This paper proposes fault-tolerant control design for uncertain nonlinear systems described under Takagi-Sugeno fuzzy systems with local nonlinear models that satisfy the Lipschitz condition. First, by transforming sensor faults as ‘pseudo-actuator’ faults, an adaptive sliding mode observer is designed in order to simultaneously estimate system states, actuator and sensor faults despite the presence of norm-bounded uncertainties. Second, an adaptive sliding mode controller is suggested to provide a solution to stabilize the closed-loop system, even in the event of simultaneous occurrence of faults in actuators and sensors. Next, the main objective of the fault-tolerant control strategy is to compensate for the effects of fault based on the feedback information. Therefore, using the LMI optimization method, sufficient conditions are developed with to calculate the gains of the observer and the controller. Then, particular attention is paid to the simultaneous maximization, by convex multi-objective optimization, of the Lipschitz nonlinear constant in Takagi-Sugeno fuzzy modelling and uncertainties attenuation level. The results of the simulation illustrate the effectiveness of our fault-tolerant control approach using a nonlinear inverted pendulum with a cart system.
AlwiHEdwardsCTanCP (2011) Fault Detection and Fault-tolerant Control using Sliding Modes. Springer Science & Business Media.
2.
AouaoudaSChadliMCocquempotVTarek KhadirM (2013) Multi-objective fault detection observer design for Takagi-Sugeno fuzzy systems with unmeasurable premise variables: Descriptor approach. International Journal of Adaptive Control and Signal Processing27(12): 1031–1047.
3.
BrahimABDhahriSHmidaFBSellamiA (2015) An sliding mode observer for Takagi-Sugeno nonlinear systems with simultaneous actuator and sensor faults. International Journal of Applied Mathematics and Computer Science25(3): 547–559.
4.
BrahimABDhahriSHmidaFBSellamiA (2017) Simultaneous actuator and sensor faults reconstruction based on robust sliding mode observer for a class of nonlinear systems. Asian Journal of Control19(1): 362–371.
5.
DhahriSHmidaFBSellamiAGossaM (2011) Sliding mode observer-based fault reconstruction for uncertain linear systems. American Journal of Applied Sciences8(10): 1032.
6.
DhahriSSellamiAHmidaFB (2012) Robust sliding mode observer design for fault estimation in a class of uncertain nonlinear systems with LMI optimization approach. International Journal of Control, Automation and Systems10(5): 1032–1041.
7.
EdwardsCSpurgeonSKPattonRJ (2000) Sliding mode observers for fault detection and isolation. Automatica36(4): 541–553.
8.
GaoZCecatiCDingSX (2015) A survey of fault diagnosis and fault-tolerant techniques – part I: Fault diagnosis with model-based and signal-based approaches. IEEE Transactions on Industrial Electronics62(6): 3757–3767.
9.
GaoZJiangBShiPXuY (2010) Fault accommodation for near space vehicle attitude dynamics via T-S fuzzy models. International Journal of Innovative Computing, Information and Control6(11): 4843–4856.
10.
HanJZhangHWangYLiuX (2016) Robust fault estimation and accommodation for a class of T-S fuzzy systems with local nonlinear models. Circuits, Systems, and Signal Processing35(10): 3506–3530.
11.
HmidiRBrahimABHmidaFBSellamiA (2018) Robust fault tolerant control for Lipschitz nonlinear systems with simultaneous actuator and sensor faults. In: 2018 International Conference on Advanced Systems and Electric Technologies (IC_ASET), pp. 277–283. IEEE.
12.
HmidiRBrahimABHmidaFBSellamiA (2019) Diagnosis for Lipschitz nonlinear system with sliding mode observer and virtual sensor. In: 2019 19th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA), pp. 1–6. IEEE.
13.
HmidiRBrahimABHmidaFBSellamiA (2020) Robust fault tolerant control design for nonlinear systems not satisfying matching and minimum phase conditions. International Journal of Control, Automation and Systems 11: 1–14.
14.
HuoBTongSLiY (2013) Adaptive fuzzy fault-tolerant output feedback control of uncertain nonlinear systems with actuator faults. International Journal of Systems Science44(12): 2365–2376.
15.
IchalalDMarxBRagotJMaquinD (2014) Fault detection, isolation and estimation for Takagi-Sugeno nonlinear systems. Journal of the Franklin Institute351(7): 3651–3676.
16.
KhosrowjerdiMJBarzegaryS (2014) Fault tolerant control using virtual actuator for continuous-time Lipschitz nonlinear systems. International Journal of Robust and Nonlinear Control24(16): 2597–2607.
17.
NavarbafAKhosrowjerdiMJ (2019) Fault-tolerant controller design with fault estimation capability for a class of nonlinear systems using generalized Takagi-Sugeno fuzzy model. Transactions of the Institute of Measurement and Control P. 0142331219853687.
18.
RaoufiRMarquezHZinoberA (2010) sliding mode observers for uncertain nonlinear Lipschitz systems with fault estimation synthesis. International Journal of Robust and Nonlinear Control20(16): 1785–1801.
19.
SamiMPattonRJ (2013) Active fault tolerant control for nonlinear systems with simultaneous actuator and sensor faults. International Journal of Control, Automation and Systems11(6): 1149–1161.
20.
TakagiTSugenoM (1993) Fuzzy identification of systems and its applications to modeling and control. In: Acharya UR, Bhat S, Faust O Adeli H, Chua EP, Lim WJE and Koh, JEW (eds) Readings in Fuzzy Sets for Intelligent Systems. Elsevier, 387–403.
21.
TianYZhuF (2018) Fault estimation and observer based fault tolerant controller in finite frequency domain. Transactions of the Institute of Measurement and Control40(5): 1659–1668.
22.
WangHLiuPXZhaoXLiuX (2019) Adaptive fuzzy finite-time control of nonlinear systems with actuator faults. IEEE Transactions on Cybernetics50(5): 1786–1797.
23.
WangHYeDYangG-H (2014) Actuator fault diagnosis for uncertain T-S fuzzy systems with local nonlinear models. Nonlinear Dynamics76(4): 1977–1988.
24.
WangJ (2015) fault tolerant controller design for networked control systems with time-varying actuator faults. International Journal of Innovative Computing Information and Control11(4): 1471–1481.
25.
WangZZhangBYuanJCheD (2018) Robust adaptive fault tolerant control for a class of linearly parameterized uncertain nonlinear systems: An integrated method. Transactions of the Institute of Measurement and Control40(7): 2129–2140.
26.
WuHNZhangHY (2005) Reliable mixed fuzzy static output feedback control for nonlinear systems with sensor faults. Automatica41(11): 1925–1932.
27.
YangG-HWangH (2014) Fault detection and isolation for a class of uncertain state feedback fuzzy control systems. IEEE Transactions on Fuzzy Systems23(1): 139–151.
28.
YangJZhuFWangXBuX (2015) Robust sliding mode observer based sensor fault estimation, actuator fault detection and isolation for uncertain nonlinear systems. International Journal of Control, Automation and Systems13(5): 1037–1046.
29.
ZemzemiAKamelMToumiAFarzaM (2019) Robust integral observer based fault estimation for Lipschitz nonlinear systems with time varying uncertainties. Transactions of the Institute of Measurement and Control41(7): 1965–1974.
30.
ZhangJSwainAKNguangSK (2012) Detection and isolation of incipient sensor faults for a class of uncertain non linear systems. IET Control Theory & Applications6(12): 1870–1880.
31.
ZhangJSwainAKNguangSK (2014a) Robust sensor fault estimation and fault tolerant control for uncertain lipschitz nonlinear systems. In 2014 American Control Conference, pp. 5515–5520. IEEE.
32.
ZhangJSwainAKNguangSK (2014b) Simultaneous robust actuator and sensor fault estimation for uncertain non linear Lipschitz systems. IET Control Theory & Applications8(14): 1364–1374.
33.
ZhaoXWangXMaLZongG (2019) Fuzzy-approximation-based asymptotic tracking control for a class of uncertain switched nonlinear systems. IEEE Transactions on Fuzzy Systems26(4): 632–644.
34.
ZhaoYLamJGaoH (2009) Fault detection for fuzzy systems with intermittent measurements. IEEE Transactions on Fuzzy Systems17(2): 398–410.
