My understanding is that the EEC is the Engine Electronic Control. Now if the system is anything like the tiny little gas turbine on my aircraft, the EEC has very little to do with the Fuel Control Unit, which is a hydromechanical device that functions entirely automatically and is self-powered, using fuel pressure derived from the shaft-driven HP pump as the motive power for its various servo functions.
Sounds awfully like you're trying to compare this to a GE engine, Sven?
The Rolls Royce Trent has a fuel pump and a Fuel Metering Unit. The pump is mechanically driven. The FMU is further downstream and simply meters whatever fuel comes out of the pump (according to EEC electronic input).... and delivers this metered fuel to the spray nozzles in the combustor. It would be too confusing to compare the two engine types
Rgds.
NSEU