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Empirical state-space representations for Theodorsen's lift model

Author(s): Brunton, Steven L; Rowley, Clarence W

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Abstract: In this work, we cast Theodorsen's unsteady aerodynamic model into a general form that allows for the introduction of empirically determined quasi-steady and added-mass coefficients as well as an empirical Theodorsen function. An empirically determined Theodorsen model is constructed using data from direct numerical simulations of a flat plate pitching at low Reynolds number, Re=100. Next, we develop low-dimensional, state-space realizations that are useful for either the classical Theodorsen lift model or the empirical model. The resulting model is parameterized by pitch-axis location and has physically meaningful states that isolate the effect of added-mass and quasi-steady forces, as well as the effect of the wake. A low-order approximation of Theodorsen's function is developed based on balanced truncation of a model fit to the analytical frequency response, and it is shown that this approximation outperforms other models from the literature. We demonstrate the utility of these state-space lift models by constructing a robust controller that tracks a reference lift coefficient by varying pitch angle while rejecting gust disturbances.
Publication Date: Apr-2013
Citation: Brunton, Steven L, Rowley, Clarence W. "Empirical state-space representations for Theodorsen's lift model" Journal of Fluids and Structures, 38, 174 - 186, doi:10.1016/j.jfluidstructs.2012.10.005
DOI: doi:10.1016/j.jfluidstructs.2012.10.005
ISSN: 0889-9746
Pages: 174 - 186
Type of Material: Journal Article
Journal/Proceeding Title: Journal of Fluids and Structures
Version: This is the author’s final manuscript. All rights reserved to author(s).

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