New fault tolerant control strategies for nonlinear Takagi-Sugeno systems

• Autorzy: Ichalal D. , Marx B. , Ragot J. , Maquin D.
• Języki publikacji: EN

Abstrakty

EN

New methodologies for Fault Tolerant Control (FTC) are proposed in order to compensate actuator faults in nonlinear systems. These approaches are based on the representation of the nonlinear system by a Takagi-Sugeno model. Two control laws are proposed requiring simultaneous estimation of the system states and of the occurring actuator faults. The first approach concerns the stabilization problem in the presence of actuator faults. In the second, the system state is forced to track a reference trajectory even in faulty situation. The control performance depends on the estimation quality; indeed, it is important to accurately and rapidly estimate the states and the faults. This task is then performed with an Adaptive Fast State and Fault Observer (AFSFO) for the first case, and a Proportional-Integral Observer (PIO) in the second. Stability conditions are established with Lyapunov theory and expressed in a Linear Matrix Inequality (LMI) formulation to ease the design of FTC. Furthermore, relaxed stability conditions are given with the use of Polya's theorem. Some simulation examples are given in order to illustrate the proposed approaches.

Słowa kluczowe

EN

Takagi-Sugeno model; fault tolerant control; simultaneous fault; state estimation; Polya's theorem; Lyapunov theory; input to state stability

PL

model Takagi-Sugeno; sterowanie tolerujące uszkodzenia; uszkodzenie równoczesne; estymacja stanu; twierdzenie Lapunowa

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2012
• Tom: Vol. 22, no. 1
• Strony: 197--210
• Opis fizyczny: Bibliogr. 28 poz., rys., wykr.

Twórcy

autor

Ichalal D.

autor

Marx B.

autor

Ragot J.

autor

Maquin D.

• IBISC Laboratory, University of Evry Val d'Essonne, 40, rue du Pelvoux, 91020 Courcouronnes, France,

Bibliografia

• [1] 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.
• [2] Corless, M. and Tu, J. (1998). State and input estimation for a class of uncertain systems, Automatica 34(6): 757-764.
• [3] Darouach, M., Zasadzinski, M. and Xu, S. (1994). Full-order observers for linear systems with unknown inputs, IEEE Transactions on Automatic Control 39(3): 606-609.
• [4] Gao, Z. and Ding, S. X. (2007). Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems, Automatica 43(5): 912-920.
• [5] Ibrir, S. (2004). Robust state estimation with q-integral observers, American Control Conference, Boston, MA, USA, pp. 3466-3471.
• [6] 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, MED'09, Thessaloniki, Greece, pp. 353-358.
• [7] Ichalal, D.,Marx, B., Ragot, J. and Maquin, D. (2010). Fault tolerant control for Takagi-Sugeno systems with unmeasurable premise variables by trajectory tracking, IEEE International Symposium on Industrial Electronics, Bari, Italy, pp. 2097-2102.
• [8] Koenig, D. and Mammar, S. (2002). Design of a proportional integral observer for unknown input descriptor systems, IEEE Transactions on Automatic Control 47(12): 2057-2063.
• [9] Kruszewski, A., Wang, R. and Guerra, T.M. (2008). Non quadratic stabilization conditions for a class of uncertain nonlinear discrete time T-S fuzzy models: A new approach, IEEE Transactions on Automatic Control 53(2): 606-611.
• [10] Leith, D. J. and Leithead, W. E. (1999). Survey of gains cheduling analysis design, International Journal of Control 73(11): 1001-1025.
• [11] Luenberger, D. (1971). An introduction to observers, IEEE Transactions on Automatic Control 16(6): 596-602.
• [12] Marx, B., Koenig, D. and Ragot, J. (2007). Design of observers for Takagi-Sugeno descriptor systems with unknown inputs and application to fault diagnosis, IET Control Theory and Application 1(5): 1487-1495.
• [13] Mufeed, M. M., Jiang, J. and Zhang, Z. (2003). Active Fault Tolerant Control Systems: Stochastic Analysis and Synthesis, Springer-Verlag, Berlin/Heidelberg.
• [14] Nagy, A., Mourot, G., Marx, B., Schutz, G. and Ragot, J. (2009). Model structure simplification of a biological reactor, 15th IFAC Symposium on System Identification, SYSID'09, Saint Malo, France, pp. 257-262.
• [15] Niemann, H. and Stoustrup, J. (2005). Passive fault tolerant control of a double inverted pendulum-A case study, Control Engineering Practice 13(8): 1047-1059.
• [16] Ocampo-Martinez, C., De Dona, J. and Seron, M. (2010). Actuator fault-tolerant control based on set separation, International Journal of Adaptive Control and Signal Processing 24(12): 1070-1090.
• [17] Oudghiri, M., Chadli, M. and El Hajjaji, A. (2008). Robust observer-based fault tolerant control for vehicle lateral dynamics, International Journal of Vehicle Design 48(3-4): 173-189.
• [18] Patton, R. (1997). Fault-tolerant control systems: The 1997 situation, 3rd IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, Hull, UK, pp. 1033-1054.
• [19] Patton, R. J. and Klinkhieo, S. (2009a). An LPV approach to active FTC of a two-link manipulator, 7th Workshop on Advanced Control and Diagnosis, Zielona Góra, Poland.
• [20] Patton, R. and Klinkhieo, S. (2009b). Actuator fault estimation and compensation based on an augmented state observer approach, 48th IEEE Conference Decision and Control/28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, pp. 8482-8487.
• [21] Sala, A. and Ariño, C. (2007). Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem, Fuzzy Sets and Systems 158(24): 2671-2686.
• [22] Stilwell, D. J. and Rugh, W. J. (1997). Interpolation of observer state feedback controllers for gain scheduling, IEEE Transactions on Automatic Control 44(6): 1225-1229.
• [23] 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.
• [24] Tanaka, K. and Wang, H. (2001). Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, John Wiley and Sons, Hoboken, NJ.
• [25] Tuan, H., Apkarian, P., Narikiyo, T. and Yamamoto, Y. (2001). Parameterized linear matrix inequality techniques in fuzzy control system design, IEEE Transactions on Fuzzy Systems 9(2): 324-332.
• [26] Witczak, M., Dziekan, L., Puig, V. and Korbicz, J. (2008). Design of a fault-tolerant control scheme for Takagi-Sugeno fuzzy systems, 16th Mediterranean Conference on Control and Automation, Ajaccio, France, pp. 280-285.
• [27] Zhang, K., Jiang, B. and Cocquempot, V. (2008). Adaptive observer-based fast fault estimation, International Journal of Control, Automation, and Systems 6(3): 320-326.
• [28] Zhang, K., Jiang, B. and Shi, P. (2009). A new approach to observer-based fault-tolerant controller design for Takagi-Sugeno fuzzy systems with state delay, Circuits, Systems, and Signal Processing 28(5): 679-697.