Dynamics of digitally controlled forced vibration of suspended cables

Dynamics of suspended cables with active vibration control is studied. The control device is an electrical vibration absorber that is driven by a motor and that may be fixed at any position along the cable. The absorber applies a control force that reduces vibration amplitude at the position where it is placed. The methodology is efficient for attenuating high-frequency, low-amplitude vibration due to periodic excitation that may consider wind effect. The dynamic behavior is described by a mechanical model of the absorber and the cable at the location where the absorber is attached. The model takes into account such practical problems as time delay and backlash at the driving, which lead to limitation in the applicability of control. Time delay occurs in digital control, because samples of data are taken at discrete time intervals and response is provided after the sampling delay. Backlash influences control when the direction of control force changes, since the control force is not transmitted in the small domain of backlash. The present research examines the effects of time delay and backlash on the local control of cable vibration, and assesses the range of time delay and backlash when the control can be applied successfully. Moreover, the presence of time delay and backlash together results in a motion with some irregularity what justifies the detailed study of the dynamic behavior in order to evaluate the types of motion that may arise in such systems.