In this paper, we consider the problem of regulating the displacement of an axial moving string using a control force and a control torque applied to the string via a mechanical guide. Given the hybrid model of the web system (i.e., distributed parameter field equation coupled to a discrete actuator equation), a Lyapunov-type analysis is utilized to design exact model knowledge and adaptive control laws that exponentially and asymptotically stabilize the string displacement, respectively. Dynamic simulation results demonstrate the vibration damping provided by the control strategy.

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