Boundary Vibration Control of a Variable Length Crane System in Two Dimensional Space with Output Constraints

Abstract In this paper, a hoisting cable with varying length under the external disturbances is investigated. The dynamical modeling for cable system takes into account variable length, variable tension and variable speed. The coupled vibrations of the cable in the longitudinal-transverse directions are suppressed by the designed control inputs acted on the boundary of the cable. Considering the output constraint problems, a barrier Lyapunov function (BLF)-based control is proposed to generate novel boundary control algorithms which reduce the undesirable vibrations of the flexible crane system and to prove the boundedness of the states. Effectiveness and performance of the proposed control schemes are depicted via several simulation examples.