  The fluidic pinball is a geometrically simple flow configuration with three
rotating cylinders on the vertex of an equilateral triangle. Yet, it remains
physically rich enough to host a range of interacting frequencies and to allow
testing of control laws within minutes on a laptop. The system has multiple
inputs (the three cylinders can independently rotate around their axis) and
multiple outputs (downstream velocity sensors). Investigating the natural flow
dynamics, we found that the first unsteady transition undergone by the wake
flow, when increasing the Reynolds number, is a Hopf bifurcation leading to the
usual time-periodic vortex shedding phenomenon, typical of cylinder wake flows,
in which the mean flow field preserves axial symmetry. We extract dynamically
consistent modes from the flow data in order to built a reduced-order model
(ROM) of this flow regime. We show that the main dynamical features of the
primary Hopf bifurcation can be described by a non-trivial lowest-order model
made of three degrees of freedom.
