Dynamic output feedback fault-tolerant controller design for a class of generalized Takagi-Sugeno fuzzy nonlinear systems

Document Type : Original Article

Authors

Department of Electrical Engineering, Sahand University of Technology, Sahand, Tabriz, Iran.

Abstract

A novel design approach to construct a fault-tolerant control (FTC) system for a class of nonlinear systems based on a generalized Takagi-Sugeno (GT-S) fuzzy model is proposed. The local rules of the GT-S fuzzy model consist of some multiplicative nonlinear terms. The nonlinear system is affected by actuator faults and unknown disturbances. A state/fault observer is designed and then, a dynamic output feedback scheme is proposed based on the estimated fault and state information. The sufficient conditions for observer and controller design are separately given in terms of linear matrix inequalities (LMIs). It can be shown that the number of LMIs and the computational burden is less than that of similar methods and the effectiveness of the proposed dynamic output feedback FTC approach is verified by proposing simulation results applied to an inverted pendulum system.

Keywords


[1] Y. Zhang, J. Jiang, “Bibliographical review on reconfigurable fault-tolerant control systems”, Annual Reviews in Control, vol. 32, no. 2, pp. 229-252, 2008.
[2] P. M. Frank, “Analytical and qualitative model-based fault diagnosis–a survey and some new results”, European Journal of control, vol. 2, no. 1, pp. 6-28, 1996.
[3] S. X. Ding, “Model-based fault diagnosis techniques: design schemes, algorithms, and tools”, Springer Science & Business Media, 2008.
[4] M. Witczak, “Fault diagnosis and fault-tolerant control strategies for non-linear systems: Analytical and soft computing approaches”, Springer International Publishing, 2014.
[5] J. Gertler, “Fault detection and diagnosis in engineering systems”, Routledge, 2017.
[6] R. Isermann, “Supervision, fault-detection and fault-diagnosis methods—a short introduction”, In Combustion Engine Diagnosis, pp. 25-47, Springer Vieweg, Berlin, Heidelberg, 2017.
[7] Z. Gao, C. Cecati, S. X. Ding, “A survey of fault diagnosis and fault-tolerant techniques—Part I: Fault diagnosis with model-based and signal-based approaches”, IEEE Transactions on Industrial Electronics, vol. 62, no. 6, pp. 3757-3767, 2015.
[8] Z. Gao, C. Cecati, S. X. Ding, “A survey of fault diagnosis and fault-tolerant techniques—Part II: Fault diagnosis with knowledge-based and hybrid/active approaches”, IEEE Transactions on Industrial Electronics, vol. 62, no. 6, pp. 3768-3774, 2015.
[9] H. Kargar, J. Zarei, R. Razavi-Far, “Robust fault detection filter design for nonlinear networked control systems with time-varying delays and packet dropout”, Circuits, Systems, and Signal Processing, vol. 38, no. 1, pp. 63-84, 2019.
[10] M. Li, Z. Zuo, H. Liu, C. Liu, B. Zhu, “Adaptive fault tolerant control for trajectory tracking of a quadrotor helicopter”, Transactions of the Institute of Measurement and Control, vol. 40, no. 12, pp. 3560-3569, 2018.
[11] M. Witczak, V. Puig, S. M. de Oca, “A fault-tolerant control strategy for non-linear discrete-time systems: application to the twin-rotor system”, International Journal of Control, vol. 86, no. 10, pp. 1788-1799, 2013.
[12] X. Jin, “Adaptive fault tolerant tracking control for a class of stochastic nonlinear systems with output constraint and actuator faults”, Systems & Control Letters, vol. 107, pp. 100-109, 2017.
[13] X. Yin, Z. Li, L. Zhang, M. Han, “Distributed state estimation of sensor-network systems subject to Markovian channel switching with application to a chemical process”, IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 48, no. 6, pp. 864-874, 2018.
[14] L. Liu, Y. J. Liu, S. Tong, “Neural networks-based adaptive finite-time fault-tolerant control for a class of strict-feedback switched nonlinear systems”, IEEE Transactions on Cybernetics, vol. 49, no. 7, pp. 2536-2545, 2018.
[15] X. Yun, L. Wu, Y.  Xu, “Adaptive fault-tolerant control for a class of uncertain lower-triangular nonlinear systems with actuator failures”, In 2018 Chinese Control and Decision Conference (CCDC), June 2018, Shenyang, China, pp. 795-800.
[16] A. Moradvandi, S. A. Malek, M. Shahrokhi, “Adaptive finite-time fault-tolerant controller for a class of uncertain MIMO nonlinear switched systems subject to output constraints and unknown input nonlinearities”, Nonlinear Analysis: Hybrid Systems, vol. 35, February 2020. DOI: 10.1016/j.nahs.2019.100821
[17] X. Jin, X. Zhao, J. Yu, X. Wu, J. Chi, “Adaptive fault-tolerant consensus for a class of leader-following systems using neural network learning strategy”, Neural Networks, vol. 121, pp. 474-483, 2020.
[18] A. Khodadadi, M. Shahriari-kahkeshi, A. Chatraei, “A novel scheme for actuator fault tolerant controller design based on the fault identification”, Tabriz Journal of Electrical Engineering, vol. 48, no. 2, pp. 595-608, 2018 (in persian).
[19] J. L. Castro, M. Delgado, “Fuzzy systems with defuzzification are universal approximators”, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 26, no. 1, pp. 149-152, 1996.
[20] C. W. De Silva, “Intelligent control: fuzzy logic applications”, CRC press, 2018.
[21] K. Tanaka, H. O. Wang, “Fuzzy control systems design and analysis: A linear matrix inequality approach”, John Wiley & Sons, 2004.
[22] J. Mrazgua, M. Ouahi, “Fuzzy fault-tolerant H control approach for nonlinear active suspension systems with actuator failure”, Procedia Computer Science, vol. 148, pp. 465-474, 2019.
[23] X. K. Du, H. Zhao, X. H. Chang, “Unknown input observer design for fuzzy systems with uncertainties”, Applied Mathematics and Computation, vol. 266, pp. 108-118, 2015.
[24] J. Dong, G. H. Yang, “Observer-based output feedback control for discrete-time T-S fuzzy systems with partly immeasurable premise variables”, IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no.(1), pp. 98-110, 2017.
[25] D. Ye, X. Li, “Event-triggered fault detection for continuous-time networked polynomial-fuzzy-model-based systems”, Applied Mathematics and Computation, vol. 366, February 2020. DOI: 10.1016/j.amc.2019.124729
[26] Y. Gao, F. Xiao, J. Liu, R. Wang, “Distributed soft fault detection for interval type-2 fuzzy-model-based stochastic systems with wireless sensor networks”, IEEE Transactions on Industrial Informatics, vol. 15, no. 1, pp. 334-347, 2018.
[27] S. Zeghlache, A. Djerioui, L. Benyettou, T. Benslimane, H. Mekki, A. Bouguerra, “Fault tolerant control for modified quadrotor via adaptive type-2 fuzzy backstepping subject to actuator faults”, ISA transactions, vol. 95, pp. 330-345, 2019.
[28] H. Patel and V. Shah, “Fault tolerant control using interval type-2 Takagi-Sugeno fuzzy controller for nonlinear system”, In International Conference on Intelligent Systems Design and Applications, December 2018, Vellore, India, pp. 150-164.
[29] J. Tan, S. Dian, T. Zhao, “Further studies on stability and stabilization of T-S fuzzy systems with time-varying delays via fuzzy Lyapunov-Krasovskii functional method”, Asian Journal of Control, vol. 20, no. 6, pp. 2207-2222, 2018.
[30] D. Kharrat, H. Gassara, A. El Hajjaji, M. Chaabane, “Adaptive fuzzy observer-based fault-tolerant control for Takagi-Sugeno descriptor nonlinear systems with time delay”, Circuits, Systems, and Signal Processing, vol. 37, no. 4, pp. 1542-1561, 2018.
[31] S. Asadi, A. Khayatian, M. Dehghani, N. Vafamand, “Robust TS fuzzy-based sliding mode observer design for actuator fault reconstruction: Non-quadratic Lyapunov function approach”, Tabriz Journal of Electrical Engineering, vol. 49, no. 1, pp. 25-35, 2019 (in persian).
[32] R. Rajesh, M. R. Kaimal, “T-S fuzzy model with nonlinear consequence and PDC controller for a class of nonlinear control systems”, Applied Soft Computing, vol. 7, no. 3, pp. 772-782, 2007.
[33] J. Dong, Y. Wang, G. H. Yang, “Control synthesis of continuous-time TS fuzzy systems with local nonlinear models”, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 39, no. 5, pp. 1245-1258, 2009.
[34] J. Dong, Y. Wang, G. H. Yang, “Output feedback fuzzy controller design with local nonlinear feedback laws for discrete-time nonlinear systems”, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 40, no. 6, pp. 1447-1459, 2010.
[35] J. Dong, Y. Wang, G. H. Yang, “H and mixed H2/ H control of discrete-time T-S fuzzy systems with local nonlinear models”, Fuzzy Sets and Systems, vol. 164, no. 1, pp. 1-24, 2011.
[36] H. Moodi, M. Farrokhi, “Robust observer-based controller design for Takagi-Sugeno systems with nonlinear consequent parts”, Fuzzy Sets and Systems, vol. 273, pp. 141-154, 2015.
[37] H. Moodi, A. Kazemy, “Robust controller design for Takagi-Sugeno systems with nonlinear consequent part and time delay”, International Journal of Fuzzy Systems, vol. 21, no. 3, pp. 745-754, 2019.
[38] H. Moodi, D. Bustan, “Wind turbine control using TS systems with nonlinear consequent parts”, Energy, vol. 172, pp. 922-931, 2019.
[39] H. Wang, D. Ye, G. H. Yang, “Actuator fault diagnosis for uncertain T-S fuzzy systems with local nonlinear models”, Nonlinear Dynamics, vol. 76, no. 4, pp. 1977-1988, 2014.
[40] J. Han, H. Zhang, Y. Wang, Y. Liu, “Disturbance observer based fault estimation and dynamic output feedback fault tolerant control for fuzzy systems with local nonlinear models”, ISA transactions, vol. 59, pp. 114-124, 2015.
[41] J. Han, H. Zhang, Y. Wang, X. Liu, “Robust fault estimation and accommodation for a class of T-S fuzzy systems with local nonlinear models”, Circuits, Systems, and Signal Processing, vol. 35, no. 10, pp. 3506-3530, 2016.
[42] M. Klug, E. B. Castelan, V. J. Leite, L. F. Silva, “Fuzzy dynamic output feedback control through nonlinear Takagi-Sugeno models”, Fuzzy Sets and Systems, vol. 263, pp. 92-111, 2015.
[43] S. Ochiai, J. Yoneyama, and Y. Uchida, “Guaranteed cost control design based on Takagi-Sugeno fuzzy systems with nonlinear subsystems”, In 2013 IEEE International Conference on Systems, Man, and Cybernetics, October 2013, Manchester, UK, pp. 4712-4717.
[44] J. Yoneyama, “Output feedback control design for nonlinear systems based on a generalized Takagi-Sugeno fuzzy system”, In 2014 World Automation Congress (WAC), August 2014, Waikoloa, HI, USA, pp. 313-318.
[45] J. Yoneyama, “Nonlinear control design based on generalized Takagi-Sugeno fuzzy systems”, Journal of the Franklin Institute, vol. 351, no. 7, pp. 3524-3535, 2014.
[46] K. Zhang, B. Jiang, M. Staroswiecki, “Dynamic output feedback-fault tolerant controller design for Takagi-Sugeno fuzzy systems with actuator faults”, IEEE Transactions on Fuzzy Systems, vol. 18, no. 1, pp. 194-201, 2010.
[47] J. Dong, J. Hou, “Output feedback fault-tolerant control by a set-theoretic description of T-S fuzzy systems”, Applied Mathematics and Computation, vol. 301, pp. 117-134, 2017.
[48] A. Navarbaf, M. J. Khosrowjerdi, “Fault-tolerant controller design with fault estimation capability for a class of nonlinear systems using generalized Takagi-Sugeno fuzzy model”, Transactions of the Institute of Measurement and Control, vol. 41, no. 15, pp. 4218-4229, 2019.
[49] H. D. Tuan, P. Apkarian, T. Narikiyo, Y. Yamamoto, “Parameterized linear matrix inequality techniques in fuzzy control system design”, IEEE Transactions on fuzzy systems, vol. 9, no. 2, pp. 324-332, 2001.
[50] Y. Wang, L. Xie, C. E. de Souza, “Robust control of a class of uncertain nonlinear systems”, Systems & Control Letters, vol. 19, no. 2, pp. 139-149, 1992.
[51] P. Gahinet, A. Nemirovskii, A. J. Laub, M. Chilali, “The LMI control toolbox”, In Proceedings of the 33rd IEEE Conference on Decision and Control, December 1994, Lake Buena Vista, FL, USA, pp. 2038-2041.
[53] J. Lofberg, “YALMIP: a toolbox for modeling and optimization in MATLAB”, In 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508), September 2004, New Orleans, LA, USA, pp. 284-289.