An H ∞ sliding mode observer for Takagi-Sugeno nonlinear systems with simultaneous actuator and sensor faults

Ali Ben Brahim; Slim Dhahri; Fayçal Ben Hmida; Anis Sellami

International Journal of Applied Mathematics and Computer Science (2015)

  • Volume: 25, Issue: 3, page 547-559
  • ISSN: 1641-876X

Abstract

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This paper considers the problem of robust reconstruction of simultaneous actuator and sensor faults for a class of uncertain Takagi-Sugeno nonlinear systems with unmeasurable premise variables. The proposed fault reconstruction and estimation design method with H∞ performance is used to reconstruct both actuator and sensor faults when the latter are transformed into pseudo-actuator faults by introducing a simple filter. The main contribution is to develop a sliding mode observer (SMO) with two discontinuous terms to solve the problem of simultaneous faults. Sufficient stability conditions in terms linear matrix inequalities are achieved to guarantee the stability of the state estimation error. The observer gains are obtained by solving a convex multiobjective optimization problem. Simulation examples are given to illustrate the performance of the proposed observer.

How to cite

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Ali Ben Brahim, et al. "An $H_∞$ sliding mode observer for Takagi-Sugeno nonlinear systems with simultaneous actuator and sensor faults." International Journal of Applied Mathematics and Computer Science 25.3 (2015): 547-559. <http://eudml.org/doc/271788>.

@article{AliBenBrahim2015,
abstract = {This paper considers the problem of robust reconstruction of simultaneous actuator and sensor faults for a class of uncertain Takagi-Sugeno nonlinear systems with unmeasurable premise variables. The proposed fault reconstruction and estimation design method with H∞ performance is used to reconstruct both actuator and sensor faults when the latter are transformed into pseudo-actuator faults by introducing a simple filter. The main contribution is to develop a sliding mode observer (SMO) with two discontinuous terms to solve the problem of simultaneous faults. Sufficient stability conditions in terms linear matrix inequalities are achieved to guarantee the stability of the state estimation error. The observer gains are obtained by solving a convex multiobjective optimization problem. Simulation examples are given to illustrate the performance of the proposed observer.},
author = {Ali Ben Brahim, Slim Dhahri, Fayçal Ben Hmida, Anis Sellami},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {fault reconstruction and estimation; simultaneous faults; $H_∞$ sliding mode observer; uncertain Takagi-Sugeno systems; LMI optimization; sliding mode observer},
language = {eng},
number = {3},
pages = {547-559},
title = {An $H_∞$ sliding mode observer for Takagi-Sugeno nonlinear systems with simultaneous actuator and sensor faults},
url = {http://eudml.org/doc/271788},
volume = {25},
year = {2015},
}

TY - JOUR
AU - Ali Ben Brahim
AU - Slim Dhahri
AU - Fayçal Ben Hmida
AU - Anis Sellami
TI - An $H_∞$ sliding mode observer for Takagi-Sugeno nonlinear systems with simultaneous actuator and sensor faults
JO - International Journal of Applied Mathematics and Computer Science
PY - 2015
VL - 25
IS - 3
SP - 547
EP - 559
AB - This paper considers the problem of robust reconstruction of simultaneous actuator and sensor faults for a class of uncertain Takagi-Sugeno nonlinear systems with unmeasurable premise variables. The proposed fault reconstruction and estimation design method with H∞ performance is used to reconstruct both actuator and sensor faults when the latter are transformed into pseudo-actuator faults by introducing a simple filter. The main contribution is to develop a sliding mode observer (SMO) with two discontinuous terms to solve the problem of simultaneous faults. Sufficient stability conditions in terms linear matrix inequalities are achieved to guarantee the stability of the state estimation error. The observer gains are obtained by solving a convex multiobjective optimization problem. Simulation examples are given to illustrate the performance of the proposed observer.
LA - eng
KW - fault reconstruction and estimation; simultaneous faults; $H_∞$ sliding mode observer; uncertain Takagi-Sugeno systems; LMI optimization; sliding mode observer
UR - http://eudml.org/doc/271788
ER -

References

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  1. Akhenak, A., Chadli, M. and Ragot, J. (2007). Design of a sliding mode fuzzy observer for uncertain Takagi-Sugeno fuzzy model: Application to automatic steering of vehicles, International Journal Vehicle Autonomous Systems 5(3-4): 288-305. 
  2. Akhenak, A., Chadli, M., Ragot, J. and Maquin, D. (2008). Fault detection and isolation using sliding mode observer for uncertain Takagi-Sugeno fuzzy model, 16th Mediterranean Conference on Control and Automation, Ajaccio, France, pp. 286-291. 
  3. Alwi, H., Edwards, C. and Tan, C.P. (2009). Sliding mode estimation schemes for incipient sensor faults, Automatica 45(7): 1679-1685. Zbl1184.93050
  4. Asemani, M.H. and Majd, V.J. (2013). A robust H∞ observer-based controller design for uncertain T-S fuzzy systems with unknown premise variables via LMI, Fuzzy Sets and Systems 212(1): 21-40, DOI: 10.1016/j.fss.2012.07.008. Zbl1285.93051
  5. Bouattour, M., Chadli, M., Chaabane, M. and Hajjaji, A. (2011). Design of robust fault detection observer for Takagi-Sugeno models using the descriptor approach, International Journal of Control, Automation, and Systems 9(5): 973-979. 
  6. Dhahri, S., Sellami, A. and Benhmida, F. (2012). Robust H∞ sliding mode observer design for fault estimation in a class of uncertain nonlinear systems with LMI optimization approach, International Journal of Control, Automation, and Systems 10(5): 1032-1041. 
  7. Edwards, C., Spurgeon, S.K. and Patton, R.J. (2000). Sliding mode observers for fault detection and isolation, Automatica 36(4): 541-553. Zbl0968.93502
  8. Gao, Z., Jiang, B., Shi, P. and Xu, Y. (2010). Fault accommodation for near space vehicle attitude dynamics via T-S fuzzy models, International Journal of Innovative Computing, Information and Control 6(11): 4843-4856. 
  9. Ghorbel, H., Souissi, M., Chaabane, M. and Hajjaji, A. (2012). Observer design for fault diagnosis for the Takagi-Sugeno model with unmeasurable premise variables, 20th Mediterranean Conference on Control and Automation, Barcelona, Spain, pp. 303-308. 
  10. Hamdi, H., Rodrigues, M., Mechmeche, C. and Belhadjbraiek, N. (2012). Robust fault detection and estimation for descriptor systems based on multi-models concept, International Journal of Control, Automation, and Systems 10(6): 1260-1266. 
  11. Ichalal, D., Marx, B., Ragot, J. and Maquin, D. (2009a). Simultaneous state and unknown inputs estimation with PI and PMI observers for Takagi-Sugeno model with unmeasurable premise variables, 17th Mediterranean Conference on Control and Automation, Thessaloniki, Greece, pp. 353-358. 
  12. Ichalal, D., Marx, B., Ragot, J. and Maquin, D. (2009b). State estimation of nonlinear systems using multiple model approach, American Control Conference, ACC, St. Louis, MO, USA, DOI: 10.1109/ACC.2009.5160393. 
  13. Ichalal, D., Marx, B., Ragot, J. and Maquin, D. (2010). State estimation of Takagi-Sugeno systems with unmeasurable premise variables, IET, Control Theory and Applications 4(5): 897-908. 
  14. Ichalal, D., Marx, B., Ragot, J. and Maquin, D. (2012). New fault tolerant control strategies for nonlinear Takagi-Sugeno systems, International Journal of Applied Mathematics and Computer Science 22(1): 197-210, DOI: 10.2478/v10006-012-0015-8. Zbl1273.93102
  15. Mechmeche, C., Hamdi, H., Rodrigues, M. and Braiek, N.B. (2012). State and unknown inputs estimations for multi-models descriptor systems, International Journal of Robust and Nonlinear Control 2(3): 86-93. 
  16. Ng, K.Y., Tan, C.P., Edwards, C. and Kuang, Y.C. (2007). New results in robust actuator fault reconstruction for linear uncertain systems using sliding mode observers, International Journal of Robust and Nonlinear Control 17(14): 1294-1319. Zbl1127.93313
  17. Raoufi, R., Marquez, H.J. and Zinober, A.S.I. (2010). H∞ sliding mode observers for uncertain nonlinear Lipschitz systems with fault estimation synthesis, International Journal of Robust and Nonlinear Control 20(16): 1785-1801. Zbl1202.93027
  18. Takagi, T. and Sugeno, M. (1985). Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems, Man and Cybernetics 15(1): 116-132. Zbl0576.93021
  19. Tan, C.P. and Edwards, C. (2002). Sliding mode observers for detection and reconstruction of sensor faults, Automatica 38(10): 1815-1821. Zbl1011.93505
  20. Tan, C.P. and Edwards, C. (2003a). Sliding mode observers for reconstruction of simultaneous actuator and sensor faults, 42nd IEEE Conference on Decision Control, Maui, HI, USA, pp. 7803-7924. 
  21. Tan, C.P. and Edwards, C. (2003b). Sliding mode observers for robust detection and reconstruction of actuator and sensor faults, International Journal of Robust Nonlinear Control 13(5): 443-463, DOI: 10.1002/rnc.723. Zbl1036.93025
  22. Xing-Gang, Y. and Edwards, C. (2007a). Nonlinear robust fault reconstruction and estimation using a sliding mode observer, Automatica 43(9) : 1605-1614. Zbl1128.93389
  23. Xing-Gang, Y. and Edwards, C. (2007b). Sensor fault detection and isolation for nonlinear systems based on a sliding mode observer, International Journal of Adaptive Control and Signal Processing 21(8-9): 657-673. Zbl1128.93009
  24. Xu, D., Jiang, B. and Shi, P. (2012). Nonlinear actuator fault estimation observer: An inverse system approach via a T-S fuzzy model, International Journal of Applied Mathematics and Computer Science 22(1): 183-196, DOI: 10.2478/v10006-012-0014-9. Zbl1273.93105
  25. Zhao, Y., Lam, J. and Gao, H. (2009). Fault detection for fuzzy systems with intermittent measurements, IEEE Transactions on Fuzzy Systems 17(2): 398-410. 

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