AN ACR BAE146 HAD AN ACFT EQUIP PROB ICE DETECTION MALFUNCTION. THIS LED TO CTL OSCILLATION AND ALL 4 ENGS ROLLING BACK TO LESS THAN IDLE THRUST.

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CTL COLUMN PITCH OSCILLATION NOTED AT FL290; IMC CONDITIONS. CTL COLUMN PITCH OSCILLATION CHKLIST FOLLOWED; MAX DURATION 30-45 SECONDS +/- 1 INCH YOLK OSCILLATION. ENG ROLLBACK; UNABLE TO RESTART #1 ENG. #1 ENG SHUT DOWN FOR APPROX 25 MINS. #2 ENG SHUT DOWN APPROX 5-10 MINS. #2; #3; AND #4 ENGS RECOVERED AND LANDED WITHOUT INCIDENT. ICE DETECTOR FAILED TO INDICATE ICING CONDITIONS. ACFT DIVERTED TO DSM. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTRS FLY THE BAE146 IN THE MOUNTAINS NEAR DEN. AT THE TIME OF THE INCIDENT; THEY WERE FLYING AT FL260; ABOUT 25 MI FROM ANY TSTM. THERE WERE SEVERAL TSTMS IN THE AREA AND ICING. THE CTL OSCILLATION BUCKED THE ACFT SO MUCH; 'I THOUGHT WE MIGHT GO ON OUR BACK!' THE CHKLIST REQUIRES THE ACFT TO BE SLOWED BY OPENING THE SPD BRAKES. THE RPTR DID THIS AND CLOSED THE THROTTLES AS WELL. THE OSCILLATION CAME UNDER CTL; BUT THE ENGS WENT TO 'SUB IDLE' WITH NO THRUST OUTPUT. BOTH GENERATORS AND HYD SYS WENT OFF LINE. THERE WERE ELECTRICAL PWR SPIKES WHICH MAY HAVE COMPOUNDED THE PROB. THE ACFT WAS ON BATTERY PWR ONLY. THE RPTR SHUT DOWN #2 ENG; THEN WAS ABLE TO RELIGHT IT AT 10000 FT. ENGS #3 AND #4 REGAINED PWR AT 10000 FT BY THEMSELVES. #1 ENG WAS NEVER REGAINED. THE FLC NEVER USED THE WORD 'EMER' AS THEY 'WERE FIGHTING FOR THEIR LIVES.' THEY GOT THE MESSAGE ACROSS TO ZAU; WHO GAVE THEM ASSISTANCE TO DSM. THE CREW FLEW A SIMULATOR WITH AN FAA INSPECTOR TO SHOW THAT THEY 'KNEW HOW TO DECLARE AN EMER.' THIS WAS AN EXERCISE 'JUST TO FILL A SQUARE.' THE RPTR CONFERRED WITH THE FAA; NTSB AND ENG MANUFACTURER. THE ACFT IS NOW 'RESTR TO FL260; RIGHT IN THE MIDDLE OF THE TSTMS AND ICE.' A MODIFICATION IS BEING MADE TO THE ENGS TO ADD HEAT FURTHER AFT TO HEAT THE FUEL CTLRS. THE RPTR HAS HEARD OF ANOTHER INCIDENT WHERE THE ENGS COULD NOT BE RESTARTED UNTIL 1000 FT OVER THE OCEAN. THE ENG AND TAIL ANTI-ICE WERE ON AT ALL TIMES BEFORE AND DURING THE RPTR'S INCIDENT. SUPPLEMENTAL INFO FROM ACN 336755: AS OSCILLATION WAS SUBSIDING; WE NOTED ALL 4 ENGS HAD ROLLED BACK TO SUB-IDLE AND WOULD NOT RESPOND TO THRUST LEVER INPUT. DECLARED EMER.