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Point-actuated feedback control of multidimensional interfaces
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Tomlin, Ruben J. and Gomes, Susana N. (2019) Point-actuated feedback control of multidimensional interfaces. IMA Journal of Applied Mathematics, 84 (6). pp. 1112-1142. doi:10.1093/imamat/hxz031 ISSN 0272-4960.
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Official URL: https://doi.org/10.1093/imamat/hxz031
Abstract
We consider the application of feedback control strategies with point actuators to stabilise desired interface shapes. We take a multidimensional Kuramoto--Sivashinsky equation as a test case; this equation arises in the study of thin liquid films, exhibiting a wide range of dynamics in different parameter regimes, including unbounded growth and full spatiotemporal chaos. In the case of limited observability, we utilise a proportional control strategy where forcing at a point depends only on the local observation. We find that point-actuated controls may inhibit unbounded growth of a solution, if they 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 optimal, with heavy penalties for poorly arranged actuators. We additionally consider the problem of synchronising two chaotic solutions using proportional controls. In the case when the full interface is observable, we construct feedback gain matrices using the linearised dynamics. Such controls improve on the proportional case, and are applied to stabilise non-trivial steady and travelling wave solutions.
| Item Type: | Journal Article | |||||||||
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Journal or Publication Title: | IMA Journal of Applied Mathematics | |||||||||
| Publisher: | Oxford University Press | |||||||||
| ISSN: | 0272-4960 | |||||||||
| Official Date: | 16 December 2019 | |||||||||
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| Volume: | 84 | |||||||||
| Number: | 6 | |||||||||
| Page Range: | pp. 1112-1142 | |||||||||
| DOI: | 10.1093/imamat/hxz031 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | This is a pre-copyedited, author-produced version of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record is available online at: Ruben J Tomlin, Susana N Gomes, Point-actuated feedback control of multidimensional interfaces, IMA Journal of Applied Mathematics, Volume 84, Issue 6, December 2019, Pages 1112–1142 https://doi.org/10.1093/imamat/hxz031 | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Date of first compliant deposit: | 6 November 2019 | |||||||||
| Date of first compliant Open Access: | 18 December 2019 | |||||||||
| RIOXX Funder/Project Grant: |
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