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  5. Point-actuated feedback control of multidimensional interfaces
 
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Point-actuated feedback control of multidimensional interfaces
File(s)
hxz031.pdf (2 MB)
Published version
Author(s)
Tomlin, Ruben
Noronha Moreira Antunes Gomes, Susana
Type
Journal Article
Abstract
We consider the application of feedback control strategies with point actuators to multidimensional evolv-ing interfaces in order to stabilise desired states. We take a Kuramoto–Sivashinsky equation as a test case;this equation arises in the study of thin liquid films, exhibiting a wide range of dynamics in differentparameter regimes, including unbounded growth and full spatiotemporal chaos. The controls correspondphysically to mass-flux actuators located in the substrate on which the liquid film lies. In the case of par-tial state observability, we utilise a proportional control strategy where forcing at a point depends only onthe local observation. We find that point-actuated controls may inhibit unbounded growth of a solution,if the actuators are sufficient in number and in strength, and can exponentially stabilise the desired state.We investigate actuator arrangements, and find that the equidistant case is the most favourable for con-trol performance, with a large drop in effectiveness for poorly arranged actuators. Proportional controlsare also used to synchronise two chaotic solutions. When the interface is fully observable, we constructmodel-based controls using the linearisation of the governing equation. These improve on proportionalcontrols, and are applied to stabilise non-trivial steady and travelling wave solutions.
Date Issued
2019-12-16
Date Acceptance
2019-10-27
Citation
IMA Journal of Applied Mathematics, 2019, 84 (6), pp.1112-1142
URI
http://hdl.handle.net/10044/1/74850
URL
https://academic.oup.com/imamat/article/84/6/1112/5678719
DOI
https://www.dx.doi.org/10.1093/imamat/hxz031
ISSN
0272-4960
Publisher
Oxford University Press (OUP)
Start Page
1112
End Page
1142
Journal / Book Title
IMA Journal of Applied Mathematics
Volume
84
Issue
6
Copyright Statement
© The Author(s) 2019. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. This is an Open
Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which
permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (E
Identifier
https://academic.oup.com/imamat/article/84/6/1112/5678719
Grant Number
EP/L020564/1
EP/K034154/1
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
feedback control
interfacial dynamics
multidimensional Kuramoto-Sivashinsky equation
point actuators
proportional control
thin films
KURAMOTO-SIVASHINSKY EQUATION
NONLINEAR DISSIPATIVE SYSTEMS
FINITE DETERMINING PARAMETERS
LINEARLY IMPLICIT METHODS
FALLING LIQUID-FILMS
HYDRODYNAMIC INSTABILITY
LAMINAR FLAMES
HEAT-TRANSFER
SYNCHRONIZATION
FLOW
Applied Mathematics
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
0199 Other Mathematical Sciences
Publication Status
Published
Date Publish Online
2019-12-16
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