Empirical state-space representations for Theodorsen's lift model

Steven L. Brunton, Clarence Worth Rowley

Research output: Contribution to journalArticlepeer-review

81 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)174-186
Number of pages13
JournalJournal of Fluids and Structures
StatePublished - Apr 2013

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering


  • Reduced order model
  • State-space realization
  • Theodorsen's function
  • Unsteady aerodynamics


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