This paper concerns a repetitive-control system with an input-dead-zone (IDZ) nonlinearity. First, the expression for the IDZ is decomposed into a linear term and a disturbance-like one that depends on the parameters of the dead zone. A function of the system-state error is used to approximate the combination of the disturbancelike term and an exogenous disturbance. The estimate is used to compensate for the overall effect of the IDZ and the exogenous disturbance. Next, the state-feedback gains are obtained from a linear matrix inequality that contains two tuning parameters for adjusting control performance; and the pole assignment method is employed to design the gain of a state observer. Then, two stability criteria are used to test the stability of the closed-loop system. The method is simple, employing neither an inverse model of the plant nor an adaptive control technique. It is also robust with regard to the different parameters of the IDZ, uncertainties in the plant, and the exogenous disturbance. Finally, two numerical examples demonstrate the effectiveness of this method and its advantages over others.

References

1.
Inoue
,
T.
,
Iwai
,
S.
, and
Nakano
,
M.
,
1981
, “
High Accuracy Control of a Proton Synchrotron Magnet Power Supply
,”
8th IFAC World Congress
, pp.
3137
3142
.
2.
Hara
,
S.
,
Yamamoto
,
Y.
,
Omata
,
T.
, and
Nakano
,
M.
,
1988
, “
Repetitive Control System: A New Type Servo System for Periodic Exogenous Signals
,”
IEEE Trans. Autom. Control
,
33
(
7
), pp.
659
668
.
3.
He
,
L. Q.
,
Zhang
,
K.
,
Xiong
,
J.
, and
Fan
,
S. F.
,
2015
, “
A Repetitive Control Scheme for Harmonic Suppression of Circulating Current in Modular Multilevel Converters
,”
IEEE Trans. Ind. Electron
,
30
(
1
), pp.
471
481
.
4.
Wu
,
M.
,
Xu
,
B. G.
,
Cao
,
W. H.
, and
She
,
J.-H.
,
2014
, “
Aperiodic Disturbance Rejection in Repetitive-Control Systems
,”
IEEE Trans. Control Syst. Technol.
,
22
(
3
), pp.
1044
1051
.
5.
Zhou
,
L.
,
She
,
J.-H.
,
Wu
,
M.
, and
Zhang
,
J.
,
2011
, “
Design of Robust Modified Repetitive-Control System for Linear Periodic Plants
,”
ASME J. Dyn. Syst., Meas., Control
,
134
(
1
), p.
011023
.
6.
Mayergoyz
, I
. D.
,
1986
, “
Mathematical Models of Hysteresis
,”
IEEE Trans. Mag.
,
22
(
5
), pp.
603
608
.
7.
Yi
,
J.
,
Chang
,
S.
, and
Shen
,
Y.
,
2009
, “
Disturbance-Observer-Based Hysteresis Compensation for Piezoelectric Actuators
,”
IEEE/ASME Trans. Mechatronics
,
14
(
4
), pp.
456
464
.
8.
Wang
,
X. S.
,
Su
,
C. Y.
, and
Hong
,
H.
,
2004
, “
Robust Adaptive Control of a Class of Nonlinear Systems With Unknown Dead-Zone
,”
Automatica
,
40
(
3
), pp.
407
413
.
9.
Zhang
,
T. P.
, and
Ge
,
S. S.
,
2008
, “
Adaptive Dynamic Surface Control of Nonlinear Systems With Unknown Dead Zone in Pure Feedback Form
,”
Automatica
,
44
(
7
), pp.
1895
1903
.
10.
Recker
,
D.
,
Kokotovic
,
P.
,
Rhode
,
D.
, and
Winkelman
,
J.
,
1991
, “
Adaptive Nonlinear Control of Systems Containing a Deadzone
,”
30th IEEE Conference on Decision Control
, Brighton, UK, Dec. 11–13, pp.
2111
2115
.
11.
Zhou
,
J.
,
Wen
,
C.
, and
Zhang
,
Y.
,
2006
, “
Adaptive Output Control of Nonlinear Systems With Uncertain Dead-Zone Nonlinearity
,”
IEEE Trans. Autom. Control
,
51
(
3
), pp.
504
511
.
12.
Li
,
Z.
,
Li
,
T.
, and
Feng
,
G.
,
2016
, “
Adaptive Neural Control for a Class of Stochastic Nonlinear Time-Delay Systems With Unknown Dead Zone Using Dynamic Surface Technique
,”
Int. J. Robust Nonlinear Control
,
26
(
4
), pp.
759
781
.
13.
Wu
,
L. B.
,
Yang
,
G. H.
,
Wang
,
H.
, and
Wang
,
F.
,
2016
, “
Adaptive Fuzzy Asymptotic Tracking Control of Uncertain Nonaffine Nonlinear Systems With Non-Symmetric Dead-Zone Nonlinearities
,”
Inform. Sci.
,
348
, pp.
1
14
.
14.
Corradini
,
M. L.
, and
Orlando
,
G.
,
2002
, “
Robust Stabilization of Nonlinear Uncertain Plants With Backlash or Dead-Zone in the Actuator
,”
IEEE Trans. Control Syst. Technol.
,
10
(
1
), pp.
158
166
.
15.
Li
,
S.
,
Yang
,
J.
,
Chen
,
W. H.
, and
Chen
,
X.
,
2012
, “
Generalized Extended State Observer Based on Control for Systems With Mismatched Uncertainties
,”
IEEE Trans. Ind. Electron.
,
59
(
12
), pp.
4792
4802
.
16.
Levine
,
W. S.
,
1996
,
The Control Handbook
,
CRC Press
,
Boca Raton, FL
.
17.
Khargonekar
,
P. P.
,
Petersen
,
I. R.
, and
Zhou
,
K.
,
1990
, “
Robust Stabilization of Uncertain Linear Systems: Quadratic Stabilizability and H∞ Control Theory
,”
IEEE Trans. Autom. Control
,
35
(
3
), pp.
356
361
.
18.
Gao
,
Z.
,
2006
, “
Active Disturbance Rejection Control: A Paradigm Shift in Feedback Control System Design
,”
American Control Conference
, Minneapolis, MN, June 14–16, pp.
2399
2405
.
19.
Wu
,
S.
, and
Ren
,
G.
,
2004
, “
Delay-Independent Stability Criteria for a Class of Retarded Dynamical Systems With Two Delays
,”
J. Sound Vib.
,
270
(
4–5
), pp.
625
638
.
20.
Hu
,
S. S.
,
2007
, “Automatic Control Principle,” 5th ed.,
Science Press
,
Beijing, China
, pp.
95
97
.
You do not currently have access to this content.