Reduced-Order Model-Based Feedback Control of Flow Over an Obstacle Using Center Manifold Methods

摘要

In this paper, we consider a boundary control problem governed by the two-dimensionalnBurgers’ equation for a configuration describing convective flow over an obstacle. Flowsnover obstacles are important as they arise in many practical applications. Burgers’nequations are also significant as they represent a simpler form of the more generalnNavier–Stokes momentum equation describing fluid flow. The aim of the work is to de-nvelop a reduced-order boundary control-oriented model for the system with subsequentnnonlinear control law design. The control objective is to drive the full order system to andesired 2D profile. Reduced-order modeling involves the application of an L2 optimiza-ntion based actuation mode expansion technique for input separation, demonstrating hownone can obtain a reduced-order Galerkin model in which the control inputs appear asnexplicit terms. Controller design is based on averaging and center manifold techniquesnand is validated with full order numerical simulation. Closed-loop results are comparednto a standard linear quadratic regulator design based on a linearization of the reduced-norder model. The averaging/center manifold based controller design provides smoothernresponse with less control effort and smaller tracking error.