Well-posedness and controllability of a wind turbine tower model

Xiaowei Zhao*, George Weiss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


We derive a model for a wind turbine tower in the plane of the turbine blades, which comprises an Euler-Bernoulli beam coupled with a nacelle (rigid body) and a two-mass drive-train model (with gearbox). This model has two possible control inputs: the torque created by the electrical generator and the force created by an electrically driven mass located in the nacelle. First, we consider the case of only torque control and a possibly non-uniform tower. Using the theory of coupled linear systems (one infinite dimensional and one finite dimensional) developed by us recently, we show that this wind turbine tower model is well-posed and regular on either the energy state space Xc or the domain of its generator on Xc, denoted by Xc 1. We also show that generically, this model is exactly controllable on X1c in arbitrarily short time. More precisely, for every T > 0, we show that if we vary a certain parameter in the model, then exact controllability in time T holds for all except three values of the parameter. In the case of using both force and torque control, we derive similar well-posedness, regularity and generic exact controllability results on a state space that is larger than X1c but smaller than X c. In this second case, we assume that the tower is uniform.

Original languageEnglish
Pages (from-to)103-119
Number of pages17
JournalIMA Journal of Mathematical Control and Information
Issue number1
StatePublished - Mar 2011


FundersFunder number
Engineering and Physical Sciences Research Council
British Council
Imperial College London
Israel Science Foundation


    • SCOLE model
    • coupled system
    • exact controllability
    • well-posed linear system
    • wind turbine tower


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