  The task of implementing a supervisory controller is non-trivial, even though
different theories exist that allow automatic synthesis of these controllers in
the form of automata. One of the reasons for this discord is due to the
asynchronous interaction between a plant and its controller in implementations,
whereas the existing supervisory control theories assume synchronous
interaction. As a consequence the implementation suffer from the so-called
inexact synchronisation problem. In this paper we address the issue of inexact
synchronisation in a process algebraic setting, by solving a more general
problem of refinement. We construct an asynchronous closed loop system by
introducing a communication medium in a given synchronous closed loop system.
Our goal is to find sufficient conditions under which a synchronous closed loop
system is branching bisimilar to its corresponding asynchronous closed loop
system.
