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.

The F-35 has it, but military pilots wouldn't want it. FADEC systems have no manual override; if the FADEC quits working, so does the engine. The Air Force uses digital engine controls on planes like the C-17 and C-130J, but they'd want to be able to override the system if necessary.

I think it's Hydro-Mechanical Control.

It's actually fadec (full authority digital engine control)

The FADEC already has power prior to engine start. In fact it controls the entire start sequence. It receives power under normal starting conditions via an ECBU ; the acft will have power from either an external source, the APU, or an operating engine. The alternator stator provides power to the FADEC once the engine reaches 10% NG. This way the engine is entirely self sustaining once started and during the majority of start sequence. Should the alternator stators fail, power is then given from the ECBU again (28v DC power source).