Sliding Mode Robust Fault-Tolerant Control for Uncertain Systems with Time Delay

doi:10.1007/s12204-017-1827-3

Abstract

Abstract: Considering the modeling uncertainties and external disturbance, a kind of sliding mode robust H∞ fault-tolerant control method for time delay system with actuator fault is proposed. The upper-bound of the uncertainties is considered as a known constant, while the upper-bound of the actuator fault is unknown. A sufficient condition for the existence of an integral sliding mode dynamics is given in terms of linear matrix inequality (LMI). A novel adaptive law is given to estimate the unknown upper-bound of faults. On this basis, a type of sliding mode robust H∞ fault-tolerant control law is designed to guarantee the asymptotic stability and the H∞ performance index of the system. Finally, the simulation on quad-rotor semi-physical platform demonstrates the reliability and validity of the method.

Key words: fault-tolerant control| sliding mode control| time delay| robust H∞

摘要： Considering the modeling uncertainties and external disturbance, a kind of sliding mode robust H∞ fault-tolerant control method for time delay system with actuator fault is proposed. The upper-bound of the uncertainties is considered as a known constant, while the upper-bound of the actuator fault is unknown. A sufficient condition for the existence of an integral sliding mode dynamics is given in terms of linear matrix inequality (LMI). A novel adaptive law is given to estimate the unknown upper-bound of faults. On this basis, a type of sliding mode robust H∞ fault-tolerant control law is designed to guarantee the asymptotic stability and the H∞ performance index of the system. Finally, the simulation on quad-rotor semi-physical platform demonstrates the reliability and validity of the method.

关键词: fault-tolerant control| sliding mode control| time delay| robust H∞

CLC Number:

TP 273

YANG Pu* (杨蒲), NI Jiangfan (倪江帆), PAN Xu (潘旭), GUO Ruicheng (郭瑞诚). Sliding Mode Robust Fault-Tolerant Control for Uncertain Systems with Time Delay[J]. Journal of shanghai Jiaotong University (Science), 2017, 22(2): 240-246.

References 20

[1]	ZHAO B, LI Y C. Active substituting decentralizedfault-tolerant control for reconfigurable manipulatorswith multi-sensor failures [J]. Control and Decision,2014, 29(2): 226-230 (in Chinese).
[2]	YUAN K, HU S S. Multi-fault tolerance of aircraft controlsurface based on fault-tolerant multi-agent system[J]. Electronics Optics and Control, 2011, 18(5): 46-49(in Chinese).
[3]	JIN X Z, YANG G H, CHANG X H, et al. Robustfault-tolerant H∞ Control with adaptive compensation[J]. Acta Automatica Sinica, 2013, 39(1): 31-42 (inChinese).
[4]	SHEN Y, LIU L J, DOWELL E H. Adaptive faulttolerantrobust control for a linear system with adaptivefault identification [J]. IET Control Theory Application,2013, 7(2): 246-252.
[5]	SUN H B, LI S H, SUN C Y. Adaptive fault-tolerantcontroller design for air breathing hypersonic vehiclewith input saturation [J]. Systems Engineering andElectronics, 2013, 24(3): 488-499.
[6]	SU X M, WANG M Y, DONG H G, et al. Robustfault-tolerant control for time-varying descriptor systems[J]. Mathematics in Practice and Theory, 2014,49(10): 1869-1875 (in Chinese).
[7]	CHEN X Q, HU F F, SUN Y H, et al. Robust faulttolerantattitude control of three-axis stabilized satellite[C]//Proceedings of the 26th Chinese Control andDecision Conference. [s.l.]: IEEE, 2014: 1254-1259.
[8]	CHEN G, SONG Y D. Robust fault-tolerant cooperativecontrol of multi-agent systems with actuatorfaults [C]//Proceedings of the 26th Chinese Controland Decision Conference. [s.l.]: IEEE, 2014: 2891-2896.
[9]	AGHILI F. Optimal and fault-tolerant torque controlof servo motors subject to voltage and current limits[J]. IEEE Transactions on Control Systems Technology,2013, 21(4): 1440-1448.
[10]	SONG X Q, LIU C S, SUN J H, et al. Optimal faulttoleranttracking control of systems with parameteruncertainty [C] //Proceedings of the IEEE InternationalConference on System Science and Engineering(ICSSE). [s.l.]: IEEE, 2014: 119-123.
[11]	ZHAO D J, WANG Y J, LIU L, et al. Robust faulttolerantcontrol of launch vehicle via GPI observerand integral sliding mode control [J]. Asian Journalof Control, 2013, 15(2): 614-623.
[12]	MIRSHAMS M, KHOSROJERDI M, HASANI M.Passive fault-tolerant sliding mode attitude control forflexible spacecraft with faulty thrusters [J]. Journal ofAerospace Engineering, 2013, 228(12): 2343-2357.
[13]	ALMEIDA S, ARAUJO R E. Fault-tolerant controlusing sliding mode techniques applied to multi-motorelectric vehicle [C]//Proceedings of the IEEE Conferenceof the Industrial Electronics Society. [s.l.]: IEEE,2013: 3530-3535.
[14]	HUA C C, WANG Q G, GUAN X P. Memoryless statefeedback controller design for time delay systems withmatched uncertain nonlinearities [J]. IEEE Transactionson Automatic Control, 2008, 53(3): 801-808.
[15]	LIAN J G, DIMIROVSKI G M, ZHAO J. Robust H∞SMC of uncertain switched systems with time delay[C]//Proceedings of the American Control Conference.Washington, USA: IEEE, 2008: 11-13.
[16]	WANG C H, HUANG T M. Delay-independent variablestructure control of time delay systems with mismatcheduncertainties [C]//Proceedings of 46th Conferenceon Decision and Control. New Orleans, USA:IEEE, 2007: 2065-2070.
[17]	XIA Y Q, JIA Y M. Robust sliding-mode controlof uncertain time delay systems: An LMI approach[J]. IEEE Transactions on Automatic Control, 2003,48(5): 1086-1092.
[18]	CHOI H H. LMI-Based sliding surface design for integralsliding mode control of mismatched uncertainsystems [J]. IEEE Transactions on Automatic Control,2007, 52(4): 736-742.
[19]	YANG P, NI J F, JIANG B, et al. The adaptive globalrobust sliding mode control for uncertain systems withtime-varying delay [J]. Control and Decision, 2014,29(9): 1688-1692 (in Chinese).
[20]	XIE L H, FU M Y, DE SOUZA C E. H∞ control andquadratic stabilization of systems with parameter uncertaintyvia output feedback [J]. IEEE Transactionson Automatic Control, 1992, 37(8): 1253-1256.