What was found
MAIN HYDRAULICS: DURING A CLIMB GOING THROUGH 11,500 FEET WE HAD A STAB-MIS-COMP ANNUNCIATOR LIGHT COME ON , AFTER ABOUT 30 SECONDS THE AUTO PILOT DISCONNECTED AND THE AIRPLANE PITCHED DOWN AGGRESSIVELY. IT TOOK THE PIC AND SIC TOGETHER TO PULL BACK ON THE YOKE TO STOP THE DESCENT. THE TRIM WHEEL WOULD NOT MOVE FORWARD OR AFT WHEN TRYING TO MOVE IT. AFTER SLOWING DOWN TO 200KTS WE WERE ABLE TO MOVE TRIM WHEEL AND CONTROL THE AIRPLANE. WE RAN THE APPROPRIATE CHECKLIST AND THE STAB-MIS-COMP ANNUNCIATOR LIGHT WENT OUT. HOWEVER, ON FINAL THE STAB-MIS-COMP CAME BACK ON AND STAYED ON UNTIL WE SHUT DOWN THE ENGINES AT FBO // SIGNOFF// APPLIED AIR DATA TEST SET. TESTED STAB SYSTEM SEVERAL TIMES. NOTED THE AIR SPEED SWITCH WORKING INTERMITTENTLY. REMOVED OLD AND INSTALLED NEW SWITCH. LEAK AND OPERATIONAL CHECKS OF SYSTEM GOOD. WORK DONE IAW 560XL MM CH 34-11-01. OLD P/N D45C-24 S/N 2233 NEW P/N D45C-24 S/N 2321