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access icon free Multiple observer design for a non-linear Takagi–Sugeno system submitted to unknown inputs and outputs

© The Institution of Engineering and Technology
Received 08/10/2012, Accepted 17/06/2013, Revised 03/05/2013, Published

In this study, the authors focus on the state estimation of a non-linear system described by a Takagi–Sugeno multiple model submitted to unknown inputs and outputs. The proposed approach consists of a mathematical transformation which enables to consider the unknown outputs as unknown inputs that can be eliminated by a designed multiple observer. To evaluate the efficiency of the proposed approach, the convergence conditions of the state estimation error are formulated as linear matrix inequalities. Simulation examples are given to illustrate the proposed methods.

Inspec keywords: nonlinear systems; linear matrix inequalities; mathematical analysis; observers; signal processing

Other keywords: unknown input; linear matrix inequality; state estimation error; nonlinear Takagi-Sugeno multiple system; mathematical transformation; signal processing; multiple observer design; unknown output

Subjects: Mathematical analysis; Algebra; Mathematical analysis; Signal processing theory; Algebra; Signal processing and detection

References

    1. 1)
      • 25. Akhenak, A., Chadli, M., Ragot, J., Maquin, D.: ‘Design of observers for Takagi–Sugeno fuzzy models for fault detection and isolation’. Seventh IFAC Symp. on Fault Detection, Supervision and Safety of Technical Processes, Safeprocess'2009, Barcelona, Spain, 30 June–3 July 2009.
    2. 2)
      • 29. Boyd, S., Elghaoui, L., Feron, E., Balakrishnan, V.: ‘Linear matrix inequality in system and control theory’ (SIAM, 1994).
    3. 3)
      • 27. Akhenak, A.: ‘Conception d'observateurs non linéaires par approche multimodèle: application au diagnostic’. Thèse de doctorat, Institut National Polytechnique de Lorraine, France, 16December2004.
    4. 4)
      • 3. Akhenak, A., Chadli, M., Ragot, J., Maquin, D.: ‘Design of sliding mode unknown input observer for uncertain Takagi–Sugeno model’. 15th Mediterranean Conf. on Control and Automation, MED'07, Athens, Greece, 27–29 June 2007.
    5. 5)
      • 5. Sharma, R., Aldeen, M.: ‘Estimation of unknown disturbances in nonlinear systems’. Control 2004, University of Bath, UK, 6–9 September 2004.
    6. 6)
      • 17. Johansen, T.A., Foss, A.B.: ‘Constructing NARMAX using ARMAX models’, Int. J. Control, 1993, 58, (5), pp. 1125–1153 (doi: 10.1080/00207179308923046).
    7. 7)
      • 26. Tanaka, K., Ikeda, T., Wang, H.: ‘Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs’, IEEE Trans. Fuzzy Syst., 1998, 6, (2), pp. 250–265 (doi: 10.1109/91.669023).
    8. 8)
      • 21. Ichalal, D., Marx, B., Ragot, J., Maquin, D.: ‘State estimation of Takagi–Sugeno systems with unmeasurable premise variables’, IET Control Theory Appl., 2010, 4, (5), pp. 897–908 (doi: 10.1049/iet-cta.2009.0054).
    9. 9)
      • 2. Luenberger, D.G.: ‘An introduction to observers’, IEEE Trans. Autom. Control, 1971, 16, (6), pp. 596–602 (doi: 10.1109/TAC.1971.1099826).
    10. 10)
      • 18. Orjuela, R.: ‘Contribution à l'estimation d’état et au diagnostic des systèmes représentés par des multimodèles’. Thèse de doctorat, Institut National Polytechnique de Lorraine, France, 2008.
    11. 11)
      • 12. Chadli, M., Maquin, D., Ragot, J.: ‘Multiple observers for discrete-time multiple models’. Fifth IFAC Symp. on Fault Detection, Supervision and Safety for Technical Processes, Safeprocess’ 2003, Washington, D.C., USA, 9–11 June 2003.
    12. 12)
      • 6. Darouach, M., Zasadzinski, M., Xu, S.S.J.: ‘Full order observers for linear systems with unknown inputs’, IEEE Trans. Autom. Control, 1994, 39, (3), pp. 606–609 (doi: 10.1109/9.280770).
    13. 13)
      • 11. Akhenak, A., Chadli, M., Ragot, J., Maquin, D.: ‘State estimation via Multiple observer with unknown input. Application to the three tank system’. Fifth IFAC Symp. on Fault Detection Supervision and Safety for Technical Processes, Safe process, Washington, US, 9–11 June 2003, pp. 245–251.
    14. 14)
      • 20. Marx, B., Koenig, D., Ragot, J.: ‘Design of observers for Takagi Sugeno descriptor systems with unknown inputs and application to fault diagnosis’, IET Control Theory Appl., 2007, 1, (5), pp. 1487–1495 (doi: 10.1049/iet-cta:20060412).
    15. 15)
      • 19. Ichalal, D., Marx, B., Ragot, J., Maquin, D.: ‘Simultaneous state and unknown inputs estimation with PI and PMI observers for Takagi Sugeno model with unmeasurable premise variables’. 17th Mediterranean Conf. on Control and Automation, MED'09, Thessaloniki, Greece, 24–26 June 2009.
    16. 16)
      • 9. Akhenak, A., Maquin, D., Ragot, J.: ‘Process input estimation with a multimodel. Application to communication’. Mediterranean Conf. on Control and Automation, Limassol, Cyprus, 27–29 June 2005.
    17. 17)
      • 30. Zolghadri, A., Henry, D., Monsion, M.: ‘Design of nonlinear observers for fault diagnosis: a case study’, Control Eng. Pract., 1996, 4, (11), pp. 1535–1544 (doi: 10.1016/0967-0661(96)00167-0).
    18. 18)
      • 23. Zhang, K., Jiang, B., Shi, P.: ‘Fault estimation observer design for discrete-time Takagi–Sugeno fuzzy systems based on piecewise Lyapunov functions’, IEEE Trans. Fuzzy Syst., 2012, 20, (1), pp. 192–200 (doi: 10.1109/TFUZZ.2011.2168961).
    19. 19)
      • 1. Yan, L.P., Zhou, D.H., Fu, M.Y., Xia, Y.Q.: ‘State estimation for asynchronous multirate multisensor dynamic systems with missing measurements’, IET Signal Process., 2010, 4, (6), pp. 728–739 (doi: 10.1049/iet-spr.2009.0215).
    20. 20)
      • 16. Orjuela, R., Marx, B., Ragot, J., Maquin, D.: ‘Observer design for nonlinear systems described by multiple models’. Seventh IFAC Symp. on Fault Detection, Supervision and Safety of Technical Processes, Safeprocess'2009, Barcelona, Spain, 30th June–3rd July 2009.
    21. 21)
      • 8. Wang, S.H., Davison, E.J., Dorato, P.: ‘Observing the states of systems with unmeasurable disturbances’, IEEE Trans. Autom. Control, 1995, 20, pp. 716–717 (doi: 10.1109/TAC.1975.1101076).
    22. 22)
      • 28. Zhang, K., Jiang, B., Cocquempot, V.: ‘Adaptive observer-based fast fault estimation’, Int. J. Control, Autom. Syst., 2008, 6, (3), pp. 320–326.
    23. 23)
      • 22. Zhang, K., Jiang, B., Staroswiecki, M.: ‘Dynamic output feedback fault tolerant controller design for Takagi–Sugeno fuzzy systems with actuator faults’, IEEE Trans. Fuzzy Syst., 2010, 18, (1), pp. 194–201 (doi: 10.1109/TFUZZ.2009.2036005).
    24. 24)
      • 24. Akhenak, A., Chadli, M., Ragot, J., Maquin, D.: ‘Estimation of state and unknown inputs of a nonlinear system represented by a multiple model’. 11th IFAC Symp. on Automation in Mining, Mineral and Metal Processing, MMM 2004, Nancy, France, 8–10 September 2004.
    25. 25)
      • 7. Sename, O.: ‘Unknown input robust observer for time delay system’, IEEE Conf. Decis. Control, 1997, 2, pp. 1629–1630.
    26. 26)
      • 13. Murray-Smith, R., Johansen, T.A.: ‘Multiple model approaches to modelling and control’ (Taylor Francis, London, 1997).
    27. 27)
      • 14. Zhang, Z., Ji, L., Huang, Z., Wu, J.: ‘Multi-model adaptation for thigh movement using accelerometers’, IET Signal Process., 2011, 5, (8), pp. 709–716 (doi: 10.1049/iet-spr.2010.0146).
    28. 28)
      • 4. Edwards, C.: ‘A comparison of sliding mode and unknown input observers for fault reconstruction’. IEEE Conf. on Decision and Control, Atlantis, Paradise Island, Bahamas, 14–17 December 2004, pp. 5279–5284.
    29. 29)
      • 10. Guan, Y., Saif, M.: ‘A novel approach to the design of unknown input observers’, IEEE Trans. Autom. Control, 1991, 36, (5), pp. 632–635 (doi: 10.1109/9.76372).
    30. 30)
      • 15. Johansen, T.A., Shorten, R., Murray-Smith, R.: ‘Fuzzy identification of systems and its application to modeling and control’, IEEE Trans. Syst. Man Cybern. C, 1985, 15, pp. 116–132.
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