Stabilisation of falling liquid films with restricted observations

TL;DR

This paper develops a control method to stabilize falling liquid films using limited observations and actuators, by approximating the complex Navier-Stokes equations with simpler models and applying the control strategy to the full system.

Contribution

It introduces a novel control approach for stabilizing thin liquid films with restricted observations, bridging simplified models and complex PDEs.

Findings

Control strategy successfully stabilizes the film in simulations.

Hierarchical approximation enables practical control despite complex PDEs.

Method addresses challenges of limited observations in fluid control.

Abstract

We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the system state is challenging in physical settings, so methods able to take this into account are important. The Navier-Stokes equations modelling the flow are a complex, highly nonlinear set of PDEs, so standard control theoretical results are not applicable. Instead, we chain together a hierarchy of increasingly idealised approximations, developing a control strategy for the simplified model which is shown to be successfully applied to simulations of the full system.