Constrained hierarchical dynamical coupling sliding-mode control of cable-suspended multi-loop underactuated system with non-decoupled time-varying coupling and double-pendulum nonlinearity

Abstract

For the anti-swing retrofit of heavy offshore cranes with double-pendulum nonlinearity, a cable-suspended multi-loop (CSML) crane is presented, where its underactuated end-payload is hung by multiple cables in a (2-UPU/UU)UU hybrid configuration. A concise 8-DOF linear-bilinear dynamic model is established by the influence coefficient principle. The CSML crane, which controls six DoFs with only two P pairs in 2-UPU/UU, exhibits a higher unactuated degree and complex non-decoupled nonlinear time-varying coupling, resulting in greater control challenges. A hierarchical dynamical coupling sliding-mode controller is proposed by mixing a dynamical coupling strategy after an initial decoupled design. A model-based dynamics coupling relationship matrix (DCRM) is proposed in the coupling design to capture the non-decoupled time-varying coupling of (2-UPU/UU)UU and ensure closed-loop system stability. Simulation shows that our method helps improve controllers only suitable for series underactuated systems, and exhibits efficient multi-loop anti-swing performance with double-pendulum swing suppression rates of 95.13%, 94.09%, 91.32%, and 92.5%. DCRM distribution in different mechanism scales accurately mirrors the balance of the controller’s regulation performance among four swing angles, and guides the scale optimization of (2-UPU/UU)UU. Experiments validate the robustness and reliable underactuated positioning amid harsh disturbances.