What was found
CRUISE FL370 SCANNING OVERHEAD PRIOR TO DESCENT. OBSERVED RT EEC ALTN IN MODE SWITCH. NO ACCOMPANY EICAS. REFERENCED QRH, DECIDED TO PUT BOTH EEC IN SAME MODE "ALTN". ACCOMPLISHED QRH. UPON PUSHING THROTTLES UP N1 AND EGT BEGAN FLUXING. FF AT IDLE WOULD NOT GO BELOW 4.0 AND AS WE DESCENDED IT WOULD CLIMB. AT 13,000 FT FF WAS APPROX 11.2 AND WE COULD NOT DESCEND. FUEL WAS AT APPROX 10.5. LOOKED FOR OTHER RELIEF IN QRH COULD NOT FIND ANY. AT THIS POINT ENG WAS NOT CONTROLLABLE. FOLLOWED QRH IN SHUTTING DOWN RT ENG. DECLARED EMERGENCY PRIOR TO SHUTTING ENG DOWN. WINDMILLED FOR 10-15 MIN. R&R RT ENGINE ECU AS PER MM 73-21-15-4, ALL TEST PASS ALSO R&R CONTROL ALTERNATOR AS PER MM 73-21-08-4-3 ALL TEST PASS, RAN RT ENGINE AT IDLE FOR 5 MINUTES AS PER JRH ALL PARAMETERS NORMAL, ECU P/N 2121M41P04 S/N LMDD9231. CONTROL ALTERNATOR P/N 510846-1 S/N B81013, ALL WORK WAS ALSO WORKED IN CONFUCTIONS WITH MTSI 76-00-4987, A/C OK FOR SERVICE.