Active Control of Multimodal Cable Vibrations by Axial Support Motion

Abstract

Active control for small-sag cable using the axial support motion is developed. The nonlinear motion of the cable with moving support is expressed as a bilinear system in which the product of the axial support motion and the cable responses is only the nonlinear term. A bilinear control theory based on the direct method of Liapunov is used. A controller that is composed of linear and quadratic feedback and that ensures a reduction of the energy in the cable system is obtained. An uncontrollable motion is identified as a circular swirling motion of the cable that is formed by two closely spaced antisymmetric modes. Two sets of numerical simulations are conducted, i.e., free vibrations and random vibrations. The results show that the controller efficiently suppresses the cable vibrations whenever the cable motion is controllable and stops when uncontrollable. It is observed that control spillovers occur but their effects are not significant. The controller shows a favorable efficiency in reducing the vibration energy of the cable.