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TECHNICAL PAPERS

Exponential Stabilization of a Transversely Vibrating Beam by Boundary Control Via Lyapunov’s Direct Method

[+] Author and Article Information
Mehrdad P. Fard

Department of Engineering Cybernetics, Norwegian University of Science and Technology, N7034 Trondheim, Norwaye-mail: Mehrdad.Fard@itk.ntnu.no

Svein I. Sagatun

Norsk Hydro Exploration and Production, The Research Center in Bergen, N5020 Bergen, Norwaye-mail: Svein.Ivar.Sagatun@hydro.com

J. Dyn. Sys., Meas., Control 123(2), 195-200 (Nov 02, 1999) (6 pages) doi:10.1115/1.1369111 History: Received November 02, 1999
Copyright © 2001 by ASME
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References

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Leipholtz, H., 1966, “Application of Liapunov’s Direct Method to the Stability Problem of Rods Subject to Follower Forces,” Instability of Continuous Systems, Symposium Herrenlab, Germany, Sept. 8–12.
Zubov, V. L., 1964, Methods of A. M. Liapunov and Their Application, Leningrad 1957 (English Translation), P. Noordhoff Ltd., Gorning, The Netherlands.
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Khalil,  H. K., 1996, Nonlinear Systems, Second Edition, Prentic Hall, NJ; Lee,  E. W., 1957, “Non-Linear Forced Vibration of a Stretched String,” Br. J. Appl. Phys., 8, pp. 411–413.
Fard, Mehrdad, 2000, “Modelling and Control of Mechanical Flexible Systems,” Dr. Eng. Thesis, Department of Engineering Cybernetics, The Norwegian University of Science and Technology, Trondheim, Norway.

Figures

Grahic Jump Location
A transversely vibrating beam with axial tension
Grahic Jump Location
Controlled and uncontrolled responses
Grahic Jump Location
Control force at the top boundary
Grahic Jump Location
Energy of the closed-loop system

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