Boundary Control of an Axially Moving String Via Lyapunov Method

[+] Author and Article Information
Rong-Fong Fung, Chun-Chang Tseng

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

J. Dyn. Sys., Meas., Control 121(1), 105-110 (Mar 01, 1999) (6 pages) doi:10.1115/1.2802425 History: Received December 12, 1977; Online December 03, 2007


This paper presents the active vibration control of an axially moving string system through a mass-damper-spring (MDS) controller at its right-hand side (RHS) boundary. A nonlinear partial differential equation (PDE) describes a distributed parameter system (DPS) and directly selected as the object to be controlled. A new boundary control law is designed by sliding mode associated with Lyapunov method. It is shown that the boundary feedback states only include the displacement, velocity, and slope of the string at RHS boundary. Asymptotical stability of the control system is proved by the semigroup theory. Finally, finite difference scheme is used to validate the theoretical results.

Copyright © 1999 by The American Society of Mechanical Engineers
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