Fixed-Time Tracking Control of Underactuated Overhead Cranes

摘要

In this paper, the fixed-time tracking control problem is addressed for the underactuated overhead cranes, compared with many existing results which aim to achieve the asymptotic stable as time goes to infinity. Firstly, the cranes dynamic is changed into a quasi-chain-of-integrators form through a coordinate transform. Then, for the transformed systems, a fixed-time tracking control algorithm is proposed by applying the backstepping method in conjunction with the dynamic surface control (DSC) technique applying a nonlinear first-order filter at each step, which not only can avoids the problem of explosion of complexity but also can achieves the Fixed-time tracking. According to fixed-time theory and Lyapunov stability theory, it is proven that the tracking error can converge into arbitrarily small neighborhoods around zero in a fixed settling time under the proposed control scheme. Finally, a simulation is done to verify the feasibility of the proposed control method.