Medium Transport; Low Wing; 2 Turbojet Eng
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 3
Situational Awareness; Training / Qualification; Distraction; Communication Breakdown
Airspace Violation All Types; Deviation / Discrepancy - Procedural Other / Unknown; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Provided Assistance
Aircraft; Procedure; Human Factors
I was training on Sector 1. Aircraft was cleared for the RNAV Runway 30 approach at GYY. Aircraft went missed and asked to hold while they waited for the weather to improve. Certified Professional Controller-In Training (CPC-IT) elected to vector the aircraft over Lake Michigan due to the complexity of the session (ZAU refusing handoffs on MDW departures; multiple missed approaches at MDW) and no suitable place to hold. I concurred with his decision.CPC-IT instructed Aircraft X to turn to the east; and there was no response. He tried again; and again no response. I took over the sector due to complexity and continued vectoring aircraft into MDW while attempting to contact Aircraft X on my frequency and 121.5. I also asked GYY Airport Traffic Control Tower (ATCT) and SBN Approach to reach out and issue an immediate turn to a heading of 090.Aircraft X entered a 3;300 feet MVA at 3;000 feet; almost directly over the Hancock building over downtown Chicago.  Aircraft also passed inside of ORD ATCT airspace. Communication was restored as the aircraft passed over PWK.We should have avoided issuing a heading that pointed at a higher MVA and ORD airport; even if the aircraft was 20 miles away at the time.  A 360 heading would have kept the aircraft over Lake Michigan and the aircraft would have simply flown toward Wisconsin and lower MVA's. We used a 320 heading with the intention of turning away from ORD and the higher MVA (which was attempted more than 20 times); which resulted in the NORDO aircraft violating the MVA.
C90 instructor reports of an aircraft that is NORDO and enters a MVA that is higher then the aircrafts altitude; also this aircraft violated Class B and C airspace.