang, Synthesis of observers for fault diagnosis in discrete time nonlinear systems using a Takagi-Sugeno multiple model. IEEE Trans. Fuzzy Syst. 9(3), 381–392 (2001)

    Article  Google Scholar 

  26. M. Witczak, L. Dziekan, V. Puig, J. Korbicz, in Design of a Fault Tolerant Control Scheme for Takagi–Sugeno Fuzzy Systems, 16th Mediterranean Conference on Control and Automation, Ajaccio, 2008, pp. 280–285

  27. L. Wu, X. Su, P. Shi, J. Qiu, Model approximation for discrete-time state-delay systems in the T-S fuzzy framework. IEEE Trans. Fuzzy Syst. 19(2), 366–378 (2011)

    Article  Google Scholar 

  28. L. Wu, X. Su, P. Shi, J. Qiu, A new approach to stability analysis and stabilization of discrete-time T–S fuzzy time-varying delay systems. IEEE Trans. Syst. Man Cybern. B Cybern. 41(1), 273–286 (2011)

    Google Scholar 

  29. L. Xie, C. DeSouza, Robust \(H_\infty \) control for linear systems with norm-bounded time-varying uncertainty. IEEE Trans. Autom. Control 37(1), 1188–1191 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  30. H. Yang, B. Jian, V. Cocqueompot, Fault Tolerant Control Design for Hybrid Systems (Springer-Verlag, Berlin, 2010)

    Book  Google Scholar 

  31. K. Zhang, B. Jian, M. Staroswiecki, Dynamic output feedback-fault tolerant controller design for Takagi-Sugeno fuzzy systems with actuator faults. IEEE Trans. Fuzzy Syst. 18, 194–201 (2010)

    Article  Google Scholar 

Download references

Acknowledgments

We thank the ministry of higher education and scientific research of Tunisia and AECID (A/030410/10 and AP/039213/11) for funding this work.

Author information

Authors and Affiliations

  1. National School of Engineers of Sfax, University of Sfax, Rue Soukra, BP 1173, 3038 , Sfax, Tunisia

    H. Ghorbel, M. Souissi & M. Chaabane

  2. University of Picardie Jules Vernes (UPJV), 7, Rue Moulin Neuf, Amiens, 80000, France

    A. El Hajjaji

Authors
  1. H. Ghorbel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. El Hajjaji
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Souissi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Chaabane
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. El Hajjaji.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ghorbel, H., El Hajjaji, A., Souissi, M. et al. Fault-Tolerant Trajectory Tracking Control for Takagi–Sugeno Systems with Unmeasurable Premise Variables: Descriptor Approach. Circuits Syst Signal Process 33, 1763–1781 (2014). https://doi.org/10.1007/s00034-013-9728-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-013-9728-7

Keywords

Search

Navigation