Boundary Control of an Axially Moving Steel Strip under a Spatiotemporally Varying Tension

  • YANG Kyung-Jinn
    Department of Mechanical Engineering and Intelligent Systems, University of Electro-Communications
  • HONG Keum-Shik
    School of Mechanical Engineering, Pusan National University
  • MATSUNO Fumitoshi
    Department of Mechanical Engineering and Intelligent Systems, University of Electro-Communications

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Abstract

In this paper, a vibration suppression scheme of an axially moving steel strip in the zinc galvanizing line is investigated. The moving steel strip is modeled as a moving beam, in which the tension applied to the strip is a spatiotemporally varying function. The transverse vibration of the strip is controlled by a hydraulic touch-roll actuator at the right boundary. The mathematical model of the system, which consists of a hyperbolic partial differential equation describing the dynamics of the moving beam and an ordinary differential equation describing the actuator dynamics, is derived by using the Hamilton's principle for the systems of changing mass. The Lyapunov method is employed to design a boundary control law for ensuring the vibration reduction of the system in the presence of a spatiotemporally varying tension. The exponential stability of the closed loop system under the boundary control is proved through the use of invariance principle and semigroup theory. Simulation results verify the effectiveness of the boundary control law proposed.

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