Control design of an overhead crane system from the perspective of stabilizing undesired oscillations

The feedback stabilization of a generalized model describing an overhead crane with a flexible cable is considered. The cable displacements are presented by a hyperbolic partial differential equation (PDE) in which destabilizing terms are generated. The pursued method gives a systematic technic to convert the concerned model into a well-known one using an integral transformation with a kernel satisfying an appropriate PDE. A feedback controller that asymptotically stabilizes the cable displacements is explicitly constructed in terms of the solution of the kernel PDE.

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