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Feedback control of falling liquid films

Banff International Research Station for Mathematical Innovation and Discovery

We discuss the use of feedback control in suppressing the inertial instabilities of a falling liquid film. In this setup, an input to the system, e.g. local fluid injection, is chosen in response to real time observations of the interface shape. If the control scheme is designed with perfect knowledge of the governing equations and implemented with access to instantaneous observations of the entire system state, feedback control offers almost unlimited scope to change the system dynamics. Both of these requirements fail in any practical implementation, but we would hope to be able to achieve effective control strategies based on reasonably accurate models and observations of only a few key variables. Falling liquid films have a hierarchy of long-wave models of increasing complexity, which offers an ideal environment to explore robustness to model choice. We find that the success of control schemes based on low order models is dependent on the method of actuation chosen; injection of fluid has a direct effect on interface dynamics and simple control strategies work well across many models, while selective substrate heating has a much more subtle effect on dynamics and control schemes are correspondingly more sensitive to details of the flow.

Mathematics; Fluid mechanics; Approximations and expansions; Fluid dynamics

video/mp4

Author affiliation: University of Manchester

2019-10-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72076

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/