Skyhawk 172/Cutlass 172
Flight Crew Flight Instructor
Flight Crew Total 450
Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Provided Assistance; Flight Crew Landed As Precaution; Flight Crew Returned To Departure Airport; Flight Crew Requested ATC Assistance / Clarification
Aircraft
Engine roughness that resulted in the instructor taking over controls; [notified ATC] and making a precautionary landing a ZZZ.  Engine didn't want to stay running at anything less than full power; Carburetor heat was applied but didn't seem to help the problem. Maximum power was 2100 rpm in straight and level flight.
Flight Instructor reported engine roughness resulted in a precautionary landing.