A variable gain direct velocity feedback is proposed to control vibrations in structures with two closely spaced natural frequencies using a single actuator. First, limitation of the conventional constant gain velocity feedback is discussed based on perturbation analysis of the free response of structures with two vibration modes and a single actuator. Then, a variable gain feedback is constructed from the physical intuitions obtained from these solutions. The variable feedback gain is derived in terms of the state of the system while the feedback loop remains direct velocity feedback. Numerical studies confirm the efficiency of the proposed method.
Issue Section:
Research Papers
1.
Abe´, M., 1995, “Vibration Control Using Analytically-Based Artificial Intelligence,” Ph. D. Thesis, Department of Civil Engineering, Northwestern University, Evanston, Illinois.
2.
Abe´
M.
Igusa
T.
1995
, “Tuned Mass Dampers for Structures with Closely Spaced Natural Frequencies
,” Earthquake Engineering and Structural Dynamics
, Vol. 24
, pp. 247
–261
.3.
Abe´
M.
Igusa
T.
1996
, “Semi-Active Dynamic Vibration Absorbers for Controlling Transient Vibration
,” Journal of Sound and Vibration
, Vol. 198
, pp. 547
–569
.4.
Alexandrov, A. D., Kolmogorov, A. N., and Lavrent’ev, M. A., 1963, Mathematics-Its Content, Methods and Meaning, MIT Press, Cambridge, Massachusetts.
5.
Auburn
J. N.
1980
, “Theory of the Control of Structures by Low-Authority Controllers
,” AIAA Journal of Guidance and Control
, Vol. 3
, pp. 444
–451
.6.
Balas
M. J.
1979
, “Direct Velocity Feedback Control of Large Space Structures
,” AIAA Journal of Guidance and Control
, Vol. 2
, pp. 252
–253
.7.
Balas
M. J.
1982
, “Trends in Large Space Structure Control Theory: Fondest Hopes, wildest Dreams
,” IEEE Transactions on Automatic Control
, Vol. AC-27
, pp. 522
–535
.8.
Coulter, J. P., and Duclos, T. G., 1989, “Applications of Electrorheological Materials in Vibration Control,” Proceedings of the Second International Conference on ER fluids, Raleigh, North Carolina, J. Carlson et al, ed. pp. 300–325.
9.
Den Hartog, J. P., 1956, Mechanical Vibrations, McGraw-Hill, 4th Ed., New York.
10.
Dennis, J. E., and Schnabel, R. B., 1983, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall, Englewood Cliffs, New Jersey.
11.
Ebihara, M., and Igusa, T., 1993, “A Combined Global/Local Control Concept for Truss Structures,” Proceedings of the 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, LaJolla, CA, pp. 3328–3331.
12.
Forward
R. L.
1981
, “Electronic Damping of Orthogonal Bending Modes in a Cylindrical Mast-Experiment
,” AIAA Journal of Spacecraft
, Vol. 18
, pp. 11
–17
.13.
Fujino
Y.
Abe´
M.
1993
, “Design Formulas for Tuned Mass Dampers Based on a Perturbation Technique
,” Earthquake Engineering and Structural Dynamics
, Vol. 22
, pp. 833
–854
.14.
Hokamoto
S.
Goto
N.
1994
, “LAC/HAC System with a Variable Feedback Gain for Flexible Space Structures
,” JSME International Journal, Series C
, Vol. 37
, pp. 431
–435
.15.
Horner, J. B., Meckl, P. H., and Shimosaka, H., 1990, “Modeling and Design of a Structure with Coupled Modes for Active Vibration Control,” Active Noise and Vibration Control—1990, ASME NCA-Vol. 8, ASME Winter Annual Meeting, Dallas, Texas, pp. 153–159.
16.
Horner
J. B.
Rutterman
D. J.
Meckl
P. H.
1994
, “Effect of Actuator Coupling on Active Vibration Control of Flexible Structures
,” AIAA Journal of Guidance, Control, and Dynamics
, Vol. 17
, pp. 214
–217
.17.
Hvorat
D.
Barak
P.
Rabins
M.
1983
, “Semi-Active versus Passive or Active Tuned Mass Dampers for Structural Control
,” ASCE Journal of Engineering Mechanics
, Vol. 109
, pp. 691
–705
.18.
Hyland
D. C.
Junkins
J. L.
Longman
R. W.
1993
, “Active Control Technology for Large Space Structures
,” AIAA Journal of Guidance, Control, and Dynamics
, Vol. 16
, pp. 801
–821
.19.
Joshi
S. P.
Vincent
T. L.
Lin
Y. C.
1990
, “Control for Energy Dissipation in Structures
,” AIAA Journal of Guidance, Control, and Dynamics
, Vol. 13
, pp. 751
–753
.20.
Juang
J.-N.
1984
, “Optimal design of a passive vibration absorber for a truss beam
,” AIAA Journal of Guidance, Control and Dynamics
, Vol. 7
, pp. 733
–739
.21.
Kan
C. L.
Chopra
A. K.
1977
, “Effects of Torsional Coupling on Earthquake Forces in Buildings
,” ASCE Journal of the Structural Division
, Vol. ST-103
, pp. 805
–819
.22.
Lee
A.-C.
Chen
S.-T.
1994
, “Collocated Sensor/Actuator Positioning and Feedback Design in the Control of Flexible Structure System
,” ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol. 116
, pp. 146
–154
.23.
Levine
W. S.
Athans
M.
1970
, “On the Determination of the Optimal Constant Output Feedback Gains for Linear Multivariable Systems
,” IEEE Transactions on Automatic Control
, Vol. AC-15
, pp. 44
–48
.24.
Meirovitch, L., 1990, Dynamics and Control of Structures, John Wiley & Sons, New York.
25.
Morris Jr., A. H., 1990, NSWC Library of Mathematics Subroutines, NSWC TR 90-21, Naval Surface Warfare Center, Dahlgren Virginia 22448-5000.
26.
Rao
S. S.
Pan
T. S.
Venkayya
V. B.
1990
, “Modeling, Control, and Design of Flexible Structures: A Survey
,” Applied Mechanics Review
, Vol. 43
, No. 5
, pp. 99
–117
.27.
Seto
K.
Yamanouchi
M.
1978
, “On the Effect of a Variable Stiffness-Type Dynamic Absorber with Eddy-Current Damping
,” Bulletin of the JSME
, Vol. 21
, pp. 1482
–1489
.28.
Swigert
C. J.
Forward
R. L.
1981
, “Electronic Damping of Orthogonal Bending Modes in a Cylindrical Mast—Theory
,” AIAA Journal of Spacecraft
, Vol. 18
, pp. 5
–10
.29.
Warburton
G. B.
1981
, “Optimum Absorber Parameters for Minimizing Vibration Response
,” Earthquake Engineering and Structural Dynamics
, Vol. 9
, pp. 251
–262
.30.
Warnitchai, P., 1990, “Nonlinear Vibrations and Active Control of Cable-Stayed Bridges,” Ph.D. Thesis, Department of Civil Engineering, University of Tokyo, Tokyo, Japan.
31.
White, D. A., and Sofge, D. A., 1992, Handbook of Intelligent Control: Neural, Fuzzy, and Adaptive Approaches, Van Nostrand Reinhold, New York.
32.
Xu
K.
Igusa
T.
1991
, “Dynamic Characteristics of Non-Classically Damped Structures
,” Earthquake Engineering and Structural Dynamics
, Vol. 20
, pp. 1127
–1144
.33.
Xu, K., Warnitchai, P., and Igusa, T., 1992, “Active Control of a Structure with Two Closely Spaced Natural Frequencies,” Proceedings of the 33rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Washington D. C., Vol. 3, pp. 1285–1295.
34.
Xu
K.
Warnitchai
P.
Igusa
T.
1993
, “Control of a Structure with Two Closely Spaced Natural Frequencies
,” AIAA Journal of Guidance, Control, and Dynamics
, Vol. 16
, pp. 1177
–1178
.
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