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Title: Optimal boundary control of a model thin-film fiber coating model
This paper considers the control of fluid on a solid vertical fiber, where the fiber radius is larger than the film thickness. The fluid dynamics is governed by a fourth-order partial differential equation (PDE) that models this flow regime. Fiber coating is affected by the Rayleigh–Plateau instability that leads to breakup into moving droplets. In this work, we show that control of the film profile can be achieved by dynamically altering the input flux to the fluid system that appears as a boundary condition of the PDE. We use the optimal control methodology to compute the control function. This method entails solving a minimization of a given cost function over a time horizon. We formally derive the optimal control conditions, and numerically verify that subject to the domain length constraint, the thin film equation can be controlled to generate a desired film profile with a single point of actuation. Specifically, we show that the system can be driven to both constant film profiles and traveling waves of certain speeds.  more » « less
Award ID(s):
2309774
PAR ID:
10509722
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Elsevier
Date Published:
Journal Name:
Physica D: Nonlinear Phenomena
Volume:
457
Issue:
C
ISSN:
0167-2789
Page Range / eLocation ID:
133942
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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