This paper deals with the fault observer and fault-tolerant controller design for singular Takagi–Sugeno (T–S) fuzzy systems subject to actuator faults. First, a novel proportional-integral observer is constructed to estimate the system states and faults. Sufficient conditions for the existence of the proposed observer are given in linear matrix inequality (LMI) terms. Furthermore, based on the state and fault estimation (FE), a fault-tolerant controller (FTC) is designed to effectively accommodate the influence of fault upon state and ensure that the closed-loop system is stable. Finally, a numerical example is given to show the effectiveness of the presented method.
Issue Section:
Research Papers
Topics:
Closed loop systems,
Control equipment,
Design,
Fuzzy logic,
Errors,
Actuators,
Stability,
Scalars
References
1.
Edwards
, C.
, Spurgeon
, S. K.
, and Patton
, R. J.
, 2000
, “Sliding Mode Observers for Fault Detection and Isolation
,” Automatica
, 36
(4
), pp. 541
–553
.2.
Su
, X. J.
, Liu
, X. X.
, and Song
, Y. D.
, 2017
, “Event-Triggered Sliding Mode Control for Multi-Area Power Systems
,” IEEE Trans. Ind. Electron.
, 64
(8
), pp. 6732
–6741
.3.
Koenig
, D.
, 2005
, “Unknown Input Proportional Multiple–Integral Observer Design for Linear Descriptor Systems: Application to State and Fault Estimation
,” IEEE Trans. Autom. Control
, 50
(2
), pp. 212
–217
.4.
Lee
, D. J.
, Park
, Y.
, and Park
, Y.
, 2012
, “Robust H∞ Sliding Mode Descriptor Observer for Fault and Output Disturbance Estimation of Uncertain Systems
,” IEEE Trans. Autom. Control
, 57
(11
), pp. 2928
–2934
.5.
Li
, X. J.
, and Yang
, G. H.
, 2012
, “Dynamic Observer-Based Robust Control and Fault Detection for Linear Systems
,” IET Control Theory Appl.
, 6
(17
), pp. 2657
–2666
.6.
Zhang
, P.
, Ding
, S. X.
, and Liu
, P.
, 2012
, “A Lifting Based Approach to Observer Based Fault Detection of Linear Periodic Systems
,” IEEE Trans. Autom. Control
, 57
(2
), pp. 457
–462
.7.
Nguang
, S.
, Shi
, P.
, and Ding
, S.
, 2007
, “Fault Detection for Uncertain Fuzzy Systems: An LMI Approach
,” IEEE Trans. Fuzzy Syst.
, 15
(6
), pp. 1251
–1262
.8.
Cao
, Y. Y.
, and Frank
, P. M.
, 2001
, “Stability Analysis and Synthesis of Nonlinear Time-Delay Systems Via Linear Takagi–Sugeno Fuzzy Models
,” Fuzzy Sets Syst.
, 124
(2
), pp. 213
–229
.9.
Wu
, L.
, and Ho
, D. W. C.
, 2009
, “Fuzzy Filter Design for Nonlinear Itô Stochastic Systems With Application to Sensor Fault Detection
,” IEEE Trans. Fuzzy Syst.
, 17
(1
), pp. 233
–242
.10.
Zhang
, K.
, Jiang
, B.
, and Staroswiecki
, M.
, 2010
, “Dynamic Output Feedback Fault Tolerant Controller Design for Takagi–Sugeno Fuzzy Systems With Actuator Faults
,” IEEE Trans. Fuzzy Syst.
, 18
(1
), pp. 194
–201
.11.
Zhang
, K.
, Jiang
, B.
, and Shi
, P.
, 2015
, “Analysis and Design of Robust H∞ Fault Estimation Observer With Finite-Frequency Specifications for Discrete-Time Fuzzy Systems
,” IEEE Trans. Cybern.
, 45
(7
), pp. 1225
–1235
.12.
Dong
, J. X.
, and Hou
, J. T.
, 2017
, “Output Feedback Fault-Tolerant Control by a Set-Theoretic Description of T–S Fuzzy Systems
,” Appl. Math. Comput.
, 301
, pp. 117
–134
.13.
Jia
, Q. X.
, Chen
, W.
, and Wang
, P.
, 2017
, “Design of a PD-Type Learning Observer for Reconstruction of Actuator Faults in Descriptor Systems
,” IET Control Theory Appl.
, 11
(1
), pp. 17
–24
.14.
Shen
, Q. K.
, Jiang
, B.
, and Cocquempot
, V.
, 2012
, “Fault Tolerant Control for T–S Fuzzy Systems With Application to Near-Space Hypersonic Vehicle With Actuator Faults
,” IEEE Trans. Fuzzy Syst.
, 20
(4
), pp. 652
–665
.15.
Shen
, Q. K.
, Jiang
, B.
, and Cocquempot
, V.
, 2013
, “Fuzzy Logic System-Based Adaptive Fault Tolerant Control for Near-Space Vehicle Attitude Dynamics With Actuator Faults
,” IEEE Trans. Fuzzy Syst.
, 21
(2
), pp. 289
–300
.16.
Li
, X. H.
, Zhu
, F. L.
, and Chakrabarty
, A.
, 2016
, “Nonfragile Fault Tolerant Fuzzy Observer-Based Controller Design for Nonlinear Systems
,” IEEE Trans. Fuzzy Syst.
, 24
(6
), pp. 1679
–1689
.17.
Huang
, S. J.
, and Yang
, G. H.
, 2014
, “Fault Tolerant Controller Design for T–S Fuzzy Systems With Time-Varying Delay and Actuator Faults: A K-Step Fault-Estimation Approach
,” IEEE Trans. Fuzzy Syst.
, 22
(6
), pp. 1526
–1540
.18.
Chadli
, M.
, Abdo
, A.
, and Ding
, S. X.
, 2013
, “H2/H∞ Fault Detection Filter Design for Discrete-Time Takagi–Sugeno Fuzzy System
,” Automatica
, 49
(7
), pp. 1996
–2005
.19.
Liu
, M.
, Cao
, X. B.
, and Shi
, P.
, 2013
, “Fault Estimation and Tolerant Control for Fuzzy Stochastic Systems
,” IEEE Trans. Fuzzy Syst.
, 21
(2
), pp. 221
–229
.20.
Liu
, M.
, Cao
, X. B.
, and Shi
, P.
, 2013
, “Fuzzy-Model-Based Fault Tolerant Design for Nonlinear Stochastic Systems Against Simultaneous Sensor and Actuator Faults
,” IEEE Trans. Fuzzy Syst.
, 21
(5
), pp. 789
–799
.21.
Jia
, Q. X.
, Chen
, W.
, and Zhang
, Y. C.
, 2015
, “Fault Reconstruction and Fault-Tolerant Control Via Learning Observers in Takagi–Sugeno Fuzzy Descriptor Systems With Time Delays
,” IEEE Trans. Ind. Electron.
, 62
(6
), pp. 3885
–3996
.22.
Gu
, Z.
, Liu
, J. L.
, Peng
, C.
, and Tian
, E.
, 2011
, “Fault-Distribution Dependent Reliable Control for T-S Fuzzy Time-Delayed Systems
,” ASME J. Dyn. Syst. Meas. Control
, 133
(6
), p. 064503.23.
Zhang
, K.
, Jiang
, B.
, and Shi
, P.
, 2012
, “Fault Estimation Observer Design for Discrete-Time Takagi–Sugeno Fuzzy Systems Based on Piecewise Lyapunov Functions
,” IEEE Trans. Fuzzy Syst.
, 20
(1
), pp. 192
–201
.24.
Jiang
, B.
, Zhang
, K.
, and Shi
, P.
, 2011
, “Integrated Fault Estimation and Accommodation Design for Discrete-Time Takagi–Sugeno Fuzzy Systems With Actuator Faults
,” IEEE Trans. Fuzzy Syst.
, 19
(2
), pp. 291
–304
.25.
Jiang
, B.
, Staroswiecki
, M.
, and Cocquempot
, V.
, 2004
, “Fault Estimation in Nonlinear Uncertain Systems Using Robust/Sliding-Mode Observers
,” IEE Proc.-Control Theory Appl.
, 151
(1
), pp. 29
–37
.26.
Zhang
, X. D.
, Polycarpou
, M. M.
, and Parisini
, T.
, 2010
, “Fault Diagnosis of a Class of Nonlinear Uncertain Systems With Lipschitz Nonlinearities Using Adaptive Estimation
,” Automatica
, 46
(2
), pp. 290
–299
.27.
Zhang
, X. D.
, Parisini
, T.
, and Polycarpou
, M. M.
, 2004
, “Adaptive Fault-Tolerant Control of Nonlinear Uncertain Systems: An Information-Based Diagnostic Approach
,” IEEE Trans. Autom. Control
, 49
(8
), pp. 1259
–1274
.28.
Zhang
, X. D.
, 2011
, “Sensor Bias Fault Detection and Isolation in a Class of Nonlinear Uncertain Systems Using Adaptive Estimation
,” IEEE Trans. Autom. Control
, 56
(5
), pp. 1220
–1226
.29.
Jiang
, B.
, Staroswiecki
, M.
, and Cocquempot
, V.
, 2006
, “Fault Accommodation for Nonlinear Dynamic Systems
,” IEEE Trans. Autom. Control
, 51
(9
), pp. 1578
–1583
.30.
Yan
, X. G.
, Spurgeon
, S. K.
, and Edwards
, C.
, 2013
, “State and Parameter Estimation for Nonlinear Delay Systems Using Sliding Mode Techniques
,” IEEE Trans. Autom. Control
, 58
(4
), pp. 1023
–1029
.31.
Han
, C. S.
, Zhang
, G. J.
, Wu
, L. G.
, and Zeng
, Q. S.
, 2012
, “Sliding Mode Control of T–S Fuzzy Descriptor Systems With Time-Delay
,” J. Franklin Inst.
, 349
(4
), pp. 1430
–1444
.32.
Hamdi
, H.
, Rodrigues
, M.
, Mechmeche
, C.
, and Benhadjbraiek
, N.
, 2013
, “Observer Based Fault Tolerant Control for Takagi–Sugeno Nonlinear Descriptor Systems
,” International Conference on Control, Engineering and Information Technology
, Sousse, Tunisia, June 20, pp. 52
–57
.33.
Yang
, C. Y.
, and Zhang
, Q. L.
, 2009
, “Multiobjective Control for TCS Fuzzy Singularly Perturbed Systems
,” IEEE Trans. Fuzzy Syst.
, 17
(1
), pp. 104
–115
.34.
Feng
, Z. G.
, and Shi
, P.
, 2017
, “Sliding Mode Control of Singular Stochastic Markov Jump Systems
,” IEEE Trans. Autom. Control
, 62
(8
), pp. 4266
–4273
.35.
Zhu
, Y.
, Zhong
, Z.
, Basin
, M. V.
, and Zhou
, D.
, 2018
, “A Descriptor System Approach to Stability and Stabilization of Discrete-Time Switched PWA Systems
,” IEEE Trans. Autom. Control
, 63
(10), pp. 3456–3463.36.
Li
, H.
, and Wang
, Y.
, 2017
, “Lyapunov-Based Stability and Construction of Lyapunov Functions for Boolean Networks
,” SIAM J. Control Optim.
, 55
(6
), pp. 3437
–3457
.37.
Li
, Y.
, Li
, H.
, and Sun
, W.
, 2018
, “Event-Triggered Control for Robust Set Stabilization of Logical Control Networks
,” Automatica
, 95
, pp. 556
–560
.38.
Tong
, M. S.
, Pan
, Y. L.
, Li
, Z. L.
, and Lin
, W. Y.
, 2018
, “Valid Data Based Normalized Cross-Correlation (VDNCC) for Topography Identification
,” Neurocomputing
, 308
, pp. 184
–193
.Copyright © 2019 by ASME
You do not currently have access to this content.