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Point-actuated feedback control of multidimensional interfaces

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Title: Point-actuated feedback control of multidimensional interfaces
Authors: Tomlin, R
Noronha Moreira Antunes Gomes, S
Item 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.
Issue Date: 16-Dec-2019
Date of Acceptance: 27-Oct-2019
URI: http://hdl.handle.net/10044/1/74850
DOI: 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/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (E
Funder's Grant Number: EP/L020564/1
EP/K034154/1
Keywords: 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
Online Publication Date: 2019-12-16
Appears in Collections:Mechanical Engineering
Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences
Faculty of Engineering