LOW TIME PLT IN A JET HAD LOW FUEL ON APCH AT CMH.

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I WAS RETURNING FROM AN AIR EVENT IN MY EXPERIMENTAL JET. THE HEADWINDS WERE STRONGER THAN FORECAST AND I WAS FLT PLANNED FOR A HIGHER FLT LEVEL WHICH IMPACTED MY FUEL USE. UPON RECEIVING AN AMENDED CLRNC TO A FIX; FURTHER FROM THE ARPT THAN WHAT I FILED; I COMPLIED BUT TOLD THE CTLR I WAS IN A MINIMUM FUEL SIT. HE ASKED IF I NEEDED TO DIVERT. I REPLIED THAT I WOULD BE OK TO GO TO DEST ARPT. I WAS TURNED OVER TO APCH CTLR; WAS GIVEN VECTORS AND SET UP FOR THE ILS TO RWY 28L. WHEN I WAS TURNED OVER TO THE FINAL APCH CTLR; HE TOLD ME THEY TURNED ME IN TOO TIGHT AND THAT I WOULD BE INSIDE THE MARKER AND THAT WAS UNACCEPTABLE TO HIM. I SAID IT WOULD BE ALL RIGHT AND SET THE AUTOPLT TO INTERCEPT THE LOC. THE AUTOPLT MALFUNCTIONED AND THE AIRPLANE FLEW THROUGH THE LOC. HE THEN GAVE ME A VECTOR BACK TO THE LOC. I SET THE AUTOPLT TO STAND BY AND TRIED TO TURN THE PLANE. THE AUTOPLT WAS STILL ENGAGED; SO I WENT THROUGH THE DISCONNECT PROC. BY THIS TIME AT 180 KTS; I WAS NOT GOING TO BE ABLE TO STABILIZE THE APCH. BEFORE I COULD COMMUNICATE THE MALFUNCTION TO THE CTLR; HE DECLARED AN EMER RADAR VECTOR APCH; SAYING I WAS OBVIOUSLY 'IN TROUBLE.' HE TOLD ME TO DSND TO 1500 FT AGL; GAVE ME A HDG TO FLY. I COMPLIED. I CALLED THE ARPT IN SIGHT. HE TOLD ME TO STAY WITH HIM; AND LANDED WITHOUT ANY FURTHER PROBS. THE EVENTS STARTED WITH MY MINIMUM FUEL. I COULD HAVE DIVERTED AND NOT HAD THE FUEL CONCERN. I ALSO COULD HAVE HAND FLOWN THE APCH NOT USING THE AUTOPLT; THEN THE MALFUNCTION WOULD NOT HAVE BEEN A FACTOR. THE CTLR COULD HAVE VECTORED ME FOR ANOTHER APCH. I NEVER DECLARED AN EMER. I WAS NEVER 'IN TROUBLE' AS THE CTLR SAID. I WAS FLYING THE PLANE; COPING WITH THE MALFUNCTION AND WOULD HAVE FLOWN THE APCH OVER. I BELIEVE THAT I EVEN MAINTAINED ALT IN SPITE OF THE MALFUNCTION. THE CTLR WAS VERY UPSET DURING THE WHOLE EVENT AND PERHAPS WAS CONCERNED ABOUT OTHER ACFT. BUT HAD I BEEN ABLE TO EVEN TELL HIM ABOUT THE MALFUNCTION OF TO GIVE ME A VECTOR TO DO THE APCH OVER; THE SIT COULD HAVE BEEN HANDLED ROUTINELY.