# zbMATH — the first resource for mathematics

Nonlinear actuator fault estimation observer: an inverse system approach via a T-S fuzzy model. (English) Zbl 1273.93105
Summary: Based on a Takagi-Sugeno (T-S) fuzzy model and an inverse system method, this paper deals with the problem of actuator fault estimation for a class of nonlinear dynamic systems. Two different estimation strategies are developed. Firstly, T-S fuzzy models are used to describe nonlinear dynamic systems with an actuator fault. Then, a robust sliding mode observer is designed based on a T-S fuzzy model, and an inverse system method is used to estimate the actuator fault. Next, a second fault estimation strategy is developed. Compared with some existing techniques, such as adaptive and sliding mode methods, the one presented in this paper is easier to be implemented in practice. Finally, two numerical examples are given to demonstrate the efficiency of the proposed techniques.

##### MSC:
 93C42 Fuzzy control/observation systems 93B12 Variable structure systems 93B35 Sensitivity (robustness)
Full Text:
##### References:
 [1] Babuska, R. (1998). Fuzzy Modeling for Control, Kluwer Academic Publishers, Boston, MA. · Zbl 0948.65114 [2] Boukezzoula, R., Galichet, S. and Folloy, L. (2003). Nonlinear internal model control: Application of inverse model based fuzzy control, IEEE Transactions on Fuzzy Systems 11(6): 814-829. · doi:10.1109/TFUZZ.2003.819835 [3] Boukezzoula, R., Galichet, S. and Foulloy, L. (2007). Fuzzy feedback linearizing controller and its equivalence with the fuzzy nonlinear internal model control structure, International Journal of Applied Mathematics and Computer Science 17(2): 233-248, DOI: 10.2478/v10006-007-0021-4. · Zbl 1119.93357 · doi:10.2478/v10006-007-0021-4 · eudml:207834 [4] Chang, C. and Yeh, Y. (2006). Variance constrained fuzzy control for observer-based T-S fuzzy models with minimizing auxiliary performance index, Journal of Intelligent and Fuzzy Systems 17(1): 59-69. · Zbl 1114.93061 [5] Chen, J. and Patton, R. (1999). Robust Model-Based Fault Diagnosis for Dynamic Systems, Kluwer, Boston, MA. · Zbl 0920.93001 [6] Chen, W. and Saif, M. (2010). Fuzzy nonlinear unknown input observer design with fault diagnosis applications, Journal of Vibration and Control 16(3): 377-401. · Zbl 1269.93014 · doi:10.1177/1077546309106525 · gateway.webofknowledge.com [7] Christophe, C., Cocquempot, V. and Jiang, B. (2002). Link between highgain observer-based residual and parity space one, Proceedings of the American Control Conference, Anchorage, AK, USA, pp. 2100-2105. [8] Ding, X. and Frank, M. (1993). An adaptive observer-based fault detection schme for nonlinear systems, Proceedings of the 12th IFAC World Congress, Sydney, Australia, pp. 307-312. [9] Edwards, C., Spurgeon, S. and Patton, R. (2000). Sliding mode observers for fault detection and isolation, Automatica 36(2): 541-553. · Zbl 0968.93502 · doi:10.1016/S0005-1098(99)00177-6 [10] Fu, Y., Duan, G. and Song, S. (2004). Design of unknown input observer for linear time-delay systems, International Journal of Control, Automation, and Systems 2(4): 530-535. [11] Gao, H., Zhao, Y. and Chen, T. (2009). H\infty fuzzy control of nonlinear systems under unreliable communication links, IEEE Transactions on Fuzzy Systems 17(2): 265-278. [12] 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. [13] Gu, Z., Peng, C. and Tian, E. (2010). Reliable control for a class of discrete-time state-delayed nonlinear systems with stochastic actuators failures, ICIC Express Letters pp. 2475-2480. [14] Guan, Y. and Saif, M. (1991). Novel approach to the design of unknown input observers, IEEE Transactions on Automatic Control 36(5): 632-635. · doi:10.1109/9.76372 [15] Guo, Y., Jiang, B. and Shi, P. (2010). Delay-dependent adaptive reconfiguration control in the presence of input saturation and actuator faults, International Journal of Innovative Computing, Information and Control 6(4): 1873-1882. [16] Isermann, R. (2005). Model-based fault detection and diagnosis status and application, Annual Reviews in Control 29(1): 71-85. · doi:10.1016/j.arcontrol.2004.12.002 [17] Isermann, R. (2006). Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance, Springer, Berlin. [18] Jiang, B., Staroswiecki, M. and Cocquempot, V. (2001). Fault diagnosis for a class of nonlinear systems with unknown paramenters, Proceedings of the 4th IFAC Workshop on Online Fault Detection and Supervision in the Chemical Process Industries, Seoul, South Korea, pp. 181-186. [19] Jiang, B., Staroswiecki, M. and Cocquempot, V. (2006). Fault accommodation for nonlinear dynamic systems, IEEE Transactions on Automatic Control 51(9): 1805-1809. · Zbl 1366.93694 [20] Jiang, B., Zhang, K. and Shi, P. (2010). Less conservative criteria for fault accommodation of time-varying delay systems using adaptive fault diagnosis observer, International Journal of Adaptive Control and Signal Processing 24(4): 322-334. · Zbl 1193.93166 · doi:10.1002/acs.1138 · gateway.webofknowledge.com [21] Kabore, R., Othman, S., Mckenna, T. and Hammouri, H. (2000). Observer-based fault diagnosis for a class of nonlinear systems-application to a free radical copolymerization reaction, International Journal of Control 73(9): 787-803. · Zbl 1006.93512 · doi:10.1080/00207170050029287 [22] Kabore, R. and Wang, H. (2001). Design of fault diagnosis filters and fault-tolerant control for a class of nonlinear systems, IEEE Transactions on Automatic Control 46(11): 1805-1810. · Zbl 1006.93068 · doi:10.1109/9.964696 · gateway.webofknowledge.com [23] Lendek, Z., Guerra, T., Babuska, R. and Schutter, B. (2010a). Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models, Springer, Berlin. · Zbl 1221.93003 · doi:10.1007/978-3-642-16776-8 [24] Lendek, Z., Lauberb, J. and Guerra, T. (2010b). Adaptive observers for T-S fuzzy systems with unknown polynomial inputs, Fuzzy Sets and Systems 16(1): 2043-2065. · Zbl 1194.93116 · doi:10.1016/j.fss.2010.03.010 [25] Nguang, S. and Shi, P. (2003). H\infty fuzzy output feedback control design for nonlinear systems: An LMI approach, IEEE Transactions on Fuzzy Systems 11(3): 331-340. · doi:10.1109/TFUZZ.2003.812691 [26] Nguang, S., Shi, P. and Ding, X. (2007). Fault detection for uncertain fuzzy systems: An LMI approach, IEEE Transactions on Fuzzy Systems 15(6): 1251-1262. · Zbl 05516307 · doi:10.1109/TFUZZ.2007.894983 [27] Pang, H. and Tang, G. (2010). Global robust optimal sliding mode control for a class of nonlinear systems with uncertainties, ICIC Express Letters 4(6): 2501-2508. [28] Patton, R., Toribiot, C. and Simanit, S. (2001). Robust fault diagnosis in a chemical process using multiple-model approach, Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, FL, USA, pp. 149-154. [29] Persis, C. and Isidori, A. (2001). A geometric approach to nonlinear fault detection and isolation, IEEE Transactions on Automatic Control 46(6): 853-865. · Zbl 1009.93003 · doi:10.1109/9.928586 · gateway.webofknowledge.com [30] Polycarpou, M. (2001). Fault accommodation of a class of multivariable nonlinear dynamical systems using learing approach, IEEE Transactions on Automatic Control 46(5): 736-742. · Zbl 1006.93074 · doi:10.1109/9.920792 [31] Seliger, R. and Frank, M. (1991). Fault diagnosis by disturbance decoupled nonlinear observers, Proceedings of the 30th IEEE Control Decision Conference, Brighton, UK, pp. 2248-2253. [32] Shumsky, A. (2007). Redundancy relations for fault diagnosis in nonlinear uncertain systems, International Journal of Applied Mathematics and Computer Science 17(4): 477-489, DOI: 10.2478/v10006-007-0040-1. · Zbl 1228.62129 · doi:10.2478/v10006-007-0040-1 · eudml:207853 [33] Staroswiecki, M. and Gehin, A. (2001). From control to supervision, Annual Reviews in Control 25(1): 1-11. · doi:10.1016/S1367-5788(01)00002-5 [34] Takagi, T. and Sugeno, M. (1985). Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems, Man, and Cybernetics-Part B 17(2): 116-132. · Zbl 0576.93021 · doi:10.1109/TSMC.1985.6313399 [35] Tanaka, K. and Wang, H. (2001). Fuzzy Control System Design and Analysis: A Linear Matrix Inequality Approach, John Wiley and Sons, New York, NY. [36] Vachtsevanos, G., Lewis, F. and Roemer, F. (2006). Intelligent Fault Diagnosis and Prognosis for Engineering Systems, John Wiley and Sons Ltd., Hoboken, NJ. [37] Wu, L., Su, X., Shi, P. and Qiu, J. (2011). Model approximation for discrete-time state-delay systems in the T-S fuzzy framework, IEEE Transactions on Fuzzy Systems 19(2): 366-378. [38] Xie, X., Zhou, D. and Jin, Y. (1999). Strong tracking filter based adaptive generic model control, Journal of Process Control 9(4): 337-350. · doi:10.1016/S0959-1524(98)00052-3 [39] Xu, Y., Jiang, B., Tao, G. and Gao, Z. (2011a). Fault accommodation for near space hypersonic vehicle with actuator fault, International Journal of Innovative Computing, Information and Control 7(5): 2187-2200. [40] Xu, Y., Jiang, B., Tao, G. and Gao, Z. (2011b). Fault tolerant control for a class of nonlinear systems with application to near space vehicle, Circuits, Systems, and Signal Processing 30(3): 655-672. · Zbl 1215.93041 · doi:10.1007/s00034-010-9239-8 · gateway.webofknowledge.com [41] Yan, X. and Edwards, C. (2007). Nonlinear robust fault reconstruction and estimation using a sliding mode observer, Automatica 43(9): 1605-1614. · Zbl 1128.93389 · doi:10.1016/j.automatica.2007.02.008 · gateway.webofknowledge.com [42] Yang, Q. (2004). Model-based and Data Driven Fault Diagnosis Methods with Applications to Process Monitoring, Ph.D. thesis, Case Western Reserve University, Cleveland, OH. [43] Zhang, K. and Jiang, B. (2010). Dynamic output feedback fault tolerant controller design for Takagi-Sugeno fuzzy systems with actuator faults, IEEE Transactions on Fuzzy Systems 18(1): 194-201. · doi:10.1109/TFUZZ.2009.2036005 · gateway.webofknowledge.com [44] Zhang, K., Jiang, B. and Shi, P. (2009). Fast fault estimation and accommodation for dynamical systems, IET Control Theory and Applications 3(2): 337-350. · gateway.webofknowledge.com [45] Zhang, Y. and Jiang, J. (2008). Bibliographical review on reconfigurable fault-tolerant control systems, Annual Reviews in Control 32(1): 229-252. · doi:10.1016/j.arcontrol.2008.03.008 · gateway.webofknowledge.com [46] Zhou, S., Lam, J. and Zheng, W. (2007). Control design for fuzzy systems based on relaxed nonquadratic stability and H\infty performance conditions, IEEE Transactions on Fuzzy Systems 15(2): 188-199. · Zbl 05452667 · doi:10.1109/TFUZZ.2006.879996 · gateway.webofknowledge.com
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.