Infinite dimensional and reduced order observers for Burgers equation
Date
2005Source Title
International Journal of Control
Print ISSN
0020-7179
Publisher
Taylor & Francis
Volume
78
Issue
11
Pages
864 - 874
Language
English
Type
ArticleItem Usage Stats
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Abstract
Obtaining a representative model in feedback control system design problems is a key step and is generally a challenge. For spatially continuous systems, it becomes more difficult as the dynamics is infinite dimensional and the well known techniques of systems and control engineering are difficult to apply directly. In this paper, observer design is reported for one-dimensional Burgers equation, which is a non-linear partial differential equation. An infinite dimensional form of the observer is demonstrated to converge asymptotically to the target dynamics, and proper orthogonal decomposition is used to obtain the reduced order observer. When this is done, the corresponding observer is shown to be successful under certain circumstances. The paper unfolds the connections between target dynamics, observer and their finite dimensional counterparts. A set of simulation results has been presented to justify the theoretical claims of the paper.
Keywords
Computer simulationPartial differential equations
Problem solving
Control engineering
One-dimensional Burger's equations
Feedback control