PVT INSTRUCTOR PLT GETS INVOLVED WITH UNEXPECTED WX FACTORS UPON HIS RETURN TO HIS HOME ARPT.

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ON MY RETURN TO BHM; I ENCOUNTERED UNFORECAST RAIN AND TURB AS I NEARED BHM. AFTER SEVERAL VECTORS BY APCH FOR SPACING; I WAS FINALLY CLRED FOR THE APCH. PRIOR TO THE OM I STUDIED THE APCH PLATE TO CHK THE DSCNT PROFILE. I COMMENCED DSCNT TO THE FIRST STEP DOWN ALT. DURING THE DSCNT I NOTICED THAT MY ATTITUDE INDICATOR WAS NOT AGREEING WITH THE OTHER INSTS; SO I RETRIEVED MY COVER FROM THE GLOVE BOX AND COVERED THE INSTR FACE. ABOUT THIS TIME BHM APCH CALLED AND ASKED MY ALT; I RESPONDED 'PASSING THROUGH 1900.' I THEN REALIZED 1900 WAS 100 FT BELOW THE PRESCRIBED ALT; SO I CLBED BACK TO 2000 TO WAIT FOR THE DSCNT TO THE MDA WHICH WAS 1200 FT MSL. ON THE DSCNT I ENCOUNTERED VERY HVY RAIN; AND IMMEDIATE TURB; AND NOTICED THAT QUITE A BIT OF R CRAB WAS NEEDED TO TRACK THE LOC. AT 1220 FT; I STILL DID NOT HAVE THE RWY ENVIRONMENT IN SIGHT; AND I WAS CONSIDERABLY S OF THE LOC. AS I STARTED CORRECTING TO RETURN TO THE LOC; BHM TWR CALLED AND ADVISED THAT THEY HAD RECEIVED A LOW ALT ALERT ON MY ACFT. SURE ENOUGH MY ALTIMETER INDICATED APPROX 1100 FT. I CALLED FOR A MISSED APCH; BUT TWR ASKED ME TO LEVEL OFF AT MDA AND FLY RWY HDG AND LET THEM KNOW IF I SAW THE 'LIGHTS.' AFTER A FEW SECONDS I DID SEE THE 'LIGHTS;' ADVISED TWR AND WAS CLRED TO LAND. WHEN THE AI FAILED; I SHOULD HAVE REQUESTED AN ASR APCH AND NOTIFIED ATC OF THE FAILURE. I ALSO SHOULD HAVE GOTTEN MORE THAN THE 6 HRS SLEEP I GOT THE PREVIOUS NIGHT; AND I SHOULD HAVE EATEN BREAKFAST. I BELIEVE THAT FATIGUE; AND HUNGER PLAYED A MAJOR ROLE IN MY POOR PERFORMANCE DURING THIS FLT.