Active Vibration Control of the Axially Moving String in the S Domain

A new method is presented for active vibration control of the axially moving string, one of the most common models of axially moving continua. The control is formulated in the Laplace transform domain. The transfer function of a closed-loop system, consisting of the plant, a feedback control law and the dynamics of the sensing and actuation devices, is derived. Analysis of the root loci of the closedloop system gives two stability criteria. Stabilizing controller design is carried out of both collocation and noncollocation of the sensor and actuator. It is found that all the modes of vibration can be stabilized and that in principle the spillover instability can be avoided. Also, the steady-state response of the stabilized string to periodic, external excitation is presented in closed form.