Wide open question with a lot of grey area.
Basically:
A plc is told to go and it does it thing until either a predetermined set of conditions is met or somebody pulls the plug on it.
Distributed control can be made up of a group of plc's communicating to a supervisor that can cause interaction with various plc's process controllers etc.
Typically, the supervisor will "download" operating parameters to the distributed units ie set points....
The unit is then responsible for achieving that setpoint.
This is very generic. Can you be more specific?
