This paper presents a controller for uncertain structures that are minimum phase and potentially subject to unknown-and-unmeasured disturbances. The controller combines dynamic inversion with a low-pass filter to yield a single-parameter high-gain-stabilizing controller. Filtered dynamic inversion requires limited model information, is independent of system order, requires only output feedback, and makes the average power of the command following error arbitrarily small despite the presence of unknown disturbances. The controller is applied to structures modeled by finite-dimensional vector second-order systems with unknown and arbitrarily large order. We also present an adaptive filtered-dynamic-inversion controller, which uses a high-gain adaptive law to increase the controller parameter until the desired performance is achieved. Finally, the controller is extended to vector second-order nonlinear systems, in which case full-state feedback may be required. Examples are given to demonstrate the application and performance of the controller.

References

References
1.
Balas
,
M.
,
1982
, “
Trends in Large Space Structure Control Theory: Fondest Hopes, Wildest Dreams
,”
IEEE Trans. Autom. Control
,
27
, pp.
533
535
.10.1109/TAC.1982.1102953
2.
Hong
,
J.
, and
Bernstein
,
D. S.
,
1998
, “
Bode Integral Constraints, Colocation, and Spillover in Active Noise and Vibration Control
,”
IEEE Trans. Control Syst. Technol.
,
6
, pp.
111
120
.10.1109/87.654881
3.
Goh
,
C. J.
, and
Caughey
,
T. K.
,
1985
, “
On the Stability Problem Caused by Finite Actuator Dynamics in Collocated Control of Large Space Structures
,”
Int. J. Control
,
43
, pp.
787
802
.10.1080/0020718508961163
4.
Davison
,
E. J.
,
1976
, “
The Robust Control of a Servomechanism Problem for Linear Time-Invariant Multivariable Systems
,”
IEEE Trans. Autom. Control
,
1
,
25
34
.10.1109/TAC.1976.1101137
5.
Francis
,
B. A.
, and
Wonham
,
W. A.
,
1976
, “
The Internal Model Principle of Control Theory
,”
Automatica
,
12
, pp.
457
465
.10.1016/0005-1098(76)90006-6
6.
Doyle
,
J. C.
,
1978
, “
Guaranteed Margins for LQG Regulators
,”
IEEE Trans. Autom. Control
,
23
, pp.
756
757
.10.1109/TAC.1978.1101812
7.
Singh
,
S. N.
, and
Schy
,
A. A.
,
1986
, “
Control of Elastic Robotic Systems by Nonlinear Inversion and Modal Damping
,”
ASME J. Dyn. Sys., Meas., Control
,
108
(3), pp.
180
189
.10.1115/1.3143766
8.
De Luca
,
A.
, and
Siciliano
,
B.
,
1989
, “
Trajectory Control of a Nonlinear One Link Flexible Arm
,”
Int. J. Control
,
5
, pp.
1699
1715
.10.1080/00207178908953460
9.
Modi
,
V. J.
,
Karray
,
F.
, and
Chan
,
J. K.
,
1993
, “
On the Control of a Class of Flexible Manipulators Using Feedback Linearization Approach
,”
Acta Astronaut.
,
29
, pp.
17
27
.10.1016/0094-5765(93)90065-5
10.
Singh
,
S. N.
, and
Zhang
,
R.
,
2004
, “
Adaptive Output Feedback Control of Spacecraft With Flexible Appendages by Modeling Error Compensation
,”
Acta Astronaut.
,
54
, pp.
229
243
.10.1016/S0094-5765(03)00030-4
11.
Ko
,
J.
,
Kurdila
,
A. J.
, and
Strganac
,
T. W.
,
1997
, “
Nonlinear Control of a Prototypical Wing Section With Torsional Nonlinearity
,”
J. Guid. Control, Dyn.
,
20
, pp.
1181
1189
.10.2514/2.4174
12.
Moon
,
S. H.
,
Chwa
,
D.
, and
Kim
,
S. J.
,
2005
, “
Feedback Linearization Control for Panel Flutter Suppression With Piezoelectric Actuators
,”
AIAA J.
,
43
, pp.
2069
2073
.10.2514/1.12964
13.
Hoagg
,
J. B.
, and
Seigler
,
T. M.
,
2013
, “
Filtered-Dynamic-Inversion Control for Unknown Minimum-Phase Systems With Unknown-and-Unmeasured Disturbances
,”
Int. J. Control
,
86
(
3
), pp.
449
468
.10.1080/00207179.2012.738938
14.
Doyle
,
J. C.
,
Francis
,
B. A.
, and
Tannenbaum
,
A. R.
,
2009
,
Feedback Control Theory
,
Dover
,
New York
.
15.
Lin
,
J.-L.
, and
Juang
,
J.-N.
,
1995
, “
Sufficient Conditions for Minimum-Phase Second-Order Linear Systems
,”
J. Vib. Control
,
1
, pp.
183
199
.10.1177/107754639500100204
16.
Meirovitch
,
L.
,
1996
,
Principles and Techniques of Vibrations
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
17.
Mareels
,
I.
,
1984
, “
A Simple Self-Tuning Controller for Stably Invertible Systems
,”
Syst. Control Lett.
,
4
, pp.
5
16
.10.1016/S0167-6911(84)80045-6
18.
Hoagg
,
J. B.
, and
Bernstein
,
D. S.
,
2007
, “
Direct Adaptive Stabilization of Minimum-Phase Systems With Bounded Relative Degree
,”
IEEE Trans. Autom. Control
,
52
, pp.
610
621
.10.1109/TAC.2007.894512
19.
Hoagg
,
J. B.
, and
Bernstein
,
D. S.
,
2007
, “
Direct Adaptive Command Following and Disturbance Rejection for Minimum Phase Systems With Unknown Relative Degree
,”
Int. J. Adapt. Control Signal Process
,
21
, pp.
49
75
.10.1002/acs.945
20.
Miller
,
D. E.
, and
Davison
,
E. J.
,
1991
, “
An Adaptive Controller Which Provides an Arbitrarily Good Transient and Steady-State Response
,”
IEEE Trans. Autom. Control
,
36
, pp.
68
81
.10.1109/9.62269
21.
Sastry
,
S.
,
1999
,
Nonlinear Systems: Analysis, Stability, and Control
,
Springer-Verlag
,
Berlin
.
22.
Byrnes
,
C. I.
, and
Isidori
,
A.
,
1991
, “
Asymptotic Stabilization of Minimum Phase Nonlinear Systems
,”
IEEE Trans. Autom. Control
,
36
, pp.
1122
1137
.10.1109/9.90226
23.
Bernstein
,
D. S.
,
2009
,
Matrix Mathematics: Theory, Facts, and Formulas With Application to Linear Systems Theory
,
Princeton University Press
,
Princeton, NJ
.
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