Boundary Control and Stabilization of an Axially Moving Viscoelastic String under a Boundary Disturbance

Abstract

In this paper, we consider a system modelling an axially moving viscoelastic string subject to an unknown boundary disturbance. It is controlled by a hydraulic touch-roll actuator at the right boundary which is capable of suppressing the transverse vibrations that occur during the movement of the string. The multiplier method is employed to design a robust boundary control law to ensure the reduction of the transvesre vibrations of the string.

Keywords:

• axially moving string
• dynamic actuator
• viscoelasticity
• boundary control

AMS Subject Classification:

• 35L20
• 65N30
• 74G25
• 74G30
• 93D15
• 93D20