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Adaptive control of a nonlinear two-dimensional wing-flap system operating in an incompressible flowfield is studied. An output feedback control law is implemented, and its performance toward suppressing flutter and limit cycle oscillations, as well as reducing the vibrational level in the subcritical flight speed range, is demonstrated. The control law proposed here is applicable to minimum phase systems, and conditions for stability of the zero dynamics are provided. The control objective is to design a control strategy to drive the pitch angle to a setpoint while adaptively compensating for uncertainties in all of the aeroelastic model parameters. It is shown that all of the states of the closed-loop system are asymptotically stable. Furthermore, an extension is presented to include flap actuator dynamics. Simulations have been presented to validate the efficacy of the proposed strategy. Pertinent conclusions have been outlined. Nomenclature b = semichord of airfoil c h , c α = structural damping coefficients in plunge and pitch c lα , c mα = lift and moment curve slopes per angle of attack c lβ , c mβ = lift and moment curve slopes per control surface deflection h = plunging displacement I α = mass moment of inertia of airfoil about elastic axis k h , k α = structural spring stiffness in plunge and pitch L = aerodynamic lift M = aerodynamic moment m = mass of airfoil t = time U = freestream velocity x, y = horizontal and vertical coordinates x α = dimensionless distance from elastic axis to midchord, positive rearward α = pitch angle β = flap angle ρ = air density

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This paper presents a numerical validation of a thin‐walled beam (TWB) finite element (FE) model of a realistic wind turbine rotor blade. Based on the theory originally developed by Librescu et al. and later extended to suit FE modelling by Phuong, Lee and others, this computationally efficient yet accurate numerical model is capable of capturing most of the features found in large blades including thin‐walled hollow cross section with variable thickness along the section's contour, inner reinforcements, arbitrary material layup and non‐linear anisotropic fibre‐reinforced composites; the present application is, for the time being, restricted to linearity. This one‐dimensional (1D) FE model allows retaining information of different regions of the blade's shell and therefore approximates the behaviour of more complex three‐dimensional (3D) shell or solid FE models more accurately than typical 1D FE beam models. A 9.2 m rotor blade, previously reported in specialized literature, was chosen as a case study to validate the static and dynamic behaviour predicted by a TWB model against an industry‐standard 3D shell model built in a commercial software tool. Given the geometric and material complexities involved, an excellent agreement was found for static deformation curves, as well as a good prediction of the lowest frequency modes in terms of resonance frequencies, mode shapes and frequency response functions; the highest (sixth) frequency mode shows only a fair agreement as expected for an FE model. It is concluded that despite its simplicity, a TWB FE model is sufficiently accurate to serve as a design tool for the recursive analyses required during design and optimization stages of wind turbines using only readily available computational tools. Copyright © 2011 John Wiley & Sons, Ltd.

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