Well-posedness and stabilization of a nonuniform wind turbine tower with distributed delay

Abstract

This study focuses on the boundary control of a wind turbine tower considering distributed delay, modeled as a non-uniform Euler-Bernoulli beam. A control input is imposed at the top boundary to suppress tower vibrations. The well-posedness result is achieved through the semi-group approach, and employing Lyapunov method confirms the stabilization of the tower to a small neighborhood of zero. Numerical simulations are provided to visually depict and validate the efficacy of the proposed control.