The invention relates to a system for the active adjustment of a radial gap size (S) between a blade tip (13) of at least one compressor stage (11) and / or at least one turbine stage (12) of an aircraft engine (100) and a housing (10) at least one compressor stage (11) and / or at least one turbine stage (12) surrounded, characterized by a) a model-based adjusting device (M), wherein the time-dependent gap size (S) by the model-based adjusting device (M) is approximated and taken into account only the influencing variables whose time-dependent, deformation behavior is equal to or slower than the time-dependent deformation behavior of the housing (10), where b) serves as setpoint (w) the gap size in the cold state (Sk), this is reduced by at least one pre-stored value of a gap component (Sm) determined at maximum thrust of the aircraft engine (100), and c) by the model-based actuator g (M) a manipulated variable (y) for a cooling system (200) of the housing (10) can be determined. The invention further relates to an aircraft engine with such a system (1).
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