In this paper, the periodic tracking problem is considered for a class of continuous system with uncertainty, time-varying delay, and unknown bounded external disturbances. To be precise, in order to attenuate the unknown disturbance effectively, the equivalent-input-disturbance (EID) approach is incorporated into the developed algorithm. Then, the sufficient conditions that guarantee the asymptotic tracking performance of the system understudy are established based on the Lyapunov stability theorem. More precisely, Schur complement and free-weighting matrix approach are utilized to derive the main results. Moreover, the proposed EID-based modified repetitive controller (MRC) not only rejects the unknown external disturbance but also deals with the dead zone effect. Finally, two simulation examples are presented to verify the superiority of the proposed EID-based repetitive controller over the conventional repetitive controller.

References

References
1.
Costa-Castello
,
R.
,
Olm
,
J. M.
, and
Ramos
,
G. A.
,
2011
, “
Design and Analysis Strategies for Digital Repetitive Control Systems With Time-Varying Reference/Disturbance Period
,”
Int. J. Control
,
84
(
7
), pp.
1209
1222
.
2.
Niu
,
B.
,
Karimi
,
H. R.
,
Wang
,
H.
, and
Liu
,
Y.
,
2017
, “
Adaptive Output-Feedback Controller Design for Switched Nonlinear Stochastic Systems With a Modified Average Dwell-Time Method
,”
IEEE Trans. Syst. Man Cybern. Syst.
,
47
(
7
), pp.
1371
1382
.
3.
Zhou
,
Q.
,
Wang
,
L.
,
Wu
,
C.
,
Li
,
H.
, and
Du
,
H.
,
2017
, “
Adaptive Fuzzy Control for Nonstrict-Feedback Systems With Input Saturation and Output Constraint
,”
IEEE Trans. Syst. Man Cybern. Syst.
,
47
(
1
), pp.
1
12
.
4.
Zhou
,
L.
, and
She
,
J.
,
2015
, “
Design of a Robust Output-Feedback-Based Modified Repetitive-Control System
,”
Int. J. Syst. Sci.
,
46
(
5
), pp.
808
817
.
5.
Fedele
,
G.
, and
Ferrise
,
A.
,
2016
, “
On the Uncertainty on the Phase of a Stable Linear System in the Periodic Disturbance Cancellation Problem
,”
IEEE Trans. Autom. Control
,
61
(
9
), pp.
2720
2726
.
6.
Jafari
,
S.
,
Ioannou
,
P.
,
Fitzpatrick
,
B.
, and
Wang
,
Y.
,
2015
, “
Robustness and Performance of Adaptive Suppression of Unknown Periodic Disturbances
,”
IEEE Trans. Autom. Control
,
60
(
8
), pp.
2166
2171
.
7.
Chen
,
X.
, and
Tomizuka
,
M.
,
2014
, “
New Repetitive Control With Improved Steady-State Performance and Accelerated Transient
,”
IEEE Trans. Control Syst. Technol.
,
22
(
2
), pp.
664
675
.
8.
Sun
,
M. X.
,
Yu
,
L. J.
, and
He
,
H. G.
,
2013
, “
Discrete Adaptive Repetitive Control: Convergence Analysis and Implementation
,”
Acta Autom. Sin.
,
39
(
4
), pp.
400
406
.
9.
Chung
,
C. H.
, and
Chen
,
M. S.
,
2012
, “
A Robust Adaptive Feed Forward Control in Repetitive Control Design for Linear System
,”
Automatica
,
48
(
1
), pp.
183
190
.
10.
Kurniawan
,
E.
,
Cao
,
Z.
, and
Man
,
Z.
,
2014
, “
Design of Robust Repetitive Control With Time-Varying Sampling Periods
,”
IEEE Trans. Ind. Electron.
,
61
(
6
), pp.
2834
2841
.
11.
Joo
,
Y.
,
Park
,
G.
,
Back
,
J.
, and
Shim
,
H.
,
2015
, “
Embedding Internal Model in Disturbance Observer With Robust Stability
,”
IEEE Trans. Autom. Control
,
61
(
10
), pp.
3128
3133
.
12.
Guo
,
B. Z.
, and
Zhou
,
H. C.
,
2015
, “
The Active Disturbance Rejection Control to Stabilization for Multi-Dimensional Wave Equation With Boundary Control Matched Disturbance
,”
IEEE Trans. Autom. Control
,
60
(
1
), pp.
143
157
.
13.
Na
,
J.
,
Grino
,
R.
,
Costa-Castello
,
R.
,
Ren
,
X.
, and
Chen
,
Q.
,
2010
, “
Repetitive Controller for Time-Delay Systems Based on Disturbance Observer
,”
IET Control Theory Appl.
,
4
(
11
), pp.
2391
2404
.
14.
Song
,
J.
,
Song
,
S.
,
Guo
,
Y.
, and
Zhou
,
H.
,
2015
, “
Nonlinear Disturbance Observer-Based Fast Terminal Sliding Mode Guidance Law With Impact Angle Constraints
,”
Int. J. Innovative Comput. Inf. Control
,
11
(
3
), pp.
787
802
.http://www.ijicic.org/ijicic-14-06012.pdf
15.
Hao
,
R.
,
Wang
,
J.
,
Zhao
,
J.
, and
Wang
,
S.
,
2016
, “
Observer-Based Robust Control of 6-DOF Parallel Electrical Manipulator With Fast Friction Estimation
,”
IEEE Trans. Autom. Sci. Eng.
,
13
(
3
), pp.
1399
1408
.
16.
Li
,
J.
,
Ren
,
H. P.
, and
Zhong
,
Y. R.
,
2015
, “
Robust Speed Control of Induction Motor Drives Using First-Order Auto-Disturbance Rejection Controllers
,”
IEEE Trans. Ind. Appl.
,
51
(
1
), pp.
712
720
.
17.
Flores
,
J. L.
,
Avalos
,
J. L. B.
,
Ramirez
,
H. S.
, and
Ordaz
,
M. A. C.
,
2012
, “
Robust Passivity-Based Control of a Buckboost-Converter/DC-Motor System: An Active Disturbance Rejection Approach
,”
IEEE Trans. Ind. Appl.
,
48
(
6
), pp.
2362
2371
.
18.
Mendez
,
A. H.
,
Flores
,
J. L.
,
Ramirez
,
H. S.
,
Castellanos
,
J. F. G.
, and
Aguilar
,
G. M.
,
2017
, “
A Backstepping Approach to Decentralized Active Disturbance Rejection Control of Interacting Boost Converters
,”
IEEE Trans. Ind. Appl.
,
53
(
4
), pp.
4063
4072
.
19.
Li
,
C. X.
,
Gu
,
G. Y.
,
Yang
,
M. J.
, and
Zhu
,
L. M.
,
2017
, “
High-Speed Tracking of a Nanopositioning Stage Using Modified Repetitive Control
,”
IEEE Trans. Autom. Sci. Eng.
,
14
(
3
), pp.
1467
1477
.
20.
Zhao
,
S.
, and
Gao
,
Z.
,
2014
, “
Modified Active Disturbance Rejection Control for Time-Delay Systems
,”
ISA Trans.
,
53
(
4
), pp.
882
888
.
21.
Ahn
,
C. K.
,
Shi
,
P.
, and
Basin
,
M. V.
,
2015
, “
Two-Dimensional Dissipative Control and Filtering for Roesser Model
,”
IEEE Trans. Autom. Control
,
60
(
7
), pp.
1745
1759
.
22.
Wu
,
M.
,
Xu
,
B.
,
Cao
,
W.
, and
She
,
J.
,
2014
, “
Aperiodic Disturbance Rejection in Repetitive-Control Systems
,”
IEEE Trans. Control Syst. Technol.
,
22
(
3
), pp.
1044
1051
.
23.
She
,
J.
,
Fang
,
M. X.
,
Ohyama
,
Y.
,
Hashimoto
,
H.
, and
Wu
,
M.
,
2008
, “
Improving Disturbance-Rejection Performance Based on an Equivalent-Input-Disturbance Approach
,”
IEEE Trans. Ind. Electron.
,
55
(
1
), pp.
380
389
.
24.
Zhou
,
L.
,
She
,
J.
,
Wu
,
M.
,
He
,
Y.
, and
Zhou
,
S.
,
2014
, “
Estimation and Rejection of Aperiodic Disturbance in a Modified Repetitive-Control System
,”
IET Control Theory. Appl.
,
8
(
10
), pp.
882
889
.
25.
Yang
,
X.
,
Wu
,
L.
,
Lam
,
H. K.
, and
Su
,
X.
,
2014
, “
Stability and Stabilization of Discrete-Time T-S Fuzzy Systems With Stochastic Perturbation and Time-Varying Delay
,”
IEEE Trans. Fuzzy Syst.
,
22
(
1
), pp.
124
138
.
26.
Li
,
H.
,
Jing
,
X.
, and
Karimi
,
H. R.
,
2014
, “
Output-Feedback-Based H∞ Control for Vehicle Suspension Systems With Control Delay
,”
IEEE Trans. Ind. Electron.
,
61
(
1
), pp.
436
446
.
27.
Samidurai
,
R.
,
Manivannan
,
R.
,
Ahn
,
C. K.
, and
Karimi
,
H. R.
,
2018
, “
New Criteria for Stability of Generalized Neural Networks Including Markov Jump Parameters and Additive Time Delays
,”
IEEE Trans. Syst. Man Cybern. Syst.
,
48
(
4
), pp.
485
499
.
28.
Zeng
,
H. B.
,
He
,
Y.
,
Wu
,
M.
, and
She
,
J.
,
2015
, “
Free-Matrix Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay
,”
IEEE Trans. Autom. Control
,
60
(
10
), pp.
2768
2772
.
29.
Li
,
H.
,
Wang
,
J.
,
Lam
,
H. K.
,
Zhou
,
Q.
, and
Du
,
H.
,
2016
, “
Adaptive Sliding Mode Control for Interval Type-2 Fuzzy Systems
,”
IEEE Trans. Syst. Man Cybern. Syst.
,
46
(
12
), pp.
1654
1663
.
30.
Lam
,
H. K.
,
2012
, “
Stabilization of Nonlinear Systems Using Sampled-Data Output-Feedback Fuzzy Controller Based on Polynomial-Fuzzy-Model-Based Control Approach
,”
IEEE Trans. Syst. Man Cybern., Part B
,
42
(
1
), pp.
258
267
.
31.
Li
,
Y. X.
, and
Yang
,
G. H.
,
2017
, “
Robust Adaptive Fault-Tolerant Control for a Class of Uncertain Nonlinear Time Delay Systems
,”
IEEE Trans. Syst. Man Cybern. Syst.
,
47
(
7
), pp.
1554
1563
.
32.
Su
,
X.
,
Shi
,
P.
,
Wu
,
L.
, and
Basin
,
M. V.
,
2014
, “
Reliable Filtering With Strict Dissipativity for T-S Fuzzy Time-Delay Systems
,”
IEEE Trans. Cybern.
,
44
(
12
), pp.
2470
2483
.
33.
Na
,
J.
,
Ren
,
X.
,
Costa-Castello
,
R.
, and
Guo
,
Y.
,
2014
, “
Repetitive Control of Servo Systems With Time Delays
,”
Rob. Auton. Syst.
,
62
(
3
), pp.
319
329
.
34.
Li
,
J.
, and
Yue
,
H.
,
2015
, “
Adaptive Fuzzy Tracking Control for Stochastic Nonlinear Systems With Unknown Time-Varying Delays
,”
Appl. Math. Comput.
,
256
, pp.
514
528
.
35.
Sakthivel
,
R.
,
Mathiyalagan
,
K.
, and
Marshal Anthoni
,
S.
,
2012
, “
Robust Stability and Control for Uncertain Neutral Time Delay Systems
,”
Int. J. Control
,
85
(
4
), pp.
373
383
.
36.
Kwon
,
O. M.
,
Park
,
M. J.
,
Park
,
J. H.
,
Lee
,
M.
, and
Cha
,
E. J.
,
2013
, “
Analysis on Robust H∞ Performance and Stability for Linear Systems With Interval Time-Varying State Delays Via Some New Augmented Lyapunov-Krasovskii Functional
,”
Appl. Math. Comput.
,
224
, pp.
108
122
.
37.
Tong
,
S.
,
Zhang
,
L.
, and
Li
,
Y.
,
2016
, “
Observed-Based Adaptive Fuzzy Decentralized Tracking Control for Switched Uncertain Nonlinear Large-Scale Systems With Dead Zones
,”
IEEE Trans. Syst. Man Cybern. Syst.
,
46
(
1
), pp.
37
47
.
38.
Medvedeva
,
I. V.
, and
Zhabko
,
A. P.
,
2015
, “
Synthesis of Razumikhin and Lyapunov-Krasovskii Approaches to Stability Analysis of Time-Delay Systems
,”
Automatica
,
51
, pp.
372
377
.
39.
Liu
,
R. J.
,
Liu
,
G. P.
,
Wu
,
M.
,
She
,
J.
, and
Nie
,
Z. Y.
,
2014
, “
Robust Disturbance Rejection in Modified Repetitive Control System
,”
Syst. Control Lett.
,
70
, pp.
100
108
.
40.
Zhou
,
L.
,
She
,
J.
, and
Wu
,
M.
,
2014
, “
A One-Step Method of Designing an Observer-Based Modified Repetitive-Control System
,”
Int. J. Syst. Sci.
,
46
(
14
), pp.
2617
2627
.
41.
Zhou
,
L.
,
She
,
J.
,
Wu
,
M.
, and
He
,
Y.
,
2013
, “
Design of a Robust Observer-Based Modified Repetitive-Control System
,”
ISA Trans.
,
52
(
3
), pp.
375
382
.
42.
Wu
,
M.
,
Zhou
,
L.
, and
She
,
J.
,
2011
, “
Design of Observer-Based Robust Repetitive-Control System
,”
IEEE Trans. Autom. Control
,
56
(
6
), pp.
1452
1457
.
43.
Weiss
,
G.
, and
HaKfele
,
M.
,
1999
, “
Repetitive Control of MIMO Systems Using H∞ Design
,”
Automatica
,
35
(
7
), pp.
1185
1199
.
44.
Seuret
,
A.
, and
Gouaisbaut
,
F.
,
2013
, “
Wirtinger-Based Integral Inequality: Application to Time-Delay Systems
,”
Automatica
,
49
(
9
), pp.
2860
2866
.
45.
Mathiyalagan
,
K.
,
Park
,
J. H.
,
Sakthivel
,
R.
, and
Marshal Anthoni
,
S.
,
2014
, “
Delay Fractioning Approach to Robust Exponential Stability of Fuzzy Cohen-Grossberg Neural Networks
,”
Appl. Math. Comput.
,
230
, pp.
451
463
.
46.
Zhou
,
L.
,
She
,
J.
, and
Zhou
,
S.
,
2014
, “
A 2D System Approach to the Design of a Robust Modified Repetitive-Control System With a Dynamic Output-Feedback Controller
,”
Int. J. Appl. Math. Comput. Sci.
,
24
(
2
), pp.
325
334
.
47.
She
,
J.
,
Makino
,
K.
,
Ouyang
,
L.
, and
Hashimoto
,
H.
,
2014
, “
Estimation of Normalized Longitudinal Force for an Electric Cart Using Equivalent-Input-Disturbance Approach
,”
IEEE Trans. Veh. Technol.
,
63
(
8
), pp.
3642
3650
.
48.
She
,
J.
,
Xin
,
X.
, and
Pan
,
Y.
,
2011
, “
Equivalent-Input-Disturbance Approach-Analysis and Application to Disturbance Rejection in Dual-Stage Feed Drive Control System
,”
IEEE Trans. Mechatronics
,
16
(
2
), pp.
330
340
.
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