Wave control of suspended rope based on finite difference model

Abstract

This paper treats the wave control of suspended ropes by a control law based on the finite difference model. The control is acted on one finite difference interval inside of the upper fixed end. The control input is the distributed force equivalent to the difference between the boundary node equations and the interior node one. This control compensation of the boundary condition with use of the wave propagating solution of the interior node equation makes the boundary state as if it were the interior nodes. The wave propagating solution of the finite difference model of suspended rope is obtained as the transfer function between adjacent node displacements in the frequency domain that gives the convolution integral kernel function in the time domain. The simulation of the suspended rope systems with or without load mass at the free lower end boundary and with load mass at the fixed lower end boundary have been conducted. The frequency response analysis and numerical time simulation have confirmed the presented wave control effectiveness. The lower end boundary condition of a suspended rope has been also discussed.