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In this paper, we present a discussion of the proper orthogonal decomposition (POD) as applied to simulation and feedback control of the one dimensional heat equation. We provide two examples of input collections to which the POD process is applied. First, we apply POD directly to the nite element basis of linear B-splines. Next we additionally include time… (More)

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… (More)

Two variations of a method for reducing controllers for systems described by partial diierential equations (PDEs) are compared. In the rst method, the controller reduction is accomplished by projection of a large scale nite element approximation of the PDE controller onto a low order basis that is computed using the proper orthogonal decomposition (POD).… (More)

- Belinda B. King
- Universität Trier, Mathematik/Informatik…
- 1997

- Belinda B. King, Ekkehard W. Sachs
- Comp. Opt. and Appl.
- 2000

In this paper, the compensator based reduced order control design framework of 2] is modiied to yield low order systems with guaranteed stability margins. This result is achieved through use of a logarithmic barrier function. In addition, a reduced basis method is formulated in which the compensator equations are approximated on uneven grids; guaranteed… (More)

- Jeanne A. Atwell, Belinda B. King
- SIAM J. Scientific Computing
- 2004

A method for reducing controllers for systems described by partial diierential equations PDEs is presented. This approach diiers from an often used method of reducing the model and then designing the controller. The controller reduction is accomplished by projection of a large scale nite element approximation of the PDE controller onto low order bases that… (More)

- Anthony L. Faulds, Belinda B. King
- 2000

The task of placing sensors for purposes of feedback control is vital in order to obtain information necessary for accurate state estimation. In this paper, we present a method for optimal location of sensors which is motivated by the feedback control law for the distributed parameter system. In particular , we show how feedback functional gains reflect… (More)

This note is concerned with the formulation of a damped second order system as a rst order dynamical system on a product space. This problem comes from the desire to have explicit representations of the innitesimal generator of the rst order system and, in particular, of the domain of this operator. This analysis is motivated by the need to nd specic… (More)

An important technique in design of controllers for uid ow is that of compensator design. The use of compensators allows for measurement of the state at a small number of places in the uid and estimation of the state based on those measurements. However, questions arise regarding what states to measure, what locations to place sensors and how to design low… (More)

We consider the problem of obtaining integral representation of feedback operators for damped hyperbolic control systems. We show that for the wave equation with Kelvin-Voigt damping and non-compact input operator, the feedback gain operator is Hilbert-Schmidt. This result is then used to provide an explicit integral representation for the feedback operator… (More)