A new hierarchical modelling framework for active control: making waves in interfacial flow-based technologies

We are surrounded by situations that depend on a controlled outcome in our day-to-day lives, ranging from controlling the evacuation of crowds, to efficient drug delivery, or designing efficient cooling systems inside high performance computing centres. Most real-life scenarios rely on complicated models which are too complex to tackle analytically or computationally, and so it is common to use simplified models which provide a tractable setting, allowing not only for a detailed description and analysis of the problem, but also for the development of rigorous control approaches to drive the behaviour of the system towards a desired state.

Such control methodologies focus on the underlying models and it is not always clear how the resulting controls affect the original real-world system itself. The aim of this proposal is to develop a systematic modelling approach with control at its heart at multiple simplification levels, accounting for the physical effects of a chosen actuation mechanism.

The simplified models will not only provide us with a framework where controls can be rigorously derived, but also facilitate the translation of their action closer to the real-world scenario in an integrated manner for the first time.

In order to concentrate the developed mathematical and computational capabilities, the proposal will tackle a canonical problem at the interface between fluid mechanics, control theory, scientific computing and industrial mathematics, namely the control of falling liquid films. This problem has received significant attention within all of the above research communities, with key contributions from the present investigators.

In recent years, attention has shifted towards the ability to use the resulting mathematical models and controls as guidance for specific applications, such as preventing defects in coatings for LCD screen manufacturing or enhancing heat/mass transfer for microchip cooling. We will analyse controls acting through the automated use of mechanical inputs such as air blades (or air jets) in order to steer the dynamics of the liquid-air interface to a desired outcome. Within this context, the available mathematical toolkit can be characterised as:

1.Weakly nonlinear models: the simpler models we consider, highly versatile and efficient. They provide an environment where mathematical analysis, control design and rapid numerical calculations are possible. However they are only applicable for very simple scenarios.

2. Advanced reduced-order models: more realistic models, but their complex nature renders analytical results almost impossible. However control development based on certain assumptions is still viable, and the resulting controls were recently shown to be reliable.

3. Direct numerical simulations: provide highly accurate solutions of the full model and do not rely on any modelling assumptions. However they are restrictively expensive unless efficiently guided.

The above levels are to be bound together by a novel model-predictive control (MPC) approach that will enable efficient communication between the various models and subsequent experimental data. We will focus on the usage of air jets as the control actuation mechanism - a targeted liquid cooling approach which comes in answer to the highly relevant industrial challenge of improving the efficiency of large scale computing and data storage centres.

The key overarching challenge lies in the robust translation of novel mathematical control techniques towards a level in which they become informative and can steer technological progress. While seemingly intuitive, this is in a context in which the main communities are often separated ideologically. This work, through the research itself as well as an ambitious and non-traditional dissemination plan, aims to heal this divide and provide a framework for advancement of control-theoretical results towards exciting new regimes of significant practical interest.