Control of an extending nonlinear elastic cable with an active vibration control strategy

•An establishment of a multi-dimensional dynamic system of an extending nonlinear elastic cable.•A development of an active control strategy applicable to a nonlinear multi-dimensional dynamic system.•The discovery of a large-amplitude vibration in the established nonlinear multi-dimensional dynamic system.•An active vibration control of the large amplitude vibration discovered.

An active control strategy based on the fuzzy sliding mode control (FSMC) is developed in this research for controlling the large-amplitude vibrations of an extending nonlinear elastic cable. The geometric nonlinearity of the cable and the fixed–fixed boundary of the cable are considered. For effectively and accurately control the motion of the cable with the active control strategy developed, the governing equation of the elastic cable is established and transformed into a multi-dimensional dynamic system with the 3rd order Galerkin method. The active control strategy is developed on the basis of the dynamic system, and the control strategy is applicable to multi-dimensional dynamic systems. In the numerical simulation, large-amplitude vibrations of the cable are effectively controlled with the control strategy. The results of the research demonstrate significances for controlling the cable vibrations of an elevator in practice.