Effect and Compensation of Time-delay on Semiactive Control of Cable Vibration

The stability of controlled inclined stay cables under support motions with time delay effect is studied. The partial differential equation of the parametrically excited transverse vibration of a controlled inclined stay cable with sag under support motions is derived by using two transformations of displacements and converted into ordinary differential equations for the cable mode vibration according to the Galerkin method. The parametrically excited instability of the cable vibration is noticeable affected by increasing the time delay in control over a certain value, which effects need to be taken into account for the cable instability control. And the time delay compensation is treated by expresses the delayed control action using a truncated Taylor's series in terms of the current control action and its derivatives. The controlled response considering the delay is obtained by applying the designed active control on the actual nonlinear model. The results of the stability and the time delay compensation are discussed using a numerical example.