Active Control of Multimodal Cable Vibrations by Axial Support Motion
Publication: Journal of Engineering Mechanics
Volume 121, Issue 9
Abstract
Active control for small-sag cable using the axial support motion is developed. The nonlinear motion of the cable with moving support is expressed as a bilinear system in which the product of the axial support motion and the cable responses is only the nonlinear term. A bilinear control theory based on the direct method of Liapunov is used. A controller that is composed of linear and quadratic feedback and that ensures a reduction of the energy in the cable system is obtained. An uncontrollable motion is identified as a circular swirling motion of the cable that is formed by two closely spaced antisymmetric modes. Two sets of numerical simulations are conducted, i.e., free vibrations and random vibrations. The results show that the controller efficiently suppresses the cable vibrations whenever the cable motion is controllable and stops when uncontrollable. It is observed that control spillovers occur but their effects are not significant. The controller shows a favorable efficiency in reducing the vibration energy of the cable.
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References
1.
Benallou, A., Mellichamp, D. A., and Seborg, D. E.(1988). “Optimal stabilizing controllers for bilinear systems.”Int. J. Control, 48(4), 1487–1501.
2.
Chen, J. C.(1984). “Response of large space structures with stiffness control.”J. Spacecraft Rockets, 21(5), 463–467.
3.
Derese, I., and Noldus, E.(1980). “Design of linear feedback laws for bilinear systems.”Int. J. Control, 31(2), 219–237.
4.
Fujino, Y., Pacheco, B. M., Nakamura, S., and Warnitchai, P. (1993a). “Synchronization of human walking observed during lateral vibration of a congested pedestrian bridge.”Earthquake Engrg. and Struct. Dynamics.
5.
Fujino, Y., Warnitchai, P., and Pacheco, B. M. (1993b). “Active stiffness control of cable vibration.”J. Appl. Mech.
6.
Genesio, R., and Tesi, A.(1988). “Feedback of SISO bilinear systems.”Int. J. Control, 48(3), 1319–1326.
7.
Gutman, P.(1981). “Stabilizing controllers for bilinear systems.”IEEE Trans. Automatic Control, 26(4), 917–922.
8.
Hagedorn, P. (1989). “Active vibration damping in large flexible structures.”Theoretical and applied mechanics. P. Germain, M. Piam, and D. Caillerie, eds., Elsevier Science Publisher B.V., (North Holland), 83–100.
9.
Hahn, W. (1963). Theory and application of Liapunov's direct method . Prentice-Hall, Englewood Cliffs, N.J.
10.
Hikami, Y. (1986). “Rain vibrations of cables in cable-stayed bridge.”J. Wind Engrg., Japan, 27(3), 17–28 (in Japanese).
11.
Longchamp, R.(1980a). “Stable feedback control of bilinear systems.”IEEE Trans. Automatic Control, 25(2), 302–306.
12.
Longchamp, R.(1980b). “Controller design for bilinear systems.”IEEE Trans. Automatic Contlrol, 25(3), 547–548.
13.
Mohler, R. R. (1973). Bilinear control processes . Academic Press, New York, N.Y.
14.
Mohler, R. R. (1991a). Nonlinear systems; Vol. 1, Dynamics and control . Prentice-Hall, Englewood Cliffs, N.J.
15.
Mohler, R. R. (1991b). Nonlinear systems; Vol. 2, Applications to bilinear control. Prentice-Hall, Englewood Cliffs, N.J.
16.
Natori, M., Miura, K., and Ichida, K. (1989). “Vibration control of membrane space structures through the change of support tension.”Proc., 40th Congr. Int. Astronaut. Federation, IAF-89-335, 1–6.
17.
Nayfeh, A. H., and Mook, D. T. (1979). Nonlinear oscillations . John Wiley & Sons, New York, N.Y.
18.
Ogata, K. (1967). State space analysis of control systems. Prentice-Hall, Englewood Cliffs, N.J.
19.
Ohshima, K., and Nanjo, M. (1987). “Aerodynamic stability of the cables of a cable-stayed bridge subject to rain (A case study of Ajigawa bridge).”Proc., 3rd US-Japan Bridge Workshop (May), 324–335.
20.
Quinn, J. P.(1980). “Stabilization of bilinear systems by quadratic feedback controls.”J. Math. Anal. Appl., 75, 66–80.
21.
Slemrod, M.(1978). “Stabilization of bilinear control systems with applications to nonconservative problems in elasticity.”SIAM J. Control Optimization, 16(1), 131–141.
22.
Susumpow, T. (1993). Dynamics of cable-structure systems and active control of cable by axial support motion . D. Eng. thesis, Univ. of Tokyo, Tokyo, Japan.
23.
Susumpow, T., and Fujino, Y. (1993). “An experimental study on active control of planar cable vibration by axial support motion.”Earthquake Engrg. and Struct. Dynamics.
24.
Tani, J., Echigoya, W., and Futamura, T. (1992). “Vibration and control of a pendulum by active change of parameters.”Proc., 2nd Joint Japan-U.S. Conf. Adaptive Struct., 340–348.
25.
Thaler, G. J., and Pastel, M. P. (1962). Analysis and design of nonlinear feedback control systems. McGraw-Hill, New York, N.Y.
26.
Vidyasagar, M.(1986). “New direction of research in nonlinear system theory.”Proc., IEEE, 74(8), 1060–1091.
27.
Warnitchai, P., Fujino, Y., Pacheco, B. M., and Agret, R.(1993a). “An experimental study on active control of cable-stayed bridges.”Earthquake Engrg. and Struct. Dynamics, 22, 93–111.
28.
Warnitchai, P., Fujino, Y., and Susumpow, T. (1993b). “A nonlinear dynamic model of cables and its application to a cable-structure system.”J. Sound Vibration.
29.
Watson, S. C., and Stafford, D.(1988). “Cables in trouble.”Civil Engrg., ASCE, 58(4), 38–41.
30.
Yamaguchi, H., and Dung, N. N. (1992). “Active wave control of sagged cable vibration.”Proc., 1st Int. Conf. on Motion Vibration Control, 134–139.
31.
Yang, X., Chen, L., and Burton, R. M.(1989). “Stability of discrete bi-linear systems with output feedback.”Int. J. Control, 50(5), 2085–2092.
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Copyright © 1995 American Society of Civil Engineers.
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Published online: Sep 1, 1995
Published in print: Sep 1995
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