ACTIVE CONTROL OF MULTIMODAL CABLE VIBRATIONS BY AXIAL SUPPORT MOTION

Active control for small-sag cable using the axial support motion is d eveloped. The nonlinear motion of the cable with moving support is exp ressed 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 contr oller that is composed of linear and quadratic feedback and that ensur es a reduction of the energy in the cable system is obtained. An uncon trollable motion is identified as a circular swirling motion of the ca ble that is formed by two closely spaced antisymmetric modes. Two sets of numerical simulations are conducted, i.e., free vibrations and ran dom vibrations. The results show that the controller efficiently suppr esses the cable vibrations whenever the cable motion is controllable a nd stops when uncontrollable. It is observed that control spillovers o ccur but their effects are not significant. The controller shows a fav orable efficiency in reducing the vibration energy of the cable.