Boundary Vibration Control of Variable Length Crane Systems in Two-Dimensional Space With Output Constraints

A variable length crane system under the external disturbances and constraints is studied in the two-dimensional space. The dynamical analysis of the cable system considers the variable length, variable tension, variable speed, and the coupled vibrations of the cable in longitudinal-transverse directions. Considering output constraint problems, boundary control algorithms with output signal barriers are designed and acted on the boundary of the cable to reduce the coupled vibrations of the flexible crane cable, and to ensure the stability of the system in theory. Effectiveness and performance of the proposed control schemes are depicted via several simulation examples.