C560 AUTOPLT UNEXPECTEDLY DISCONNECTED DURING DSCNT CAUSING THE ACFT TO CLB RATHER THAN DSND AS CLRED.

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MY COPLT AND I WERE FERRYING FROM APF TO TPA FOR A PAX TRIP TO PBI. WE WERE IN CRUISE FLT AT 14000 FT MSL; APPROX 50 MI S OF TPA. THE COPLT WAS FLYING WITH THE AUTOPLT ENGAGED. THIS WAS A SHORT FLT SO MY WORKLOAD WAS HIGH WITH PUTTING CHARTS AWAY. GETTING THE ATIS AND TALKING ON THE RADIO. ZMA CALLED AND ASKED US TO DSND TO 11000 FT MSL. I ACKNOWLEDGED ZMA WITH A READBACK TO 11000 FT MSL AND THEN DIALED 11000 FT INTO THE ALT ALERTER AND MY COPLT CONFIRMED 11000 FT WITH ME. THE COPLT STARTED THE AIRPLANE DOWN TO 11000 FT MSL WITH THE AUTOPLT ENGAGED. MY ATTN WAS DIVERTED AWAY FROM THE INST PANEL WHEN ALL OF A SUDDEN THE AUTOPLT DISENGAGED AND THE PLANE ABRUPTLY PITCHED UP AND STARTED A RAPID ASCENT. I THEN LOOKED UP AND NOTICED ON THE ALTIMETER THAT WE WERE GOING THROUGH 14700 FT MSL. I TOOK THE CTLS AND PITCHED THE PLANE DOWN. THE DEV WASN'T MORE THAN 20-30 SECONDS. ZMA NEVER MENTIONED ANYTHING ABOUT THE DEV AND HANDED US OFF TO TPA APCH. I BELIEVE THE PROB AROSE FROM THE AUTOPLT BEING MISTRIMMED. I NOTICED THE AUTOPLT MISTRIM ANNUNCIATOR LIGHT WHEN I TOOK CORRECTIVE ACTION. WHEN YOU GET AN AUTOPLT MISTRIM ANNUNCIATOR LIGHT; YOU MUST TAKE CORRECTIVE ACTION OR THE AUTOPLT WILL DISENGAGE! I BELIEVE MY LACK OF ATTN AND FATIGUE CONTRIBUTED TO THIS DEV. I ALSO BELIEVE MY COPLT'S LACK OF EXPERIENCE AND LACK OF KNOWLEDGE OF THE AUTOPLT SYS CONTRIBUTED TO THE DEV. THIS WAS MY COPLT'S FIRST TOUR AFTER INITIAL IOE.