Application of feedforward wave-based control to tether vibration suppression in airborne wind energy systems

Kilometer-scale ultra-long flexible tethers, critical force-transmission components in ground-based high-altitude wind power systems, are prone to large-amplitude vibrations under time-varying wind loads and periodic traction. Finite-speed stress wave propagation along tethers causes pronounced second-scale time delays, whose coupling with flexible wave dynamics leads to system instability and degraded energy transmission efficiency—features that conventional models assuming instantaneous stress transmission fail to capture. Based on elastic wave theory, this paper establishes a lumped-parameter dynamic model incorporating stress wave propagation delays, with strain-rate-dependent viscoelastic damping to describe amplitude attenuation. An active feedforward control strategy is further proposed: sensor-captured incident wave signals are used to predict wavefront arrival via propagation delay, and counter-phase control forces are generated in real time to achieve destructive wave interference. This work provides a novel approach for active vibration control of ultra-long flexible tethers.