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978-3-8439-1704-9, Reihe Mathematik
Optimal flow control based on POD and MPC and an application to the cancellation of Tollmien-Schlichting waves
221 Seiten, Dissertation Technische Universität Darmstadt (2014), Softcover, B5
We present a reduced-order model based on Proper Orthogonal Decomposition (POD) which is suitable for active control of fluid dynamical systems. The basis functions are generated from appropriate snapshots of Finite Element based simulations. We propose a special snapshot ensemble which can be generated beforehand and takes the possible variation of controls into account. Thus the problem of unmodelled dynamics in the POD approach can be avoided.
Due to the choice of the snapshot ensemble we can quantify the approximation properties of POD based schemes under control and obtain an a-priori error estimate.
We combine the reduced order model with a Model Predictive Control (MPC) approach for the cancellation of Tollmien-Schlichting waves in the boundary layer of a flat plate. In order to influence the flow a body force is induced by a plasma actuator. By optimal control of the plasma actuator parameters it is possible to reduce or even cancel the Tollmien-Schlichting waves and delay the transition to turbulence.
The effectiveness of the approach is shown in numerical experiments.