New Directions in Flow Control: Reduced Order Modeling, Nonlinear Analysis and Control Design Methods for the Control of Fluid Flow Problems

Flow control refers to the ability to manipulate fluid flow so as to achieve a desired change in its behavior, which offers many potential technological benefits, such as reducing fuel costs for vehicles and improving effectiveness of industrial processes. Presently there is a lack of sufficient mathematical analysis and control design tools for flow control problems. This includes mathematical models that are amenable to control design. The research presented in this book makes an effort at closing this gap by 1) presenting a reduced-order modeling method utilizing a novel technique for input separation on Proper Orthogonal Decomposition (POD)/Galerkin Projection (GP) based models, 2) introducing a technique based on averaging theory and center manifold theory so as to reveal certain structures embedded in the model, and 3) developing nonlinear analysis and control design approaches for the resulting model. The theory is complemented by examples and case studies as appropriate, including the case of cavity flow control.