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Control and exponential stabilization for the equation of an axially moving viscoelastic strip
Author(s) -
Kelleche Abdelkarim,
Tatar Nassereddine
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4452
Subject(s) - mathematics , axial symmetry , viscoelasticity , transverse plane , partial differential equation , control theory (sociology) , boundary value problem , differential equation , mathematical analysis , multiplier (economics) , vibration , actuator , exponential function , displacement (psychology) , control (management) , physics , geometry , computer science , structural engineering , engineering , artificial intelligence , economics , psychotherapist , thermodynamics , quantum mechanics , psychology , macroeconomics
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 [Figure 1. Axially moving strip ...]). 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.