Disturbance Observer-Based Prescribed-Time Control for Flexible Rope Systems

This article addresses an issue of prescribed-time control (PTC) for flexible rope systems with disturbances. Initially, we introduce the prescribed-time disturbance observer (PTDO) to evaluate external perturbations, achieving zero error estimation within a specified time. Subsequently, utilizing the PTDO and the idea of feedback linearization, a PTC method is formulated to ensure that the elastic deformation velocity of systems converges to the origin within a specified time. It is proved by Lyapunov theory that the designed scheme not only guarantees the disturbances estimation and velocity stabilization within the specified time, but also presets the stabilization time through parameters assignment. Eventually, a numerical simulation is employed to demonstrate the feasibility and efficiency of the presented algorithm.