Optimal Control of an Oscillating Body Using the Adjoint Equation and ALE Finite Element Methods

Abstract

The purpose of this study is to determine the optimal angle of wings which is attached to an oscillating body located in an incompressible flow. At present, there are some bridges with wings to prevent oscillation by the wind. The angle of the wing is very important so as to minimize the oscillation of bridge. In this study, the angle to minimize the oscillation is presented by optimal control theory. In order to minimize the oscillation, the performance function which is expressed by the displacement of body is introduced. The performance function should be minimized satisfying state equation. This problem can be transformed into the minimization problem by the Lagrange multiplier method. As a minimization technique, the weighted gradient method is applied. For the discretization, the arbitrary Lagrangan-Eulerian(ALE) finite element method is applied to solve the FSI problem. The optimal control of an oscillating bridge is shown as numerical study.