Vibration Control of Axially Moving System with Variable Speed, Tension and Length

In this paper, an active vibration control of an axially moving system with varying speed and tension is investigated. The dynamics of the translating string are described by a partial differential equation as a governing equation coupled with ordinary differential equations as a boundary condition. The time rate of change of energy is considered to calculate that of Lyapunov functional. A time varying control law based on Lyapunov's second method is proposed in stabilizing the transverse vibrations of the system. Exponential stability of the closed-loop system in case of extension is verified

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