This paper explores the fault-tolerant control problem for uncertain impulsive singular linear time-variant (LTV) systems in the presence of bounded-power or L∞ disturbances. Here, a saturation avoidance mechanism is employed to prevent faulty actuators from overloading. Also, the conflict between attenuating the effect of L∞ disturbances and enlarging the domain of attraction is tackled by proposing a nonconstant state feedback controller. In addition, the proposed method is capable of tolerating time-varying faults. The suggested method is implemented on a mechanical viscoelastic model of cortical bone with impulsive and time-varying nature to evaluate its competency.
Issue Section:
Research Papers
References
1.
Jiang
, J.
, and Yu
, X.
, 2012
, “Fault-Tolerant Control Systems: A Comparative Study Between Active and Passive Approaches
,” Annu. Rev. Control
, 36
(1
), pp. 60
–72
.2.
Lunze
, J.
, and Richter
, J. H.
, 2008
, “Reconfigurable Fault-Tolerant Control: A Tutorial Introduction
,” Eur. J. Control
, 14
(5
), pp. 359
–386
.3.
Fan
, J.
, Zhang
, Y.
, and Zheng
, Z.
, 2013
, “Adaptive Observer-Based Integrated Fault Diagnosis and Fault-Tolerant Control Systems Against Actuator Faults and Saturation
,” ASME J. Dyn. Syst., Meas., Control
, 135
(4
), p. 041008
.4.
Hamayun
, M. T.
, Edvards
, C.
, and Alwi
, H.
, 2014
, “Augmentation Scheme for Fault-Tolerant Control Using Integral Sliding Modes
,” IEEE Trans. Control Syst. Technol.
, 22
(1
), pp. 307
–313
.5.
Xiao
, B.
, Hu
, Q.
, and Friswell
, M. I.
, 2011
, “Robust Fault Tolerant Control for Spacecraft Attitude Stabilization Under Actuator Faults and Bounded Disturbance
,” ASME J. Dyn. Syst., Meas., Control
, 133
(5
), p. 051006
.6.
Wu
, L. B.
, Yang
, G. H.
, and Ye
, D.
, 2014
, “Robust Adaptive Fault-Tolerant Control for Linear Systems With Actuator Failures and Mismatched Parameter Uncertainties
,” IET Control Theory Appl.
, 8
(6
), pp. 441
–449
.7.
Yu
, X.
, and Jiang
, J.
, 2012
, “Hybrid Fault-Tolerant Flight Control System Design Against Partial Actuator Failures
,” IEEE Trans. Control Syst. Technol.
, 20
(4
), pp. 871
–886
.8.
Fan
, J.
, Zhang
, Y.
, and Zheng
, Z.
, 2012
, “Robust Fault-Tolerant Control Against Time-Varying Actuator Faults and Saturation
,” IET Control Theory Appl.
, 6
(14
), pp. 2198
–2208
.9.
Hu
, T.
, Lin
, Z.
, and Chen
, B. M.
, 2002
, “An Analysis and Design Method for Linear Systems Subject to Actuator Saturation and Disturbance
,” Automatica
, 38
(2
), pp. 351
–359
.10.
Kim
, S. H.
, 2015
, “Reliable Piecewise Control Design for Systems With Actuator Saturation and Fault
,” Int. J. Syst. Sci.
, 46
(3
), pp. 385
–393
.11.
Yuan
, C.
, and Wu
, F.
, 2015
, “Switching Control of Linear Systems Subject to Asymmetric Actuator Saturation
,” Int. J. Control
, 88
(1
), pp. 204
–215
.12.
Sun
, L.
, Wang
, Y.
, and Feng
, G.
, 2015
, “Control Design for a Class of Affine Nonlinear Descriptor Systems With Actuator Saturation
,” IEEE Trans. Autom. Control
, 60
(8
), pp. 2195
–2200
.13.
Feng
, Y.
, and Yagoubi
, M.
, 2016
, “Comprehensive Admissibility for Descriptor Systems
,” Automatica
, 66
, pp. 271
–275
.14.
Rodrigues
, M.
, Hamdi
, H.
, Braiek
, N. B.
, and Theilliol
, D.
, 2014
, “Observer-Based Fault Tolerant Control Design for a Class of LPV Descriptor Systems
,” J. Franklin Inst.
, 351
(6
), pp. 3104
–3125
.15.
Feng
, Z.
, and Shi
, P.
, 2017
, “Two Equivalent Sets: Application to Singular Systems
,” Automatica
, 77
, pp. 198
–205
.16.
Lin
, Z.
, and Lv
, L.
, 2007
, “Set Invariance Conditions for Singular Linear Systems Subject to Actuator Saturation
,” IEEE Trans. Autom. Control
, 52
(12
), pp. 2351
–2355
.17.
Lin
, D.
, Lan
, W.
, and Li
, M.
, 2011
, “Composite Nonlinear Feedback Control for Linear Singular Systems With Input Saturation
,” Syst. Control Lett.
, 60
(10
), pp. 825
–831
.18.
Lv
, L.
, and Lin
, Z.
, 2008
, “Analysis and Design of Singular Linear Systems Under Actuator Saturation and L2/L∞ Disturbances
,” Syst. Control Lett.
, 57
(11
), pp. 904
–912
.19.
Zhou
, L.
, Xiao
, X.
, and Lu
, G.
, 2012
, “Simultaneous Semi-Global Lp-Stabilization and Asymptotical Stabilization for Singular Systems Subject to Input Saturation
,” Syst. Control Lett.
, 61
(3
), pp. 403
–411
.20.
Zuo
, Z.
, Ho
, D. W. C.
, and Wang
, Y.
, 2010
, “Fault-Tolerant Control for Singular Systems With Actuator Saturation and Nonlinear Perturbation
,” Automatica
, 46
(3
), pp. 569
–576
.21.
Zuo
, Z.
, Wang
, Y.
, and Yang
, W.
, 2015
, “L2-Gain Fault-Tolerant Control of Singular Lipschitz Systems in the Presence of Actuator Saturation
,” Int. J. Robust Nonlinear Control
, 25
(12
), pp. 1751
–1766
.22.
Takaba
, K.
, 1998
, “Robust H2 Control of Descriptor System With Time-Varying Uncertainty
,” Int. J. Control
, 71
(4
), pp. 559
–579
.23.
Barbosa
, K. A.
, and Cipriano
, A.
, 2011
, “Robust H∞ Filter Design for Singular Systems With Time-Varying Uncertainties
,” IET Control Theory Appl.
, 5
(9
), pp. 1085
–1091
.24.
Aouaouda
, S.
, Bouarar
, T.
, and Bouhali
, O.
, 2014
, “Fault-Tolerant Tracking Control Using Unmeasurable Premise Variables for Vehicle Dynamics Subject to Time Varying Faults
,” J. Franklin Inst.
, 351
(9
), pp. 4514
–4537
.25.
Liu
, C.
, and Jiang
, B.
, 2014
, “H∞ Fault-Tolerant Control for Time-Varied Actuator Fault of Nonlinear System
,” Int. J. Syst. Sci.
, 45
(12
), pp. 2447
–2457
.26.
Xie
, C. H.
, and Yang
, G. H.
, 2016
, “Approximate Guaranteed Cost Fault-Tolerant Control of Unknown Nonlinear Systems With Time-Varying Actuator Faults
,” Nonlinear Dyn.
, 83
(1
), pp. 269
–282
.27.
Wan
, Z.
, and Kothare
, M. V.
, 2002
, “Robust Output Feedback Model Predictive Control Using Off-Line Linear Matrix Inequalities
,” J. Process Control
, 12
(7
), pp. 763
–774
.28.
Boyd
, S.
, El Ghaoui
, L.
, Feron
, E.
, and Balakrishnan
, V.
, 1994
, Linear Matrix Inequalities in Systems and Control Theory
(Studies in Applied and Numerical Mathematics, Vol. 15
), SIAM
, Philadelphia, PA
.29.
Johnson
, T. P. M.
, Socrate
, S.
, and Boyce
, M. C.
, 2010
, “A Viscoelastic, Viscoplastic Model of Cortical Bone Valid at Low and High Strain Rates
,” Acta Biomater.
, 6
(10
), pp. 4073
–4080
.30.
Hu
, T.
, and Lin
, Z.
, 2003
, “Composite Quadratic Lyapunov Functions for Constrained Control System
,” IEEE Trans. Autom. Control
, 48
(3
), pp. 440
–450
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