Research on double pendulum anti-swing of cable-driven multi-point collaborative lifting for shipboard boom crane based on tension optimization

The variable and unpredictable marine environment will not only inevitably cause the double pendulum phenomenon of shipboard boom crane lifting system, but also directly threaten the safe and efficient lifting operation. In this paper, in view of the above problems, firstly, the mathematical model of ocean random wind is established, and the mathematical model of wave is established by using the Pierson-Moskowitz (PM) method, so as to obtain an environmental disturbance model of the shipboard boom crane in this way. Then, the Lagrange equation is used to establish the dynamic equation of the double pendulum for the multi-point collaborative lifting of shipboard boom crane under the influence of roll, pitch, and environmental disturbance. After that, a fractional-order PID (FOPID) constant tension optimization control (CTOC) method based on the particle swarm optimization (PSO) algorithm is proposed, which is used to optimize the anti-swing cable tension. At the same time, a nonlinear hierarchical sliding mode controller (HSMC) with CTOC is designed, and the stability of the HSMC with CTOC is proved by the Lyapunov stability theorem and Barbalat’s lemma. Finally, the experimental results show that the FOPID can reduce the tension fluctuation range of the anti-swing cables by more than 63.5%, and the HSMC with CTOC method can reduce the out-of-plane angle swing of the hook and payload by more than 85.5% and 87.3%, respectively, as well as the in-plane angle swing by more than 80.9% and 91.8%, respectively.