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Control of an axially moving viscoelastic Kirchhoff string
Authors:Abdelkarim Kelleche  Nasser-eddine Tatar
Institution:1. Faculté des Sciences et de la Technologie, Université Djilali Bounaama, Route Theniet El Had, Soufay 44225 Khemis Miliana, Algeria.;2. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia.
Abstract:The control problem of axially moving strings occurs in a large class of mechanical systems. In addition to the longitudinal displacement, the strings are subject to undesirable transversal vibrations. In this work, in order to suppress these vibrations, we consider a control by a hydraulic touch-roll actuator at the right boundary. We prove uniform stability of the system using a viscoelastic material and an appropriate boundary control force applied to the touch rolls of the actuator. The features of the present work are: taking into account the mass flow entering in and out at the boundaries due to the axial movement of the string and overcoming the difficulty raised by the Kirchhoff coefficient which does not allow us to profit from the dissipativity of the system (as in the existing works so far). We shall make use of an inequality which is new in this theory.
Keywords:Moving Kirchhoff string  dynamic actuator  viscoelasticity  uniform stability
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