EXECUTING A GAR AT TYS DUE TO WINDSHEAR ALERT; CARJ-200 FO BECOMES FOCUSED WITH INCORRECT AUTOPLT OP; OVERSHOOTS ASSIGNED ALT; REQUIRING CAPT TO TAKE ACFT CTL.

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THE FO WAS FLYING A VISUAL APCH TO RWY 23L; KNOXVILLE ARPT. ON SHORT FINAL; WE GOT A WINDSHEAR ALERT ON OUR PFD'S. THE FO EXECUTED A MISSED APCH WITH THE PROPER CALLS. I WAS RESPONDING TO THE MISSED APCH CALLS AND ALSO COMMUNICATING WITH ATC. WHEN I CALLED THE TWR AND TOLD THEM OF THE MISSED APCH; THE TWR CLRED US TO 4000 FT; AND CHANGED US TO APCH CTL. AFTER CLEANING UP THE ACFT AND CHANGING FREQS; I NOTICED WE WERE CLBING THROUGH 4000 FT AT A GOOD RATE OF CLB. I TOLD THE FO TO LEVEL AT 4000 FT. THE FO KEPT REPEATING THAT THE ACFT WAS NOT RESPONDING. I TOLD HIM TO PUSH THE NOSE DOWN AND LEVEL AT 4000 FT. AGAIN HE SAID THE ACFT WAS NOT RESPONDING. THE ACFT HAD CLBED TO 5000 FT; AT WHICH TIME I TOOK CTL OF THE ACFT AND DSNDED TO 4000 FT. WE RETURNED TO THE ARPT AND LANDED WITHOUT FURTHER INCIDENT. WHEN ON THE GND; I ASKED THE FO WHY HE DIDN'T LEVEL AT 4000 FT AND WHY HE KEPT SAYING THAT THE ACFT WAS NOT RESPONDING; AS IT FLEW FINE. HE SAID THAT HE THOUGHT THE AUTOPLT WAS ENGAGED; SO DURING THE MISSED APCH; HE WAS PUSHING THE BUTTONS ON THE FCP; BUT NOTHING WAS HAPPENING. THE FO HAD BECOME ENGROSSED WITH WHY THE AUTOPLT WAS NOT DOING WHAT HE WAS TELLING IT TO DO. HE HAD BECOME FOCUSED ON THE AUTOMATION AND IT NEVER OCCURRED TO HIM TO HAND FLY THE ACFT. I WAS LATE IN TAKING CTL OF THE ACFT BECAUSE OF TALKING ON THE RADIOS AND PERFORMING PNF DUTIES. THIS INCIDENT HAPPENED LATE AT NIGHT. WE BOTH HAD BEEN ON DUTY FOR 11+ HRS; AND IT WAS OUR 5TH LEG OF THE DAY. AUTOMATION IS GREAT; BUT IF IT'S NOT DOING WHAT YOU WANT; YOU MUST TAKE CTL.