Lyapunov-Based Model Predictive Control for Shipboard Boom Cranes Under Input Saturation

A Lyapunov-based model predictive control (MPC) scheme is firstly developed for shipboard boom cranes with ship rolling, while considering optimization and input saturation. By integrating the ship rolling into original state variables, the shipboard boom crane model is transformed to facilitate the successive controller design. A Lyapunov-based MPC framework is then constructed for the new dynamical model, while respecting actuator capability. To ensure the recursive feasibility and stability of the established framework, a contractive constraint with a bounded energy-based controller is further introduced, for which the bounds are intrinsical with the utilization of the arctan function. Stability analysis for the bounded controller is also discussed based on Lyapunov theory and LaSalle’s invariance principle. Compared with the bounded controller, optimization is taken into account by the Lyapunov-based MPC. Suboptimal solutions are also accepted to ease the computational burden. Moreover, the conservation existing in the bounded controller can be entirely circumvented by the Lyapunov-based MPC, so the capacity of actuators can be fully exploited while obeying the input saturation. Finally, numerical simulations are elaborately devised and implemented to show the effectiveness of the bounded controller and superiority of the Lyapunov-based MPC controller.
Note to Practitioners
—Shipboard crane is an important industrial equipment in ocean transportation and offshore engineering. Cranes are installed on ship deck, so the movements of ship, such as rolling, and pitching, may introduce difficulties, inefficiency, and unsafety to the manual operation. The conditions mentioned above motivate the study of automation control for shipboard cranes. A Lyapunov-based model predictive control (MPC) framework is constructed in this paper. Based on this framework, the payload can be conveyed to the desired location accurately and eliminate the swing quickly. Simultaneously, optimization is considered, thus, better control performance can be achieved by consuming less energy. Moreover, the physical limits of the actuators can be satisfied all the time. The present research only considers 3 degrees of freedom (DOF) shipboard boom cranes, for which the slew movement of boom and payload tangential swing are not involved. In the future research, the 5-DOF shipboard boom cranes will be studied to promote the application of the method proposed in this paper.