BE55 PLT HAD A TRACK AND ALTDEV AFTER THE ACFT FLT GUIDANCE SYS DID NOT TURN TO THE HEADING THE PLT EXPECTED.

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AFTER RUN-UP; I CONTACTED BIRMINGHAM TWR AND ADVISED I WAS READY FOR DEP RWY 24 INTXN H4. I WAS IMMEDIATELY CLRED FOR DEP. AFTER DEPARTING WITH THE KFC 200 FLT DIRECTOR ENGAGED; I ENGAGED THE AUTOPLT; WHICH HAD BEEN PRESET TO A HEADING OF 240 DEGS; AND SET THE ELEVATOR TRIM FOR THE PROPER RATE OF CLB. AFTER HDOF TO BIRMINGHAM DEP CTL AND CONTINUING CLB THROUGH 1000 FT; I WAS INSTRUCTED TO TURN TO HEADING 040 DEGS TO INTERCEPT V417; CLB AND MAINTAIN 5000 FT. I DIALED IN THE ASSIGNED HEADING AND THE PLANE BEGAN A STANDARD TURN TO THE ASSIGNED HEADING. AT THIS TIME; I AM CLBING THROUGH; AS I RECALL; 2500-3000 FT; WHEN I REALIZED THE PLANE WAS CONTINUING THROUGH THE ASSIGNED HEADING AND WAS IN A FAIRLY STEEP TURN AND SLIGHT DSCNT. I ADVISED THE CTLR THAT I HAD AN EQUIP PROB AND WHEN ASKED OF MY INTENTIONS; I FIRST INDICATED I WOULD LIKE TO RETURN TO THE ARPT. I AM AT THIS TIME RECOVERING FROM AN UNUSUAL ATTITUDE. AFTER HEARING OTHER PLTS RPTING THE TOPS OF 4200-4500 FT; I ADVISED THE CTLR THAT I WOULD PREFER TO CONTINUE MY CLB ABOVE THE TOPS AND EVALUATE THE SIT ONCE VFR ON TOP. I HAD ALREADY DISENGAGED THE AUTOPLT AND THE EQUIP FAILURE APPEARED TO BE CONNECTED WITH THE KFC 200 FLT DIRECTOR/AUTOPLT. THE CTLR; WHO WAS VERY HELPFUL THROUGHOUT THE INCIDENT; TOLD ME TO DO WHATEVER I NEEDED TO DO. AFTER BREAKING THROUGH THE TOPS AND ADVISING THE CTLR; I WAS INSTRUCTED TO TURN TO A HEADING; AS I RECALL OF 350 DEGS; TO JOIN V417. THE FLT WAS CONTINUED VIA 'VFR ON TOP' UNTIL MY RETURN TO JASPER/WALKER COUNTY (JFX) WHERE I ELECTED THE ILS APCH TO RWY 27. THE ACFT HAS BEEN TAKEN IN FOR INSPECTION.