In this paper, we consider a system modelling an axially moving vis-
coelastic 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 mul-
tiplier method is employed to design a robust boundary control law to ensure the
reduction of the transvesre vibrations of the string.