COMMUTER FLC FAILS TO MAKE XING RESTR IN DSCNT.

Narrative

ACFT WAS DIRECT TO CGX MEIGS FIELD; CHICAGO CGX FROM BVT VOR. AT APPROX 60 MI FROM CGX; I WAS CLRED TO CROSS 10 MI S OF CGT VOR AT 4000 FT. THIS NAVAID WAS NOT IN FMS FLT PLAN OR ON OUR RTE OF FLT. I STARTED ACFT DOWN AS COPLT FOUND AND TUNED CGT. ACFT RATE OF DSCNT INITIALLY WAS FINE TO CROSS ON ALT. AT THE SAME TIME I WAS RECEIVING ATIS FOR MEIGS AND WAS DISCOVERING IT WAS GOING BELOW MINIMUMS; AND WE NEEDED TO GET READY FOR AN APCH TO MDW. COULDN'T GET ATIS EARLIER AS IT WAS VERY BROKEN. THE ACFT WAS DSNDING INTO SOLID IMC; ICING AND IT WAS BECOMING MODERATE TURB AS WELL. I SLOWED THE ACFT TO REDUCE THE TURB. AUTOPLT WAS ON. I WAS DISTR FROM RECOGNIZING SLOWER RATE OF DSCNT BY SEVERAL ISSUES IN COCKPIT: RAPIDLY DECAYING WX AT DEST AND ALT; TURB; AND SETTING UP ACFT FOR NEW APCH; AND INFORMING PAX OF OUR PLANS. I CROSSED ASSIGNED FIX AT APPROX 1500 FT ABOVE ASSIGNED ALT. JUST PRIOR TO XING; I DISCOVERED PROB AND STARTED TO INCREASE RATE OF DSCNT. CTLR QUESTIONED US ON OUR POS. COPLT TOLD HIM WE WERE 5500 FT.