| Summary: | Active control of a stay cable through changing its tension is an effective way to lower the vibration amplitude. In this paper, active tendon control of a stay cable using a giant magnetostrictive actuator (GMA), which can generate axial deformation in a short period (normally less than 10 ms) under magnetic fields, is studied considering the time-delay. The bilinear controlled state equation of the small-sag cable is established by employing the Lagrange formulation. The linearization method for the bilinear controlled state equation is proposed and validated by numerical simulations. A GMA is designed and manufactured to actively control a stay cable model and the relationship between the output force and the input voltage is obtained by experiments. Based on the phase-shifting method, a multi-mode control algorithm with the time-delay compensation is proposed, and the time-delay compensation matrix based on the state feedback control algorithm is obtained. Based on a 1:20 scaled cable model, simulations and experiments are conducted to investigate the control performance of the proposed method under different external loads including the free vibration, harmonic excitation and random excitation. The results show that the tendon control of cable vibration by a GMA may be invalid and even amplify the vibration amplitude when the compensation of time-delay is not considered. Moreover, the excellent control performance can be achieved by using the proposed time-delay compensation method.
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