In this paper, a state and extended disturbance observer (DO) is designed for mismatched uncertain systems. Apart from system states and disturbances, the proposed observer estimates the derivatives of the disturbances and thereby improves the accuracy of estimation of disturbances as well as the states. No knowledge of bounds of disturbances or their derivatives is assumed. An observer–controller combination for a sliding mode controller that requires the estimates of the derivatives of disturbances is described, and the ultimate boundedness of the overall system is proved. The proposed observer is illustrated by simulation of a numerical example and a rotary hydraulic actuator. The proposed observer–controller combination is validated on a serial flexible joint manipulator in laboratory.

References

References
1.
Drazenovich
,
B.
,
1969
, “
The Invariance Conditions in Variable Structure Systems
,”
Automatica
,
5
(
3
), pp.
287
295
.10.1016/0005-1098(69)90071-5
2.
Yang
,
J.
,
Li
,
S.
, and
Yu
,
X.
,
2013
, “
Sliding-Mode Control for Systems With Mismatched Uncertainties Via a Disturbance Observer
,”
IEEE Trans. Ind. Electron.
,
60
(
1
), pp.
160
169
.10.1109/TIE.2012.2183841
3.
Ginoya
,
D.
,
Shendge
,
P. D.
, and
Phadke
,
S. B.
,
2014
, “
Sliding Mode Control for Mismatched Uncertain Systems Using an Extended Disturbance Observer
,”
IEEE Trans. Ind. Electron.
,
61
(
4
), pp.
1983
1992
.10.1109/TIE.2013.2271597
4.
Olfati-Saber
,
R.
,
2002
, “
Normal Forms for Underactuated Mechanical Systems With Symmetry
,”
IEEE Trans. Autom. Control
,
47
(
2
), pp.
305
308
.10.1109/9.983365
5.
Chen
,
Y.-F.
, and
Huang
,
A.-C.
,
2012
, “
Controller Design for a Class of Underactuated Mechanical Systems
,”
IET Control Theory Appl.
,
6
(
1
), pp.
103
110
.10.1049/iet-cta.2010.0667
6.
Wen
,
C. C.
, and
Cheng
,
C. C.
,
2008
, “
Design of Sliding Surface for Mismatched Uncertain Systems to Achieve Asymptotical Stability
,”
J. Franklin Inst.
,
345
(
8
), pp.
926
941
.10.1016/j.jfranklin.2008.06.003
7.
Swaroop
,
D.
,
Hedrick
,
J.
,
Yip
,
P.
, and
Gerdes
,
J.
,
2000
, “
Dynamic Surface Control for a Class of Nonlinear Systems
,”
IEEE Trans. Autom. Control
,
45
(
10
), pp.
1893
1899
.10.1109/TAC.2000.880994
8.
Liang
,
Y.-W.
,
Ting
,
L.-W.
, and
Lin
,
L.-G.
,
2012
, “
Study of Reliable Control Via an Integral-Type Sliding Mode Control Scheme
,”
IEEE Trans. Ind. Electron.
,
59
(
8
), pp.
3062
3068
.10.1109/TIE.2011.2162211
9.
Choi
,
H.
,
2007
, “
LMI-Based Sliding Surface Design for Integral Sliding Mode Control of Mismatched Uncertain Systems
,”
IEEE Trans. Autom. Control
,
52
(
4
), pp.
736
742
.10.1109/TAC.2007.894543
10.
Cao
,
Y.
, and
Chen
,
X.
,
2014
, “
Disturbance-Observer-Based Sliding-Mode Control for a 3-DOF Nanopositioning Stage
,”
IEEE/ASME Trans. Mechatronics
,
19
(
3
), pp.
924
931
.10.1109/TMECH.2013.2262802
11.
Liu
,
J.
,
Laghrouche
,
S.
, and
Wack
,
M.
,
2014
, “
Observer-Based Higher Order Sliding Mode Control of Power Factor in Three-Phase AC/DC Converter for Hybrid Electric Vehicle Applications
,”
Int. J. Control
,
87
(
6
), pp.
1117
1130
.10.1080/00207179.2013.868609
12.
Cui
,
R.
,
Ren
,
B.
, and
Ge
,
S.
,
2012
, “
Synchronised Tracking Control of Multi-Agent System With High Order Dynamics
,”
IET Control Theory Appl.
,
6
(
5
), pp.
603
614
.10.1049/iet-cta.2011.0011
13.
Guan
,
Y.
, and
Saif
,
M.
,
1991
, “
A Novel Approach to the Design of Unknown Input Observers
,”
IEEE Trans. Autom. Control
,
36
(
5
), pp.
632
635
.10.1109/9.76372
14.
Chen
,
W. H.
,
2003
, “
Nonlinear Disturbance Observer-Enhanced Dynamic Inversion Control of Missiles
,”
J. Guid., Control, Dyn.
,
26
(
1
), pp.
161
166
.10.2514/2.5027
15.
Deshpande
, V
. S.
, and
Phadke
,
S. B.
,
2012
, “
Control of Uncertain Nonlinear Systems Using an Uncertainty and Disturbance Estimator
,”
ASME J. Dyn. Syst., Meas., Control
,
134
(
2
), p.
024501
.10.1115/1.4005042
16.
Jiang
,
L.
, and
Wu
,
Q.
,
2002
, “
Nonlinear Adaptive Control Via Sliding-Mode State and Perturbation Observer
,”
IEE Proc. Control Theory Appl.
,
149
(
4
), pp.
269
277
.10.1049/ip-cta:20020470
17.
Han
,
J.
,
2009
, “
From PID to Active Disturbance Rejection Control
,”
IEEE Trans. Ind. Electron.
,
56
(
3
), pp.
900
906
.10.1109/TIE.2008.2011621
18.
Li
,
S.
,
Jun, Chen
,
W.-H.
, and
Chen
,
X.
,
2012
, “
Generalized Extended State Observer Based Control for Systems With Mismatched Uncertainties
,”
IEEE Trans. Ind. Electron.
,
59
(
12
), pp.
4792
4802
.10.1109/TIE.2011.2182011
19.
Corless
,
M.
, and
Leitmann
,
G.
,
1981
, “
Continuous State Feedback Guaranteeing Uniform Ultimate Boundedness for Uncertain Dynamic Systems
,”
IEEE Trans. Autom. Control
,
26
(
5
), pp.
1139
1144
.10.1109/TAC.1981.1102785
20.
Yao
,
J.
,
Xia
,
J.
, and
Ma
,
D.
,
2014
, “
Extended-State-Observer-Based Output Feedback Nonlinear Robust Control of Hydraulic Systems With Backstepping
,”
IEEE Trans. Ind. Electron.
,
61
(
11
), pp.
6285
6293
.10.1109/TIE.2014.2304912
21.
Yao
,
J.
,
Jiao
,
Z.
,
Ma
,
D.
, and
Yan
,
L.
,
2014
, “
High-Accuracy Tracking Control of Hydraulic Rotary Actuators With Modeling Uncertainties
,”
IEEE/ASME Trans. Mechatronics
,
19
(
2
), pp.
633
641
.10.1109/TMECH.2013.2252360
22.
Daher
,
N.
, and
Ivantysynova
,
M.
,
2014
, “
An Indirect Adaptive Velocity Controller for a Novel Steer-By-Wire System
,”
ASME J. Dyn. Syst., Meas., Control
,
136
(
5
), p.
051012
.10.1115/1.4027172
23.
Xie
,
Y.
,
Alleyne
,
A. G.
,
Greer
,
A.
, and
Deneault
,
D.
,
2013
, “
Fundamental Limits in Combine Harvester Header Height Control
,”
ASME J. Dyn. Syst., Meas., Control
,
135
(
3
), p.
034503
.10.1115/1.4023209
24.
Han
,
S.
,
Jiao
,
Z.
,
Yao
,
J.
, and
Shang
,
Y.
,
2014
, “
Compound Velocity Synchronizing Control Strategy for Electro-Hydraulic Load Simulator and Its Engineering Application
,”
ASME J. Dyn. Syst., Meas., Control
,
136
(
5
), p.
051002
.10.1115/1.4026921
25.
Singh
,
K. B.
,
Arat
,
M. A.
, and
Taheri
,
S.
,
2013
, “
An Intelligent Tire Based Tire-Road Friction Estimation Technique and Adaptive Wheel Slip Controller for Antilock Brake System
,”
ASME J. Dyn. Syst., Meas., Control
,
135
(
3
), p.
031002
.10.1115/1.4007704
26.
Ahn
,
K.
,
Nam
,
D.
, and
Jin
,
M.
,
2014
, “
Adaptive Backstepping Control of an Electrohydraulic Actuator
,”
IEEE/ASME Trans. Mechatronics
,
19
(
3
), pp.
987
995
.10.1109/TMECH.2013.2265312
27.
Quanser Inc.
,
2008
, “Dynamic Equations for the First Stage of the Serial Flexible Joint (2DSFJ) Robot—Maple Worksheet.”
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