Exponential Stabilization of an Axially Moving Tensioned Strip by Passive Damping and Boundary Control

Abstract

In this paper, we investigate an active vibration control of a translating tensioned steel strip in the zinc galvanizing line. The dynamics of the moving strip is modeled as a Euler-Bernoulli beam with non-linear tension. The control objective is to suppress the transverse vibrations of the strip via boundary control. A right boundary control law based upon the Lyapunov second method is derived. It is revealed that a time-varying boundary force and a suitable passive damping at the right boundary can successfully suppress the transverse vibrations. The exponential stability of the closed-loop system is proved. The effectiveness of the control laws proposed is demonstrated via simulations.