Rejecting Unknown Harmonic Disturbances in 2 \times 2 Linear Hyperbolic PDEs

In this paper, we solve the problem of rejecting a harmonic disturbance containing unknown frequencies and bias entering a linear hyperbolic system of 1-D partial differential equations at one boundary, using boundary sensing and actuation anticollocated with the disturbance. By combining a full sta...

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Bibliographic Details
Published inIEEE transactions on control systems technology Vol. 25; no. 6; pp. 1935 - 1946
Main Authors Anfinsen, Henrik, Strecker, Timm, Aamo, Ole Morten
Format Journal Article
LanguageEnglish
Published IEEE 01.11.2017
Subjects
Adaptive observers
Backstepping
distributed systems
Frequency control
Frequency estimation
Harmonic analysis
hyperbolic partial differential equations (PDEs)
managed pressure drilling
Observers
Partial differential equations
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Summary:In this paper, we solve the problem of rejecting a harmonic disturbance containing unknown frequencies and bias entering a linear hyperbolic system of 1-D partial differential equations at one boundary, using boundary sensing and actuation anticollocated with the disturbance. By combining a full state feedback controller with an adaptive observer that estimates system states and the disturbance's bias, frequencies, amplitudes, and phases with exponential convergence, the effect of the disturbance is rejected exponentially fast. The theoretical results are applied to a relevant problem from the oil and gas industry, and the performance is demonstrated in a computer simulation.
ISSN:1063-6536
1558-0865
DOI:10.1109/TCST.2016.2631511