Control and exponential stabilization for the equation of an axially moving viscoelastic strip |
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| Authors: | Abdelkarim Kelleche Nasser‐eddine Tatar |
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| Affiliation: | 1. Faculté des Sciences et de la Technologie, Université Djilali Bounaama, Route Theniet El HadKhemis Miliana, Algeria;2. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia |
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| Abstract: | The aim through this work is to suppress the transverse vibrations of an axially moving viscoelastic strip. A controller mechanism (dynamic actuator) is attached at the right boundary to control the undesirable vibrations. The moving strip is modeled as a moving beam pulled at a constant speed through 2 eyelets. The left eyelet is fixed in the sense that there is no transverse displacement (see Figure 1 ). The mathematical model of this system consists of an integro‐partial differential equation describing the dynamic of the strip and an integro‐differential equation describing the dynamic of the actuator. The multiplier method is used to design a boundary control law ensuring an exponential stabilization result. |
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| Keywords: | axially moving steel strip dynamic actuator exponential stability viscoelasticity |
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