Stabilization of an Axially Moving String by Nonlinear Boundary Feedback

[+] Author and Article Information
Rong-Fong Fung, Sheng-Luong Wu

Department of Mechanical Engineering, Chung-Yuan Christian University, Chung-Li, Taiwan 32023

Jinn-Wen Wu

Department of Mathematics, Chung-Yuan Christian University, Chung-Li, Taiwan 32023

J. Dyn. Sys., Meas., Control 121(1), 117-121 (Mar 01, 1999) (5 pages) doi:10.1115/1.2802428 History: Received March 25, 1997; Online December 03, 2007


In this paper, we consider the system modeled by an axially moving string and a mass-damper-spring (MDS) controller, applied at the right-hand side (RHS) boundary of the string. We are concerned with the nonlinear string and the effect of the control mechanism. We stabilize the system through a proposed boundary velocity feedback control law. Linear and nonlinear control laws through this controller are proposed. In this paper, we find that a linear boundary feedback caused the total mechanical energy of the system to decay an asymptotically, but it fails for an exponential decay. However, a nonlinear boundary feedback controller can stabilize the system exponentially. The asymptotic and exponential stability are verified.

Copyright © 1999 by The American Society of Mechanical Engineers
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