fadec should be fadeec(full authority digital electronic engine control), but fadec is way nicer to spell
ecu or eec is the brain of the fadec and the fadec includes all parts required for engine control such as fmu or hmu, vsv,vbv, throttle pos, lptcc,hptcc,P & T sensors,etc...
such as grounded27 said, pilots will only know when there's a failure with the fadec syst(depends on the nature and importance of the failure, but alert to flt crew will be different in fuction of the airplane type such as minor fault or fadec maint, etc)
during engine operation the ecu is generally getting his power from it's own generator mounted on the gearbox(for ex on cf6-80 is a dual gen and N2 tach)
FADEC - Wikipedia, the free encyclopedia
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