This paper considers the problem of reliable finite-time robust control for uncertain mechanical systems with stochastic actuator failures and aperiodic sampling. A novel model of actuator failure capable of depicting various faulty modes is developed on the basis of homogenous Markov variable. To guarantee the finite-time stability (FTS) and boundedness, a novel fault-tolerant switching controller is developed by virtue of Lyapunov–Krasovskii functional and stochastic analysis technique, simultaneously, the finite-time H performance is also ensured to attenuate the mechanical vibration caused by external disturbances. With convex optimization algorithm, the anticipated controller can be procured by solving a set of linear matrix inequalities (LMIs). Finally, two practical examples of mechanical systems, one of which is governed by lumped parameters and the other is described by distributed parameters, are proposed to prove the effectiveness of the theoretical developments of this study.

References

References
1.
Pfeiffer
,
F.
,
2008
,
Mechanical System Dynamics
,
Springer
,
Berlin
.
2.
Sun
,
W.
,
Gao
,
H.
, and
Kaynak
,
O.
,
2011
, “
Finite Frequency H∞ Control for Vehicle Active Suspension Systems
,”
IEEE Trans. Control Syst. Technol.
,
19
(
2
), pp.
416
422
.
3.
Sun
,
W.
,
Zhao
,
Y.
,
Li
,
J.
,
Zhang
,
L.
, and
Gao
,
H.
,
2012
, “
Active Suspension Control With Frequency Band Constraints and Actuator Input Delay
,”
IEEE Trans. Ind. Electron.
,
59
(
1
), pp.
530
537
.
4.
Sun
,
W.
,
Zhao
,
Z.
, and
Gao
,
H.
,
2013
, “
Saturated Adaptive Robust Control for Active Suspension Systems
,”
IEEE Trans. Ind. Electron.
,
60
(
9
), pp.
3889
3896
.
5.
Sakthivel
,
R.
,
Kumar
,
S. V.
,
Aravindh
,
D.
, and
Selvaraj
,
P.
,
2015
, “
Reliable Dissipative Sampled-Data Control for Uncertain Systems With Nonlinear Fault Input
,”
ASME J. Comput. Nonlinear Dyn.
,
11
(
4
), p.
041008
.
6.
Xu
,
S.
,
Sun
,
G.
, and
Sun
,
W.
,
2016
, “
Reliable Sampled-Data Vibration Control for Uncertain Flexible Spacecraft With Frequency Range Limitation
,”
Nonlinear Dyn.
,
86
(
2
), pp.
1117
1135
.
7.
Yao
,
J.
,
Jiao
,
Z.
,
Ma
,
D.
, and
Yan
,
L.
,
2014
, “
High-Accuracy Tracking Control of Hydraulic Rotary Actuators With Modelling Uncertainties
,”
IEEE/ASME Trans. Mechatronics
,
19
(
2
), pp.
633
641
.
8.
Liu
,
J.
,
Vazquez
,
S.
,
Wu
,
L.
,
Marquez
,
A.
,
Gao
,
H.
, and
Franquelo
,
L. G.
,
2017
, “
Extended State Observer-Based Sliding-Mode Control for Three-Phase Power Converters
,”
IEEE Trans. Ind. Electron.
,
64
(
1
), pp.
22
31
.
9.
Du
,
H.
,
Lam
,
J.
, and
Sze
,
K.
,
2005
, “
H∞ Disturbance Attenuation for Uncertain Mechanical Systems With Input Delay
,”
Trans. Inst. Meas. Control
,
27
(
1
), pp.
37
52
.
10.
Yang
,
X.
,
Gao
,
H.
,
Shi
,
P.
, and
Duan
,
G.
,
2010
, “
Robust H∞ Control for a Class of Uncertain Mechanical Systems
,”
Int. J. Control
,
83
(
7
), pp.
1303
1324
.
11.
Sakthivel
,
R.
,
Santra
,
S.
,
Mathiyalagan
,
K.
, and
Arunkumar
,
A.
,
2014
, “
Reliable Robust Control Design for Uncertain Mechanical Systems
,”
ASME J. Dyn. Syst. Meas. Control
,
137
(
2
), p.
021003
.
12.
Dharani
,
S.
,
Rakkiyappan
,
R.
, and
Cao
,
J.
,
2015
, “
Robust Stochastic Sampled-Data H∞ Control for a Class of Mechanical Systems With Uncertainties
,”
ASME J. Dyn. Syst. Meas. Control
,
137
(
10
), p.
101008
.
13.
Amato
,
F.
,
Ariola
,
M.
, and
Dorato
,
P.
,
2001
, “
Finite-Time Control of Linear Systems Subject to Parametric Uncertainties and Disturbances
,”
Automatica
,
37
(
9
), pp.
1459
1463
.
14.
Sakthivel
,
R.
,
Santra
,
S.
,
Kaviarasan
,
B.
, and
Park
,
J. H.
,
2016
, “
Finite-Time Sampled-Data Control of Permanent Magnet Synchronous Motor Systems
,”
Nonlinear Dyn.
,
86
(
3
), pp.
2081
2092
.
15.
Shi
,
P.
,
Zhang
,
Y.
, and
Agarwal
,
R. K.
,
2015
, “
Stochastic Finite-Time State Estimation for Discrete Time-Delay Neural Networks With Markovian Jumps
,”
Neurocomputing
,
151
(
1
), pp.
168
174
.
16.
Shen
,
H.
,
Park
,
J. H.
, and
Wu
,
Z. G.
,
2014
, “
Finite-Time Synchronization Control for Uncertain Markov Jump Neural Networks With Input Constraints
,”
Nonlinear Dyn.
,
77
(
4
), pp.
1709
1720
.
17.
Shen
,
H.
,
Park
,
J. H.
, and
Wu
,
Z. G.
,
2014
, “
Finite-Time Reliable L2–L∞/H∞ Control for Takagi-Sugeno Fuzzy Systems With Actuator Faults
,”
IET Control Theory Appl.
,
8
(
9
), pp.
688
696
.
18.
Cheng
,
J.
,
Zhu
,
H.
,
Zhong
,
S.
,
Zeng
,
Y.
, and
Dong
,
X.
,
2013
, “
Finite-Time H∞ Control for a Class of Markovian Jump Systems With Mode-Dependent Time-Varying Delays Via New Lyapunov Functionals
,”
ISA Trans.
,
52
(
6
), pp.
768
774
.
19.
Cheng
,
J.
,
Park
,
J. H.
,
Liu
,
Y.
,
Liu
,
Z.
, and
Tang
,
L.
,
2017
, “
Finite-Time H∞ Fuzzy Control of Nonlinear Markovian Jump Delayed Systems With Partly Uncertain Transition Descriptions
,”
Fuzzy Sets Syst.
,
314
, pp.
99
115
.
20.
Fridman
,
E.
,
Seuret
,
A.
, and
Richard
,
J. P.
,
2004
, “
Robust Sampled-Data Stabilization of Linear Systems: An Input Delay Approach
,”
Automatica
,
40
(
8
), pp.
1441
1446
.
21.
Suplin
,
V.
,
Fridman
,
E.
, and
Shaked
,
U.
,
2007
, “
Sampled-Data H∞ Control and Filtering: Nonuniform Uncertain Sampling
,”
Automatica
,
43
(
6
), pp.
1072
1083
.
22.
Fridman
,
E.
,
2010
, “
A Refined Input Delay Approach to Sampled-Data Control
,”
Automatica
,
46
(
2
), pp.
421
427
.
23.
Li
,
H.
,
Liu
,
H.
,
Gao
,
H.
, and
Shi
,
P.
,
2012
, “
Reliable Fuzzy Control for Active Suspension Systems With Actuator Delay and Fault
,”
IEEE Trans. Fuzzy Syst.
,
20
(
2
), pp.
342
357
.
24.
Liu
,
J.
,
Luo
,
W.
,
Yang
,
X.
, and
Wu
,
L.
,
2016
, “
Robust Model-Based Fault Diagnosis for PEM Fuel Cell Air-Feed System
,”
IEEE Trans. Ind. Electron.
,
63
(
5
), pp.
3261
3270
.
25.
Gao
,
H.
,
Zhan
,
W.
,
Karimi
,
H. R.
,
Yang
,
X.
, and
Yin
,
S.
,
2013
, “
Allocation of Actuators and Sensors for Coupled-Adjacent-Building Vibration Attenuation
,”
IEEE Trans. Ind. Electron.
,
60
(
12
), pp.
5792
5801
.
26.
Sasiadek
,
J. Z.
, and
Srinivasan
,
R.
,
1989
, “
Dynamic Modeling and Adaptive Control of a Single-Link Flexible Manipulator
,”
J. Guid. Control Dyn.
,
12
(
6
), pp.
838
844
.
27.
Shan
,
J.
,
Liu
,
H. T.
, and
Sun
,
D.
,
2005
, “
Modified Input Shaping for a Rotating Single-Link Flexible Manipulator
,”
J. Sound Vib.
,
285
(
1
), pp.
187
207
.
28.
Qiu
,
Z. C.
, and
Liu
,
J. G.
,
2015
, “
Experiments on Fuzzy Sliding Mode Variable Structure Control for Vibration Suppression of a Rotating Flexible Beam
,”
J. Vib. Control
,
21
(
2
), pp.
343
358
.
29.
Zeng
,
H. B.
,
He
,
Y.
,
Wu
,
M.
, and
She
,
J.
,
2015
, “
New Results on Stability Analysis for Systems With Discrete Distributed Delay
,”
Automatica
,
60
, pp.
189
192
.
30.
Peng
,
C.
,
Han
,
Q. L.
,
Yue
,
D.
, and
Tian
,
E.
,
2011
, “
Sampled-Data Robust H∞ Control for T-S Fuzzy Systems With Time Delay and Uncertainties
,”
Fuzzy Sets Syst.
,
179
(
1
), pp.
20
33
.
You do not currently have access to this content.