Empirical state-space representations for Theodorsen's lift model
S. L. Brunton and C. W. Rowley
Journal of Fluids and Structures (submitted), April 2012.
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 airfoil 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.
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