Robust TS Fuzzy-based Sliding Mode Observer Design for Actuator Fault Reconstruction: Non-quadratic Lyapunov Function Approach

Authors

Faculty of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran

Abstract

This paper proposes a sliding mode observer (SMO) for actuator fault reconstruction of nonlinear systems subjected to external disturbance. In the proposed approach, first, the nonlinear system is modelled by a Takagi-Sugeno fuzzy model with immeasurable premise variables. Then, SMO is used to estimate the states and fault. Finally, by using a non-quadratic Lyapunov function (NQLF), the stability of the error system is proved. By considering  performance criteria, the effect of the exogenous disturbance on the state estimations is minimized which provides effective fault estimation. Furthermore, the states and fault estimations asymptotically converge to their actual values for the non-perturbed systems. In the stability analysis and the observer gains design, some change of coordinates are proposed which the transformation matrix of one of them is obtained by solving linear matrix inequalities (LMIs). The proposed approach has some superiority over the existing methods. First, employing the NQLF leads to more relaxed results and better estimation performance. Second, using SMO for fault reconstruction makes the proposed approach insensitive to the uncertainties and unknown inputs and besides detecting the fault, its shape and size are determined. Third, since the premise variables are assumed to be unmeasurable, the presented approach is applicable for a wide class of nonlinear systems. Finally, a continuous stirred tank reactor (CSTR) process is considered and numerical simulation is carried out to illustrate the effectiveness and the accuracy of the proposed approach comparison with the recently published methods.

Keywords

References

[1] W. Ao, Y. Song and C. Wen, “Adaptive robust fault tolerant control design for a class of nonlinear uncertain MIMO systems with quantization,” ISA Trans., vol. 68, pp. 63–72, May 2017.
[2] H. Mekki, O. Benzineb, D. Boukhetala, M. Tadjine and M. Benbouzid, “Sliding mode based fault detection, reconstruction and fault tolerant control scheme for motor systems,” ISA Trans., vol. 57, pp. 340–351, Jul. 2015.
[3] Q. Shen, B. Jiang and V. Cocquempot, “Fuzzy Logic System-Based Adaptive Fault-Tolerant Control for Near-Space Vehicle Attitude Dynamics With Actuator Faults,” IEEE Trans. Fuzzy Syst., vol. 21, no. 2, pp. 289–300, Apr. 2013.
[4] Y. Zhang and J. Jiang, “Issues on Integration of Fault Diagnosis and Reconfigurable Control in Active Fault-Tolerant Control Systems,” IFAC Proc. Vol., vol. 39, no. 13, pp. 1437–1448, 2006.
[5] منصور اوجاقی، ناصر یزدان دوست و شهریار گل محمدزاده، ”تشخیص عیب گردش روغن در یاتاقان لغزشی موتور القایی با استفاده از هارمونیک‌های توان لحظه‌ای“، مجله مهندسی برق دانشگاه تبریز، دوره 46، شماره 4، صفحه7-17، زمستان 1395.
[6] مرتضی خرّم کشکولی و مریم دهقانی، ”تشخیص، شناسایی و جداسازی عیب توربین گاز پالایشگاه دوم پارس جنوبی با استفاده از روش‌های ترکیبی داده‌کاوی، k-means، تحلیل مؤلفه‌های اصلی (PCA) و ماشین بردار پشتیبان (SVM) “،  مجله مهندسی برق دانشگاه تبریز، دوره 47، شماره 2، صفحه501-515، تابستان 1396.
[7] S. Ahmadizadeh, J. Zarei and H. R. Karimi, “A robust fault detection design for uncertain Takagi–Sugeno models with unknown inputs and time-varying delays,” Nonlinear Anal. Hybrid Syst., vol. 11, pp. 98–117, Jan. 2014.
[8] H. Alwi, C. Edwards and C. Pin Tan, Fault Detection and Fault-Tolerant Control Using Sliding Modes, London: Springer London, 2011.
[9] M. Darouach, M. Zasadzinski and L. Boutat-Baddas, “Discussion on ”a comparison of sliding mode and unknown input observer for fault reconstruction”,” Eur. J. Control, vol. 12, no. 3, pp. 261–266, 2006.
[10] S. Mobayen, “An LMI-based robust controller design using global nonlinear sliding surfaces and application to chaotic systems,” Nonlinear Dyn., vol. 79, no. 2, pp. 1075–1084, Jan. 2015.
[11] S. Mobayen, “Fast terminal sliding mode controller design for nonlinear second-order systems with time-varying uncertainties,” Complexity, vol. 21, no. 2, pp. 239–244, Nov. 2015.
[12] S. Mobayen, “An adaptive chattering-free PID sliding mode control based on dynamic sliding manifolds for a class of uncertain nonlinear systems,” Nonlinear Dyn., vol. 82, no. 1–2, pp. 53–60, Oct. 2015.
[13] J. Yang, F. Zhu, X. Wang and X. Bu, “Robust sliding-mode observer-based sensor fault estimation, actuator fault detection and isolation for uncertain nonlinear systems,” Int. J. Control Autom. Syst., vol. 13, no. 5, pp. 1037–1046, Oct. 2015.
[14] G. H. Yang and H. Wang, “Fault Detection and Isolation for a Class of Uncertain State-Feedback Fuzzy Control Systems,” IEEE Trans. Fuzzy Syst., vol. 23, no. 1, pp. 139–151, Feb. 2015.
[15] Y. Zhao, J. Lam and H. Gao, “Fault Detection for Fuzzy Systems with Intermittent Measurements,” IEEE Trans. Fuzzy Syst., vol. 17, no. 2, pp. 398–410, Apr. 2009.
[16] A. Salem, Z. Kardous, N. B. Braiek and J. Ragot, “On the state observer based stabilization of Takagi-Sugeno systems with immeasurable premise variables,” Int. J. Control Autom. Syst., vol. 10, no. 6, pp. 1153–1163, Dec. 2012.
[17] S. Dhahri, A. Sellami and F. B. Hmida, “Robust H ∞ sliding mode observer design for fault estimation in a class of uncertain nonlinear systems with LMI optimization approach,” Int. J. Control Autom. Syst., vol. 10, no. 5, pp. 1032–1041, Oct. 2012.
[18] D. Ichalal, B. Marx, J. Ragot and D. Maquin, “Advances in observer design for Takagi-Sugeno systems with unmeasurable premise variables,” Control & Automation (MED), 2012 20th Mediterranean Conference on. IEEE, 2012, pp. 848–853,.
[19] L. Li, S. X. Ding, J. Qiu, Y. Yang and Y. Zhang, “Weighted Fuzzy Observer-Based Fault Detection Approach for Discrete-Time Nonlinear Systems via Piecewise-Fuzzy Lyapunov Functions,” IEEE Transactions on Fuzzy Systems, vol. 24, no. 6, pp. 1320–1333, Dec. 2016.
[20] A. B. Brahim, S. Dhahri, F. B. Hmida and A. Sellami, “An H∞ sliding mode observer for Takagi–Sugeno nonlinear systems with simultaneous actuator and sensor faults An,” Int. J. Appl. Math. Comput. Sci., vol. 25, no. 3, pp. 547–559, 2015.
[21] A. Ben Brahim, S. Dhahri, F. Ben Hmida and A. Sellami, “Simultaneous Actuator and Sensor Faults Reconstruction Based on Robust Sliding Mode Observer for a Class of Nonlinear Systems,” Asian J. Control, vol. 19, no. 1, pp. 362-371, Jan. 2017.
[22] F. Pöschke, S. Georg and H. Schulte, “Fault reconstruction using a Takagi-Sugeno sliding mode observer for the wind turbine benchmark,” International Conference on Control (CONTROL), 2014, pp. 456–461.
[23] A. Akhenak, M. Chadli, J. Ragot and D. Maquin, “Fault detection and isolation using sliding mode observer for uncertain Takagi-Sugeno fuzzy model,”16th Mediterranean Conference on Control and Automation, 2008, pp. 286–291.
[24] D. Ichalal, B. Marx, J. Ragot and D. Maquin, “Simultaneous state and unknown inputs estimation with PI and PMI observers for Takagi Sugeno model with unmeasurable premise variables,” in 17th Mediterranean Conference on Control and Automation, 2009, pp. 353–358.
[25] N. Vafamand, M. H. Asemani and A. Khayatiyan, “A robust L1 controller design for continuous-time TS systems with persistent bounded disturbance and actuator saturation,” Eng. Appl. Artif. Intell., vol. 56, pp. 212–221, Nov. 2016.
[26] G. He, Y. Liu, J. Ji and W. Yu, “Observer-based scheme for fault estimation and robust tolerant control: An LMI approach,” in 2016 Chinese Control and Decision Conference (CCDC), 2016, pp. 3466–3471.
[27] V. I. Utkin, Sliding Modes in Control and Optimization. Springer Science & Business Media, 2013.
[28] V. Ghaffari, S. V. Naghavi and A. A. Safavi, “Robust model predictive control of a class of uncertain nonlinear systems with application to typical CSTR problems,” J. Process Control, vol. 23, no. 4, pp. 493–499, Apr. 2013. 

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