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

• Autorzy: Ben Brahim A. , Dhahri S. , Ben Hmida F. , Sellami A.

Identyfikatory

DOI

10.1515/amcs-2015-0041

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

fault reconstruction; fault estimation; simultaneous fault; H∞ sliding mode observer; uncertain Takagi Sugeno system; LMI optimization

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2015
• Tom: Vol. 25, no. 3
• Strony: 547--559
• Opis fizyczny: Bibliogr. 25 poz., wykr.

Twórcy

autor

Ben Brahim A.

• Research Unit on Control, Monitoring and Safety of Systems, High School of Sciences and Techniques of Tunis (ESSTT) 5, av. Taha Hussein, BP 56-1008 Tunis, Tunisia

autor

Dhahri S.

• Research Unit on Control, Monitoring and Safety of Systems, High School of Sciences and Techniques of Tunis (ESSTT) 5, av. Taha Hussein, BP 56-1008 Tunis, Tunisia

autor

Ben Hmida F.

• Research Unit on Control, Monitoring and Safety of Systems, High School of Sciences and Techniques of Tunis (ESSTT) 5, av. Taha Hussein, BP 56-1008 Tunis, Tunisia

autor

Sellami A.

• Research Unit on Control, Monitoring and Safety of Systems, High School of Sciences and Techniques of Tunis (ESSTT) 5, av. Taha Hussein, BP 56-1008 Tunis, Tunisia

Bibliografia

• [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.
• [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.
• [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.
• [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.
• [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.
• [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.
• [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.
• [19] Tan, C.P. and Edwards, C. (2002). Sliding mode observers for detection and reconstruction of sensor faults, Automatica 38(10): 1815–1821.
• [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.
• [22] Xing-Gang, Y. and Edwards, C. (2007a). Nonlinear robust fault reconstruction and estimation using a sliding mode observer, Automatica 43(9) : 1605–1614.
• [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.
• [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.
• [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.