Active control of a traveling medium with varying length

Abstract

Active control of a traveling medium with varying length is studied. The control device applies a pointwise force/moment fixed either in the space or to the medium. In the first case the control action is proportional to the local velocity/angular velocity of the point of the medium instantaneously located at the position of the control device. In the latter the control action is proportional to the total velocity/angular velocity of the point of attachment of the control device to the medium. The control laws are shown to stabilize the traveling medium during both retraction and extrusion, and can be easily implemented.