Feedback Control for Aerodynamics (Preprint)
AIR FORCE RESEARCH LAB WRIGHT-PATTERSON AFB OH AIR VEHICLES DIRECTORATE
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The two-dimensional Burgers equation is used as a surrogate for the governing equations to test order-reduction and control design approaches. This scalar equation is selected because it has a nonlinearity that is similar to the Navier-Stokes equation, but it can be accurately simulated using far fewer states. However, the number of states required is still well above that for which a controller can be designed directly. Two approaches for order reduction are used. In both approaches, proper orthogonal decomposition POD, also known as Karhunen-Loeve decomposition or principal component analysis, is used with Galerkin projection. In the first method, the traditional POD approach of selecting the modes to be retained in the reduced-order model is based on the energy content of the modes. In the second method, balanced truncation is used to select the appropriate modes. Both approaches capture the dynamics of the input-output system and are used for control design.
- Fluid Mechanics