  Falling liquid films become unstable due to inertial effects when the fluid
layer is sufficiently thick or the slope sufficiently steep. This free surface
flow of a single fluid layer has industrial applications including coating and
heat transfer, which benefit from smooth and wavy interfaces, respectively.
Here we discuss how the dynamics of the system are altered by feedback controls
based on observations of the interface height, and supplied to the system via
the perpendicular injection and suction of fluid through the wall. In this
study, we model the system using both Benney and weighted-residual models that
account for the fluid injection through the wall. We find that feedback using
injection and suction is a remarkably effective control mechanism: the controls
can be used to drive the system towards arbitrary steady states and travelling
waves, and the qualitative effects are independent of the details of the flow
modelling. Furthermore, we show that the system can still be successfully
controlled when the feedback is applied via a set of localised actuators and
only a small number of system observations are available, and that this is
possible using both static (where the controls are based on only the most
recent set of observations) and dynamic (where the controls are based on an
approximation of the system which evolves over time) control schemes. This
study thus provides a solid theoretical foundation for future experimental
realisations of the control of falling liquid films.
