Boundary Control of an Overhead Crane Hoisting System with Flexible Rope in the Presence of Input Saturation

This paper develops a boundary control for an overhead crane with the input constraint, wherein the hoisting rope is considered as an axially moving string with varying length. The mathematical model of the crane consisting of a trolley, a hoisting rope, and a payload is developed by using the Hamilton principle. To deal with the input saturation, an auxiliary system is used, and a boundary control law is designed based on this system. The stability of the crane system under the proposed control law is also verified via the Lyapunov stability theory. The simulation results reveal the impressive effectiveness of the proposed control law.