The goal of this paper is to clarify the robustness and performance constraints in the design of control systems based on disturbance observer (DOB). Although the bandwidth constraints of a DOB have long been very well-known by experiences and observations, they have not been formulated and clearly reported yet. In this regard, the Bode and Poisson integral formulas are utilized in the robustness analysis so that the bandwidth constraints of a DOB are derived analytically. In this paper, it is shown that the bandwidth of a DOB has upper and lower bounds to obtain a good robustness if the plant has nonminimum phase zero(s) and pole(s), respectively. Besides that the performance of a system can be improved by using a higher order disturbance observer (HODOB); however, the robustness may deteriorate, and the bandwidth constraints become more severe. New analysis and design methods, which provide good robustness and predefined performance criteria, are proposed for the DOB based robust control systems. The validity of the proposals is verified by simulation results.

References

References
1.
Ohishi
,
K.
,
Ohnishi
,
K.
, and
Miyachi
,
K.
,
1983
, “
Torque-Speed Regulation of dc Motor Based on Load Torque Estimation
,”
Proc. IEEJ IPEC-TOKYO
,
2
, pp.
1209
1216
.
2.
Ohnishi
,
K.
,
Shibata
,
M.
, and
Murakami
,
T.
,
1996
, “
Motion Control for Advanced Mechatronics
,”
IEEE/ASME Trans. Mechatron.
,
1
(
1
), pp.
56
67
.10.1109/3516.491410
3.
Schrijver
,
E.
, and
Johannes
,
D. V.
,
2002
, “
Disturbance Observers for Rigid Mechanical Systems: Equivalence, Stability, and Design
,”
ASME J. Dyn. Syst., Meas., Control
,
124
(
4
), pp.
539
548
.10.1115/1.1513570
4.
Ohishi
,
K.
,
Miyazaki
,
T.
, and
Nakamura
,
Y.
,
1995
, “
Two-Degrees-of-Freedom Speed Controller Based on Doubly Coprime Factorization and Speed Observer
,”
21st IEEE International Conference on Industrial Electronics, Control, and Instrumentation
, Orlando, FL,
1
, pp.
602
608
.
5.
Umeno
,
T.
, and
Hori
,
Y.
,
1991
, “
Robust Speed Control of dc Servomotors Using Modern Two Degrees-Of-Freedom Controller Design
,”
IEEE Trans. Ind. Electron. Control Instrum.
,
38
(
5
), pp.
363
368
.10.1109/41.97556
6.
Guo
,
L.
, and
Tomizuka
,
M.
,
1997
, “
High-Speed and High-Precision Motion Control With an Optimal Hybrid Feed Forward Controller
,”
IEEE/ASME Trans. Mechatron.
,
2
(
2
), pp.
110
122
.10.1109/3516.588630
7.
Guvenc
,
B. A.
,
Guvenc
,
L.
, and
Karaman
,
S.
,
2010
, “
Robust MIMO Disturbance Observer Analysis and Design With Application to Active Car Steering
,”
Int. J. Robust Nonlinear Control
,
20
(
8
), pp.
873
891
.10.1002/rnc.1476
8.
Chan
,
S. P.
,
1991
, “
A Disturbance Observer for Robot Manipulators With Application to Electronic Components Assembly
,”
IEEE Trans. Ind. Electron. Control Instrum.
,
42
(
5
), pp.
487
493
.10.1109/41.464611
9.
Wang
,
C.
, and
Tomizuka
,
M.
,
2004
, “
Design of Robustly Stable Disturbance Observers Based on Closed Loop Consideration Using H∞ Optimization and its Applications to Motion Control Systems
,”
American Control Conference (ACC)
, Boston, MA,
4
, pp.
3764
3769
.
10.
Sariyildiz
,
E.
, and
Ohnishi
,
K.
,
2013
, “
Analysis the Robustness of Control Systems Based on Disturbance Observer
,”
Int. J. Control
10.1080/00207179.2013.795663,
86
, pp. 1733–1743.
11.
Yang
,
W. C.
, and
Tomizuka
,
M.
,
1994
, “
Disturbance Rejection Through an External Model for Non-Minimum Phase Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
116
(
1
), pp.
39
44
.10.1115/1.2900679
12.
Jo
,
N. H.
,
Shim
,
H.
, and
Son
,
Y. I.
,
2010
, “
Disturbance Observer for Non-minimum Phase Linear Systems
,”
Int. J. Control, Autom. Syst.
,
8
(
5
), pp.
994
1002
.10.1007/s12555-010-0508-x
13.
Chen
,
X.
,
Zhai
,
G.
, and
Fukuda
,
T.
,
2004
, “
An Approximate Inverse System for Non-Minimum-Phase Systems and Its Application to Disturbance Observer
,”
Syst. Control Lett.
,
52
(
3–4
), pp.
193
207
.10.1016/j.sysconle.2003.11.011
14.
Katsura
,
S.
,
Irie
,
K.
, and
Ohishi
,
K.
,
2008
, “
Wideband Force Control by Position-Acceleration Integrated Disturbance Observer
,”
IEEE Trans. Ind. Electron. Control Instrum.
,
55
,(
5
), pp.
1699
1706
.10.1109/TIE.2007.907664
15.
Ishikawa
,
J.
, and
Tomizuka
,
M.
,
1998
, “
Pivot Friction Compensation Using and Accelerometer and a Disturbance Observer for Hard Disk Drives
,”
IEEE/ASME Trans. Mechatron.
,
3
,(
3
), pp.
194
201
.10.1109/3516.712115
16.
Tsuji
,
T.
,
Hashimoto
,
T.
,
Kobayashi
,
H.
,
Mizuochi
,
M.
, and
Ohnishi
,
K.
,
2009
, “
A Wide-Range Velocity Measurement Method for Motion Control
,”
IEEE Trans. Ind. Electron. Control Instrum.
,
56
(
2
), pp.
510
519
.10.1109/TIE.2008.2003208
17.
Jeon
,
S.
, and
Tomizuka
,
M.
,
2007
, “
Benefits of Acceleration Measurement in Velocity Estimation and Motion Control
,”
Control Eng. Practice
,
15
(
3
), pp.
325
332
.10.1016/j.conengprac.2005.10.004
18.
Mitsantisuk
,
C.
,
Ohishi
,
K.
, and
Katsura
,
S.
,
2012
, “
Estimation of Action/Reaction Forces for the Bilateral Control Using Kalman Filter
,”
IEEE Trans. Indus. Electron.
,
59
(
11
), pp.
4383
4393
.10.1109/TIE.2011.2173092
19.
Choi
,
Y.
,
Yang
,
K.
,
Chung
,
W. K.
,
Kim
,
H. R.
, and
Suh
,
H.
,
2003
, “
On the Robustness and Performance of Disturbance Observers for Second-Order Systems
,”
IEEE Trans. Autom. Control
,
48
(
2
), pp.
315
320
.10.1109/TAC.2002.808491
20.
Shima
,
H.
, and
Jo
,
N. H.
,
2009
, “
An Almost Necessary and Sufficient Condition For Robust Stability of Closed-Loop Systems With Disturbance Observer
,”
Automatica
,
45
(
1
), pp.
296
299
.10.1016/j.automatica.2008.10.009
21.
Sariyildiz
,
E.
, and
Ohnishi
,
K.
,
2013
, “
Bandwidth Constraints of Disturbance Observer in the Presence of Real Parametric Uncertainties
,”
Eur. J. Control
,
19
(
3
), pp.
199
205
.10.1016/j.ejcon.2013.03.009
22.
Bode
,
H. W.
,
1945
,
Network Analysis and Feedback Amplifier Design
,
D. Van Nostrand Co.
,
New York
.
23.
Stein
,
G.
,
2003
, “
Respect the Unstable
,”
IEEE Control Syst. Mag.
,
23
(
4
), pp.
12
25
.10.1109/MCS.2003.1213600
24.
Horowitz
,
I. M.
,
1963
,
Synthesis of Feedback Systems
,
Academic Press
,
New York
.
25.
Freudenberg
,
J. S.
, and
Looze
,
D. P.
,
1987
, “
A Sensitivity Tradeoff for Plants With Time Delay
,”
IEEE Trans. Autom. Control
,
32
(
2
), pp.
99
104
.10.1109/TAC.1987.1104547
26.
Freudenberg
,
J. S.
, and
Looze
,
D. P.
,
1985
, “
Right Half Plane Poles and Zeros and Design Tradeoffs in Feedback Systems
,”
IEEE Trans. Autom. Control
,
30
(
6
), pp.
555
565
.10.1109/TAC.1985.1104004
27.
Skogestad
,
S.
, and
Postlethwaite
,
I.
,
2001
,
Multivariable Feedback Control:Analysis and Design
,
2nd ed.
,
John Wiley & Sons
,
New York
.
28.
Zhou
,
K.
, and
Doyle
,
J. C.
,
1997
,
Essentials of Robust Control
,
Prentice-Hall
,
Upper Saddle River, NJ
.
29.
Middleton
,
R. H.
, and
Goodwin
,
G. C.
,
1990
,
Digital control and estimation. A unified approach
,
Prentice-Hall, inc.
,
Englewood Cliffs
, NJ.
30.
Seron
,
M. M.
,
Braslavsky
,
J. H.
, and
Goodwin
,
G. C.
,
1997
,
Fundamental Limitations in Filtering and Control
,
Springer-Verlag
,
London
.
31.
Sariyildiz
,
E.
, and
Ohnishi
,
K.
,
2013
, “
A New Solution for the Robust Control Problem of Non-Minimum Phase Systems Using Disturbance Observer
,”
IEEE International Conference on Mechatronics (ICM)
, Vicenza, Italy, pp.
46
51
.
You do not currently have access to this content.