Fault Reconstruction for Lipschitz Nonlinear Systems Using Higher Terminal Sliding Mode Observer

doi:10.1007/s12204-020-2196-x

摘要/Abstract

摘要： This paper considers the design of an adaptive second order terminal observer for robust fault reconstruction
of nonlinear Lipschitz systems with unknown upper bound of derivative fault. Firstly, a linear
transforming matrix is introduced, which transforms the system into two subsystems, and thus to reduce the
dimension of the system. One of the subsystem is affected by fault and disturbances, while the other is free,
which simplifies the design of observer. Then, the design method of the observer gain matrix is transformed into
a convex optimization problem under linear matrix inequalities (LMIs). A second order non-singular terminal
sliding mode observer is designed for the transformed system to realize the accurate estimation of state and fault.
Considering the unknown upper bound of derivative fault, an adaptive algorithm is designed in the equivalent
output error injection signal to ensure the sliding mode motion reach the sliding surface within limited time.
Finally, an example demonstrates the effectiveness of the proposed method in the paper.

关键词: second order terminal sliding mode observer, linear matrix inequalities, fault reconstruction, Lipschitz
systems

Abstract: This paper considers the design of an adaptive second order terminal observer for robust fault reconstruction
of nonlinear Lipschitz systems with unknown upper bound of derivative fault. Firstly, a linear
transforming matrix is introduced, which transforms the system into two subsystems, and thus to reduce the
dimension of the system. One of the subsystem is affected by fault and disturbances, while the other is free,
which simplifies the design of observer. Then, the design method of the observer gain matrix is transformed into
a convex optimization problem under linear matrix inequalities (LMIs). A second order non-singular terminal
sliding mode observer is designed for the transformed system to realize the accurate estimation of state and fault.
Considering the unknown upper bound of derivative fault, an adaptive algorithm is designed in the equivalent
output error injection signal to ensure the sliding mode motion reach the sliding surface within limited time.
Finally, an example demonstrates the effectiveness of the proposed method in the paper.

Key words: second order terminal sliding mode observer, linear matrix inequalities, fault reconstruction, Lipschitz
systems

中图分类号:

TP 277

DAI Cong, LIU Yongzhi, SUN Haoshui . Fault Reconstruction for Lipschitz Nonlinear Systems Using Higher Terminal Sliding Mode Observer[J]. Journal of Shanghai Jiao Tong University(Science), 2020, 25(5): 630-638.

参考文献 32

[1]	VELUVOLU K C, SOH Y C. Fault reconstruction and state estimation with sliding mode observers for Lipschitz non-linear systems [J]. IET Control Theory and Applications, 2011, 5(11): 1255-1263.
[2]	DHAHRI S, SELLAMI A, HMIDA F B. Robust H∞ sliding mode observer design for fault estimation in a class of uncertain nonlinear systems with LMI optimization approach [J]. International Journal of Control,Automation and Systems, 2012, 10(5): 1032-1041.
[3]	LEE D J, PARK Y J, PARK Y S. Robust H∞ sliding mode descriptor observer for fault and output disturbance estimation of uncertain systems [J]. IEEE Transactions on Automatic Control, 2012, 57(11): 2928-2934.
[4]	LIU H Y, DUAN Z S. Actuator fault estimation using direct reconstruction approach for linear multivariable systems [J]. IET Control Theory and Applications,2012, 6(1): 141-148.
[5]	ALWI H, EDWARDS C, TAN C P. Sliding mode estimation schemes for incipient sensor faults[J].Automatica, 2009, 45(7): 1679-1685.
[6]	NG K Y, TAN C P, OETOMO D. Disturbance decoupled fault reconstruction using cascaded sliding mode observers [J]. Automatica, 2012, 48(5): 794-799.
[7]	CHEN L J, EDWARDS C, ALWI H. Sensor redundancy based FDI using an LPV sliding mode observer[J]. IET Control Theory & Applications, 2018, 12(14):1956-1963.
[8]	JIANG S H, WANG Z, LI S R, et al. Design of the neural-network-based adaptive sliding mode observer for fault reconstruction [C]//2017 Chinese Automation Congress. Jinan, China: IEEE, 2017: 4654-4659.
[9]	GONZALEZ T, MORENO J A, FRIDMAN L. Variable gain super-twisting sliding mode control [J]. IEEE Transactions on Automatic Control, 2012, 57(8):2100-2105.
[10]	UTKIN V I, POZNYAK A S. Adaptive sliding mode control with application to super-twist algorithm:Equivalent control method [J]. Automatica, 2013,49(1): 39-47.
[11]	BOUDJELLAL M, ILLOUL R. High-order sliding mode and high-gain observers for state estimation and fault reconstruction for a nonlinear CSTR [C]//6th International Conference on Systems and Control.Batna, Algeria: IEEE, 2017: 231-236.
[12]	BOUDJELLAL M, ILLOUL R. Sensor fault estimation for a nonlinear CSTR using super-twisting and high-gain observers [C]//5th International Conference on Electrical Engineering-Boumerdes. Boumerdes, Algeria:IEEE, 2017: 1-5.
[13]	R′IOS H, DAVILA J, FRIDMAN L. High-order sliding mode observers for nonlinear autonomous switched systems with unknown inputs [J]. Journal of the Franklin Institute, 2012, 349(10): 2975-3002.
[14]	FRIDMAN L, SHTESSEL Y, EDWARDS C, et al.Higher-order sliding-mode observer for state estimation and input reconstruction in nonlinear systems [J].International Journal of Robust and Nonlinear Control,2008, 18(4/5): 399-412.
[15]	ZHU F L, CEN F. Full-order observer-based actuator fault detection and reduced-order observer-based fault reconstruction for a class of uncertain nonlinear systems [J]. Journal of Process Control, 2010, 20(10):1141-1149.
[16]	FRIDMAN L, DAVILA J, LEVANT A. High-order sliding-mode observation and fault detection [C]//46th IEEE Conference on Decision and Control. New Orleans,LA, USA: IEEE, 2007: 4317-4322.
[17]	CHEN W T, SAIF M. Actuator fault diagnosis for uncertain linear systems using a high-order slidingmode robust differentiator (HOSMRD) [J]. International Journal of Robust and Nonlinear Control, 2008,18(4/5): 413-426.
[18]	ALWI H, EDWARDS C. Application of second order sliding mode observers for fault reconstruction on the ADDSAFE benchmark [C]//2011 AIAA Guidance,Navigation, and Control Conference. Portland,OR, USA: AIAA, 2011: 6682.
[19]	ALWI H, EDWARDS C. An adaptive sliding mode differentiator for actuator oscillatory failure case reconstruction[J]. Automatica, 2013, 49(2): 642-651.
[20]	TAN C P, YU X H, MAN Z H. Terminal sliding mode observers for a class of nonlinear systems [J]. Automatica,2010, 46(8): 1401-1404.
[21]	SUN H, YAN J G, QU Y H, et al. Actuator fault reconstruction based on terminal sliding mode observer for aircraft anti-skid braking system [J]. Journal of Northwestern Polytechnical University, 2016, 34(3): 386-392(in Chinese).
[22]	XIAO B, YIN S. An fast reconstruction approach for actuator fault in robot manipulators [C]//14th International Workshop on Variable Structure Systems.Nanjing, China: IEEE, 2016: 414-419.
[23]	YUAN L, SHEN J Q, XIAO F, et al. Nonsingular terminal sliding-mode observer design for interior permanant magnet synchronous motor drive at very lowspeed[J]. Acta Physica Sinica, 2013, 62(3): 030501 (in Chinese).
[24]	SHI H Y, FENG Y. High-order terminal sliding mode flux observer for induction motors [J]. Acta Automatica Sinica, 2012, 38(2): 288-294 (in Chinese).
[25]	JANG S J, LEE S H, PARK J B, et al. Adaptive fault diagnosis observer design for linear system with separated faults and disturbance [C]//11th International Conference on Control, Automation and Systems.Gyeonggi-do, Korea: IEEE, 2011: 1903-1907.
[26]	YU L. Robust control: Linear matrix inequalities (LMI) approach [M]. Beijing: Tsinghua University Press, 2002.
[27]	ZHOU L, JIANG C S, DU L L. A robust adaptive terminal sliding mode control based on backstepping[J]. Control Theory &Applications, 2009, 26(6): 678-682 (in Chinese).
[28]	DHAHRI S, HMIDA F B, SELLAMI A, et al. Actuartor fault reconstruction for linear uncertain systems using sliding mode observer [C]//3rd International Conference on Signals, Circuits and Systems. Medenine,Tunisia: IEEE, 2009: 1-6.
[29]	LIU C, JIANG B, ZHANG K. Incipient fault detection using an associated adaptive and sliding-mode observer for quadrotor helicopter attitude control systems[J]. Circuits, System, and Signal Processing,2016, 35: 3555-3574.
[30]	YAN X G, EDWARDS C. Nonlinear robust fault reconstruction and estimation using a sliding mode observer [J]. Automatica, 2007, 43(9): 1605-1614.
[31]	YAN X G, EDWARDS C. Robust sliding mode observer-based actuator fault detection and isolation for a class of nonlinear systems [J]. International Journal of Systems Science, 2008, 39(4): 349-359.
[32]	MART′INEZ-GUERRA R, RINC′ON-PASAYE J J.Fault reconstruction for nonlinear systems using sliding mode observers [C]//46th IEEE Conference on Decision and Control. New Orleans, LA, USA: IEEE,2007: 4323-4328.

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