GA PLT DEVIATES OFF COURSE DURING GPS APCH AND IS VECTORED BACK BY CTLR.

Narrative

APCHING RICHMOND; GIVEN ILS RWY 34; RADIO TFC WAS LIGHT; PRACTICE APCHS WERE BEING APPROVED. WX WAS NO CEILING; 3 MI VISIBILITY IN HAZE; SO I ASKED FOR GPS RWY 34 WITH JUNKI INTXN AS IAF; FOR PRACTICE AND PROFICIENCY PURPOSES. ALWAYS SEEM TO GET ILS WHEN TRAVELING; SO THOUGHT SLOW TIME WOULD BE GOOD TIME FOR PRACTICE. ACFT WAS ON AUTOPLT; WHICH WAS DOING A BAD JOB IN THE LOC MODE. I WAS EXPERIMENTING WITH GETTING ON COURSE USING HEADING MODE; THEN SWITCHING BACK TO LOC MODE SEEMED TO WORK BETTER. UPON PASSING FIX JUST BEFORE FAF; I STARTED DOWN FROM 2000 FT TO 1600 FT; WAS WATCHING TO MAKE SURE GPS WENT INTO FLASHING MODE; BUT FAILED TO MAKE THE L TURN TO FINAL APCH COURSE. ABOUT THE TIME I REALIZED I WAS OFF COURSE; RICHMOND APCH CALLED AND SAID GET BACK TO 2000 FT SINCE I WAS NOT ESTABLISHED ON FINAL. AS I WAS STARTING A TURN; THEY CALLED BACK FOR 'IMMEDIATE' TURN TO 300 DEGS; WHICH I DID. REESTABLISHED ON COURSE AND PROCEEDED TO LAND. TWR CALLED; I PHONED IN. THEY HAD ANOTHER PLANE ON DOWNWIND FOR ILS AND MY PATH BEFORE THE TURN; WOULD INTERFERE WITH THIS PLANE. LATER SHE CALLED AND SAID WAS NOT A PROB. MY ERRORS WERE; COMPLACENCY AND DISTR WITH AUTOPLT.