Modeling and nonlinear sliding mode controls of double pendulum cranes considering distributed mass beams, varying roped length and external disturbances

•Double pendulum crane with distributed mass beams (DMB) is considered.•Nonlinear sliding model control methods utilizing the velocity control are proposed.•State observer that adapts to the length variation of the suspension rope is designed.•Simulation and experiment verify the effectiveness of the method. Most of the existing anti-swing control methods treat the crane as a single pendulum system with fixed rope length. In this paper, considering the varying rope length, the dynamic model of the double pendulum crane system with distributed mass beams (DMB) is established. Four versions of sliding mode control are proposed by utilizing the equivalent control strategy. The system responses of the hierarchical linear sliding mode control method based on velocity control and displacement control are analyzed. Meanwhile, based on the pole placement method, a state observer that adapts to the length variation of the suspension rope is proposed. On this basis, the nonlinear sliding model control methods utilizing the velocity control, including the NTSMC and FTSMC, are presented. Simulations and experiments are conducted. Results indicate the effectiveness of the proposed methods. The control method can ensure the asymptotic stability of the system in a finite time, maintain robustness in disturbances and adapt the varying rope length.