Robust adaptive boundary control of an axially moving string under a spatiotemporally varying tension

2004 ◽  
Vol 273 (4-5) ◽  
pp. 1007-1029 ◽  
Author(s):  
Kyung-Jinn Yang ◽  
Keum-Shik Hong ◽  
Fumitoshi Matsuno
Keyword(s):  
Boundary Control ◽  
Axially Moving String ◽  
Robust Adaptive ◽  
Axially Moving ◽  
Adaptive Boundary Control

Adaptive Boundary Control of an Axially Moving String System

2002 ◽  
Vol 124 (3) ◽  
pp. 435-440 ◽  
Author(s):  
Rong-Fong Fung ◽  
Jinn-Wen Wu ◽  
Pai-Yat Lu
Keyword(s):  
Boundary Control ◽  
Tracking Error ◽  
Torque Control ◽  
Control Force ◽  
Unknown Parameters ◽  
System Equation ◽  
Axially Moving String ◽  
Coupling System ◽  
Axially Moving ◽  
Adaptive Boundary Control

This paper proposes an adaptive boundary control to an axially moving string system, which couples with a mass-damper-spring (MDS) controller at its right-hand-side (RHS) boundary. Unknown parameters appearing in the system equation are assumed constant and estimated on-line by using adaptation laws. The adaptive computed-torque control algorithm applied to robot manipulators of lumped systems is extended to design the adaptive boundary controller for the coupling system. It is found that the control force and update laws depend only on the displacement, velocity and slope of the string at the RHS boundary. Lyapunov stability guarantees the convergence of the tracking error to zero. Finally, the performance of the proposed controller is demonstrated by numerical simulations.

Boundary Control of an Axially Moving String Via Lyapunov Method

1999 ◽  
Vol 121 (1) ◽  
pp. 105-110 ◽  
Author(s):  
Rong-Fong Fung ◽  
Chun-Chang Tseng
Keyword(s):  
Boundary Control ◽  
Lyapunov Method ◽  
Sliding Mode ◽  
Semigroup Theory ◽  
Active Vibration Control ◽  
Nonlinear Partial Differential Equation ◽  
Distributed Parameter ◽  
Axially Moving String ◽  
Active Vibration ◽  
Axially Moving

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.

Suppression of Vibration in a Nonlinear Axially Moving String by the Boundary Control

1997 ◽  
Author(s):  
Shahram M. Shahruz
Keyword(s):  
Boundary Control ◽  
Negative Feedback ◽  
Linear Boundary ◽  
Axially Moving String ◽  
Axially Moving ◽  
Nonlinear String

Abstract In this note, a nonlinear axially moving string is considered. It is proved that the nonlinear string can be stabilized by the linear boundary control, which is the negative feedback of the transversal velocity of the string at one end.

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