Reduced order controllers for Burgers' equation with a nonlinear observer

Atwell, Jeanne ; Borggaard, Jeffrey ; King, Belinda

International Journal of Applied Mathematics and Computer Science, Tome 11 (2001), p. 1311-1330 / Harvested from The Polish Digital Mathematics Library

Résumé

A method for reducing controllers for systems described by partial differential equations (PDEs) is applied to Burgers' equation with periodic boundary conditions. This approach differs from the typical approach of reducing the model and then designing the controller, and has developed over the past several years into its current form. In earlier work it was shown that functional gains for the feedback control law served well as a dataset for reduced order basis generation via the proper orthogonal decomposition (POD)@. However, the test problem was the two-dimensional heat equation, a problem in which the physics dominates the system in such a way that controller efficacy is difficult to generalize. Here, we additionally incorporate a nonlinear observer by including the nonlinear terms of the state equation in the differential equation for the compensator.

Détail

Publié le : 2001-01-01

Zbl 1051.93045

EUDML-ID : urn:eudml:doc:207557

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