Feedback Controller Stabilizing Vibrations of a Flexible Cable Related to an Overhead Crane

الملخص EN

The problem of stabilizing vibrations of flexible cable related to an overhead crane is considered.

The cable vibrations are described by a hyperbolic partial differential equation (HPDE) with an update boundary condition.

We provide in this paper a systematic way to derive a boundary feedback law which restores in a closed form the cable vibrations to the desired zero equilibrium.

Such a control law is explicitly constructed in terms of the solution of an appropriate kernel PDE.

The pursued approach combines the “backstepping method” and “semigroup theory”.