Journal Article

Well-posedness and controllability of a wind turbine tower model

Xiaowei Zhao and George Weiss

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 28, issue 1, pages 103-119
Published in print March 2011 | ISSN: 0265-0754
Published online January 2011 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dnq034
Well-posedness and controllability of a wind turbine tower model

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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 Xc1. 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 Xc. In this second case, we assume that the tower is uniform.

Keywords: wind turbine tower; coupled system; SCOLE model; exact controllability; well-posed linear system

Journal Article.  0 words. 

Subjects: Mathematics

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