  This paper presents an extension of a recently proposed hierarchical control
framework applied to a cryogenic system. While in the previous work, each
sub-system in the decomposition needed to show at least one component of the
control input, in the present contribution, this condition is removed enabling
a higher flexibility in the definition of the decomposition graph. The impact
of this extended flexibility on the computation time is shown using the same
cryogenic station where a decomposition in four sub-system is made possible
(instead of two in the previous setting).
