Polynomial stability of wind turbine tower models

2025/03/28 by Fkirine, Mohamed, Paunonen, Lassi · 2 citations
#35B35 #35B40 #47D06 (47A10) #93C20 #93D15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2503.22432

Abstract

We investigate the stabilization of mathematical models describing the structural dynamics of monopile wind turbine towers. In the fore-aft plane, we show that the system becomes polynomially stable with an energy decay rate of t^-1 under static output feedback that relies on the velocity and/or angular velocity of the nacelle. Additionally, we prove that a tuned mass damper (TMD) in the nacelle ensures polynomial stability with the same energy decay rate, offering a viable alternative to active control. For the side-to-side plane, we analyze a model incorporating a hydraulic power transmission system and prove that feedback from the nacelle's angular velocity and the generator load torque leads to polynomial stability of the system.

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• Optimal stabilization rate for the wave equation with hyperbolic boundary condition
• Polynomial Stability of Non-Linearly Damped Contraction Semigroups

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