An Adaptive Hierarchical Sliding Mode Control Scheme with Accurate Positioning and Sway Suppression for Underactuated Tower Cranes

Due to the non-linearity, high-coupling and under-actuated characteristics of tower cranes, the dynamics analysis is challenging. Although a simplified dynamic model of tower cranes is advantageous for analysis, the stability and accuracy of the system are difficult ensured, especially when the state variables deviate far from equilibrium points. Furthermore, the harsh working environment of tower cranes makes it difficult to obtain accurate friction parameters. Considering these factors, an actuated dynamic model for tower cranes is developed via a model transformation approach. The model is not simplified, moreover the unknown frictions and underactuated characteristics are fully considered. Based on the developed model, an adaptive hierarchical sliding mode control (AHSMC) scheme is proposed, which can guarantee the fast and accurate arrival of the trolley and the jib to the desired positions while suppressing payload swings effectively. A hierarchical sliding mode surface is designed to suppress payload oscillations; a sliding mode convergence law is presented to attenuate chattering problem and to increase convergence rate; an adaptive friction function is used to compensate for the influence of unknown frictions. The stability of the closed-loop system is proven rigorously by utilizing the Lyapunov technique and LaSalle's invariance theory. A series of comparative simulations are carried out to verify the control performance, chattering suppression performance and robustness of the proposed method.