Exponential Stabilization of a Transversely Vibrating Beam by Boundary Control Via Lyapunov’s Direct Method-Reference-Cited by-同舟云学术

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

Published:1999-11-02 Issue:2 Volume:123 Page:195-200
ISSN:0022-0434
Container-title:Journal of Dynamic Systems, Measurement, and Control
language:en
Short-container-title:

Author:

Fard Mehrdad P.¹,Sagatun Svein I.²

Affiliation:

1. Department of Engineering Cybernetics, Norwegian University of Science and Technology, N7034 Trondheim, Norway

2. Norsk Hydro Exploration and Production, The Research Center in Bergen, N5020 Bergen, Norway

Abstract

This paper discusses the boundary stabilization of a beam in free transverse vibration. The dynamics of the beam is presented by a nonlinear partial differential equation (PDE). Based on this model a nonlinear control law is constructed to stabilize the system. The control law is a nonlinear function of the slopes and velocity at the boundary of the beam. The novelty of this article is that it has been possible to exponentially stabilize a free transversely vibrating beam via boundary control without restoring to truncation of the model. This result is achieved while the coupling between longitudinal and transversal displacements has been taken into account.

Publisher

ASME International

Subject

Computer Science Applications,Mechanical Engineering,Instrumentation,Information Systems,Control and Systems Engineering

Link

http://asmedigitalcollection.asme.org/dynamicsystems/article-pdf/123/2/195/5647296/195_1.pdf

Reference17 articles.

1. Balas, M. J., 1977, “Active Control of Flexible Systems,” Proceedings of the AIAA Symposium on Dynamic and Control of Large Flexible Spacecraft, Blacksburg, Va., pp. 217–236.

2. Meirovitch, L., and Baruh, H., 1983, “On the Problem of Observation Spillover in Self-adjoint Distributed-parameter Systems,” Journal of Optimization and Applications, 30, No. 2, pp. 269–291.

3. Fung, Rong-Fong, and Tseng, Chun-Chang, 1999, “Boundary Control of an Axially Moving String via Lyapunov Method,” ASME J. Dyn. Syst., Meas., Control, 121, pp. 105–110.

4. Shahruz, S. M., and Krishna, L. G., 1996, “Boundary Control of a Nonlinear String,” J. Sound Vib. 195, No. 1, pp. 169–174.

5. Shahruz, S. M., and Narasimha, C. A., 1997, “Suppression of Vibration in Stretched Strings by the Boundary Control,” J. Sound Vib. 204, No. 5, pp. 835–840.

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