Browsing by Subject "Proper orthogonal decomposition"

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    Low dimensional modelling and Dirichlét boundary controller design for Burgers equation
    (Taylor & Francis, 2004) Efe, M. Ö.; Özbay, Hitay
    Modelling and boundary control for the Burgers equation is studied in this paper. Modelling has been done via processing of numerical observations through proper orthogonal decomposition (POD) with Galerkin projection. This results in a set of spatial basis functions together with a set of ordinary differential equations (ODEs) describing the temporal evolution. Since the dynamics described by the Burgers equation are non-linear, the corresponding reduced-order dynamics turn out to be non-linear. The presented analysis explains how the free boundary condition appears as a control input in the ODEs and how controller design can be accomplished. The issues of control system synthesis are discussed from the point of practicality, performance and robustness. The numerical results obtained are in good compliance with the theoretical claims. A comparison of various different approaches is presented. © 2004 Taylor and Francis Ltd.
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    Proper orthogonal decomposition for reduced order modeling: 2D heat flow
    (IEEE, 2003-06) Efe, M. Ö.; Özbay, Hitay
    Modeling issues of infinite dimensional systems is studied in this paper. Although the modeling problem has been solved to some extent, use of decomposition techniques still pose several difficulties. A prime one of this is the amount of data to be processed. Method of snapshots integrated with POD is a remedy. The second difficulty is the fact that the decomposition followed by a projection yields an autonomous set of finite dimensional ODEs that is not useful for developing a concise understanding of the input operator of the system. A numerical approach to handle this issue is presented in this paper. As the example, we study 2D heat flow problem. The results obtained confirm the theoretical claims of the paper and emphasize that the technique presented here is not only applicable to infinite dimensional linear systems but also to nonlinear ones.