TY - JOUR

T1 - Well-posedness and controllability of a wind turbine tower model

AU - Zhao, Xiaowei

AU - Weiss, George

N1 - Funding Information:
The research of the second author in the area of coupled systems is supported by the grant 701/10 of the Israel Science Foundation.
Funding Information:
The first author’s research was supported by an EPSRC (Engineering and Physical Sciences Research Council) international doctoral scholorship, an ORSAS (Overseas Research Students Awards Scheme) award and a British Council RXP (Researcher Exchange Programme) Award, during his PhD study at Imperial College London.

PY - 2011/3

Y1 - 2011/3

N2 - 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.

AB - 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.

KW - SCOLE model

KW - coupled system

KW - exact controllability

KW - well-posed linear system

KW - wind turbine tower

UR - http://www.scopus.com/inward/record.url?scp=79953220469&partnerID=8YFLogxK

U2 - 10.1093/imamci/dnq034

DO - 10.1093/imamci/dnq034

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AN - SCOPUS:79953220469

SN - 0265-0754

VL - 28

SP - 103

EP - 119

JO - IMA Journal of Mathematical Control and Information

JF - IMA Journal of Mathematical Control and Information

IS - 1

ER -