This paper proposes a new active disturbance rejection (ADR) based robust trajectory tracking controller design method in state space. It can compensate not only matched but also mismatched disturbances. Robust state and control input references are generated in terms of a fictitious design variable, namely differentially flat output, and the estimations of disturbances by using differential flatness (DF) and disturbance observer (DOb). Two different robust controller design techniques are proposed by using Brunovsky canonical form and polynomial matrix form approaches. The robust position control problem of a two mass-spring-damper system is studied to verify the proposed ADR controllers.

References

1.
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
.
2.
Han
,
J.
,
2009
, “
From PID to Active Disturbance Rejection Control
,”
IEEE Trans. Ind. Electron.
,
56
(
3
), pp.
900
906
.
3.
Li
,
S. H.
,
Yang
,
J.
,
Chen
,
W. H.
, and
Chen
,
X.
,
2014
,
Disturbance Observer-Based Control Methods and Applications
, CRC Press, Boca Raton, FL.
4.
Sariyildiz
,
E.
, and
Ohnishi
,
K.
,
2015
, “
An Adaptive Reaction Force Observer Design
,”
IEEE Trans. Mechatronics
,
20
(
2
), pp.
750
760
.
5.
Li
,
S. H.
,
Yang
,
J.
,
Chen
,
W. H.
, and
Chen
,
X. S.
,
2012
, “
Generalized Extended State Observer Based Control for Systems With Mismatched Uncertainties
,”
IEEE Trans. Ind. Electron.
,
59
(
12
), pp.
4792
4802
.
6.
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
.
7.
Li
,
H.
,
Ning
,
X.
, and
Han
,
B.
,
2017
, “
Composite Decoupling Control of Gimbal Servo System in Double-Gimbaled Variable Speed CMG Via Disturbance Observer
,”
IEEE/ASME Trans. Mechatronics
,
22
(
1
), pp.
312
320
.
8.
Wei
,
X. J.
, and
Guo
,
L.
,
2010
, “
Composite Disturbance-Observer-Based Control and H-Infinity Control for Complex Continuous Models
,”
Int. J. Robust Nonlinear Control
,
20
(
1
), pp.
106
118
.
9.
Fliess
,
M.
,
Levine
,
J.
,
Martin
,
P.
, and
Rouchon
,
P.
,
1995
, “
Flatness and Defect of Nonlinear Systems: Introductory Theory and Applications
,”
Int. J. Control
,
61
(
6
), pp.
1327
1361
.
10.
Fliess
,
M.
,
Levine
,
J.
,
Martin
,
P.
, and
Rouchon
,
P.
,
1999
, “
A Lie-Backlund Approach to Equivalence and Flatness of Nonlinear Systems
,”
IEEE Trans. Autom. Control
,
44
(
5
), pp.
922
937
.
11.
Levine
,
J.
, and
Nguyen
,
D. V.
,
2003
, “
Flat Output Characterization for Linear Systems Using Polynomial Matrices
,”
Syst. Control Lett.
,
48
, pp.
69
75
.
12.
Sariyildiz
,
E.
,
Gong
,
C.
, and
Yu
,
H.
,
2017
, “
A Unified Robust Motion Controller Design for Series Elastic Actuators
,”
IEEE Trans. Mechatronics
,
22
(
5
), pp.
2229
2240
.
13.
Sangwan
,
V.
, and
Agrawal
,
S. K.
,
2017
, “
Effects of Viscous Damping on Differential Flatness-Based Control for a Class of Under-Actuated Planar Manipulators
,”
IEEE Control Syst. Lett.
,
2
(
1
), pp.
67
72
.
14.
Mills
,
A. B.
,
Kim
,
D.
, and
Frew
,
E. W.
,
2017
, “
Energy-Aware Aircraft Trajectory Generation Using Pseudospectral Methods With Differential Flatness
,”
IEEE
Conference on Control Technology and Applications
, Mauna Lani, HI, Aug. 27–30, pp.
1536
1541
.
15.
Huang
,
C.
, and
Sira-Ramirez
,
H.
,
2015
, “
Active Disturbance Rejection Control for Linear Systems With Unknown Time-Varying Coefficients
,”
Int. J. Control
,
88
(
12
), pp.
2578
2587
.
16.
Bechet
,
F.
,
Ogawa
,
K.
,
Sariyildiz
,
E.
, and
Ohnishi
,
K.
,
2015
, “
Electro-Hydraulic Transmission System for Minimally Invasive Robotics
,”
IEEE Trans. Ind. Electron.
,
62
(
12
), pp.
7643
7654
.
17.
Sariyildiz
,
E.
,
Sekiguchi
,
H.
,
Nozaki
,
T.
,
Ugurlu
,
B.
, and
Ohnishi
,
K.
,
2018
, “
A Stability Analysis for the Acceleration-Based Robust Position Control of Robot Manipulators Via Disturbance Observer
,”
IEEE/ASME Trans. Mechatronics
,
23
(
5
), pp.
2369
2378
.
18.
Antsaklis
,
P. J.
, and
Michel
,
A. N.
,
1997
,
Linear Systems
,
McGraw-Hill
,
New York
.
19.
Kailath
,
T.
,
1980
,
Linear Systems
,
Prentice Hall
,
Englewood Cliffs, NJ
.
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