Vibration Control of an Axially Moving String by Boundary Control

[+] Author and Article Information
Seung-Yop Lee, C. D. Mote

Dynamic Stability Laboratory, Department of Mechanical Engineering, University of California, Berkeley, Berkeley, CA 94720

J. Dyn. Sys., Meas., Control 118(1), 66-74 (Mar 01, 1996) (9 pages) doi:10.1115/1.2801153 History: Received July 15, 1994; Revised December 19, 1995; Online December 03, 2007


The stabilization of the transverse vibration of an axially moving string is implemented using time-varying control of either the boundary transverse motion or the external boundary forces. The total mechanical energy of the translating string is a Lyapunaov functional and boundary control laws are designed to dissipate the total vibration energy of the string at the left and/or right boundary. An optimal feedback gain determined by minimizing the energy reflected from the boundaries, is the radio of tension to the propagation velocity of an incident wave to the boundary control. Also the maximum time required to stabilize all vibration energy of the system for any initial disturbance is the time required for a wave to propagate the span of the string before hitting boundary control. Asymptotic and exponential stability of the axially moving string under boundary control are verified analytically through the decay rate of the energy norm and the use of semigroup theory. Simulations are used to verify the theoretically predicted, optimal boundary control for the stabilization of the translating string.

Copyright © 1996 by The American Society of Mechanical Engineers
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