C172R FLT CREW HAS CTL PROB; DECLARES AN EMER AND DIVERTS TO CPK.

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ON A TRAINING FLT WITH ONE OF MY STUDENTS; WE ENCOUNTERED LOSS OF AILERON CTL. WE HAD JUST RECOVERED FROM SLOW FLT; WHEN I ASKED HER TO MAKE A TURN. SHE SAID SHE COULDN'T; SO I TOOK THE CTLS AND ATTEMPTED THE TURN. IT WAS AS IF THE CTLS WERE FROZEN. I STILL HAD ELEVATOR CTL; BUT NOT AILERON CTL. I RECYCLED THE FLAPS THINKING THAT MAYBE THE AILERONS WERE STUCK. AFTER SEVERAL ATTEMPTS TO MANIPULATE THE CTLS; I DECIDED IT WAS BEST TO LAND. I CALLED NORFOLK APCH AND DECLARED AN EMER. I DECIDED TO LAND IN CHESAPEAKE AS IT WAS A SMALLER ARPT (LESS REROUTING OF TFC) AND IT WAS CLOSER. I LANDED WITHOUT INCIDENT AND SECURED THE ACFT ON THE RAMP. SEVERAL HRS LATER; MY BOSS TOLD ME THAT MY STUDENT HAD UNKNOWINGLY HIT THE AUTOPLT ENGAGE BUTTON. WHEN IT ENGAGES; IT GIVES NO INDICATION OF BEING ON AND AUTOMATICALLY GOES INTO 'STABILIZE' MODE; WHICH WOULD RENDER THE CTLS USELESS. THERE IS A SMALL LIGHT THAT ILLUMINATES WHEN IT IS ON; BUT IS ON THE FAR L SIDE AND OUT OF MY VIEW. THE AUTOPLT EXPERIENCE I HAVE IS WITH SYS THAT KEEP HDGS; ALTS; AND RATES OF CLB. ALSO; IN MY EXPERIENCE; AN AUTOPLT WOULD ALLOW CTL MOVEMENT. I DID NOT THINK TO CHK THE AUTOPLT BECAUSE I HAD NOT ENGAGED IT OR GIVEN IT AN ASSIGNED HDG. I HAVE ALWAYS THOUGHT OF WING-LEVELERS BEING ON LARGER ACFT.