fadec is the main controller of gas turbine engine like fuel supply etc and also fadec senses every action and of A/c.
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FADEC means "full authority digital engine control." A FADEC takes total control of the engine, not allowing the pilot to do anything but tell the FADEC to make the engine go faster or slower. Now here's the problem: when all the sensors feeding data to the FADEC are working properly, this is a great system but if one or more sensors feeds bad data to the FADEC, the system is more than happy to put the engines in a mode that will cause the plane to fly straight into the ground...which has happened on Airbuses.
It is possible to get a plane that doesn't have a FADEC system, but they're getting rarer.