PLT OF SMA ON IFR FLT PLAN HAS PARTIAL ENGINE FAILURE AND NEEDS ATC ASSISTANCE TO LAND AT NEARBY ARPT.

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ON AN IFR FLT TO ZZZ1; I WAS IN AND OUT OF CLOUDS AS I SKIMMED THE TOPS OF CUMULUS. THE ACFT WAS PERFORMING NORMALLY WHEN CTR ASKED ME TO CLB TO 11000 FT FOR TERRAIN CLRNC. I HAD NOT BEEN USING CARB HEAT; BUT HAD BEEN IN CLR AIR MOSTLY; WITH BRIGHT SUNSHINE. OAT WAS READING 48 DEGS F. AS I ADVANCED THE THROTTLE TO CLB; THE RPM'S DROPPED ALARMINGLY. I TURNED ON THE CARB HEAT; AND THE RPM'S DROPPED EVEN MORE. THE AIRPLANE WOULD NOT CLB; AND I ADVISED ATC. THEY SWITCHED ME TO APCH. I HESITATED; UNSURE OF WHAT TO DO. DO I GIVE THE CARB HEAT TIME TO WORK? I COULDN'T CLB TO THE HIGHER ALT. WHILE I THOUGHT; THE CTLR SUGGESTED I TURN TOWARDS ZZZ AS A PRECAUTION. I WAS RELUCTANT TO FLY AN APCH BECAUSE I WAS UNFAMILIAR WITH THE FUNCTION OF MY EFIS. WHEN I TOLD HIM THE ENG WAS NOT RESPONDING; HE DECLARED AN EMER AND DIRECTED ME TO DSND AND RPT SIGHTING THE ARPT. THE ENG WAS MAKING PWR; BUT NOT FULL PWR. I SIGHTED THE GND; AND WAS DIRECTED TO TRY TO GET UNDER THE CLOUDS; BUT THEY WERE TOO LOW. I FINALLY DID SEE THE ARPT; BUT WHILE CIRCLING TO LAND; I LOST CONTACT. THE CTLR AND I DECIDED AN ILS WAS OUR BEST BET; SO HE BEGAN VECTORING ME FOR AN INTERCEPT. I WAS UNABLE TO MANAGE FLYING AND READING THE CHART; SO THE CTLR GAVE ME A SURVEILLANCE APCH. I BROKE OUT AT 900 FT LINED UP WITH A RWY; AND MADE AN UNEVENTFUL LNDG. MY UNFAMILIARITY WITH THE LOC DEPICTION ON MY EFIS PREVENTED ME FROM FLYING A NORMAL IFR APCH. I WAS UNCERTAIN OF THE CORRECT PROC FOR APPLYING CARB HEAT IN IMC.