Low-dimensional state-space representations for classical unsteady aerodynamic models
S. L. Brunton and C. W. Rowley
AIAA Paper 2011-476, 49th AIAA Aerospace Sciences Meeting , January 2011.
This work develops reduced-order models for the unsteady aerodynamic forces on a small wing in response to agile maneuvers and gusts. In particular, the classical unsteady models of Wagner and Theodorsen are cast into a low-dimensional, state-space framework. Low order state-space models are more computationally efficient than the classical formulations, they may be naturally incorporated to the design of flight controllers, and may be extended to include nonlinearities. A method to empirically tune Theodorsen's model and cast it into state-space form is presented. Reduced order models linearized at various angles of attack, from alpha=0 to 25 degrees, are obtained from the indicial response using the eigensystem realization algorithm. The behavior and performance of the models are investigated in the frequency domain, and by testing on a rapid pitch maneuver with large angle of attack. Direct numerical simulations are performed using an immersed boundary projection method for a flat plate at Reynolds number 100.
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