How does EEC/FADEC recognize/anticipate engine acceleration/deceleration?
You probably need to go ask your professor for clarification.  But let's look at it this way: what would it mean if $Pt3 &gt; Pt3_{min}$ and $N2/\sqrt{\theta}&gt;N2/\sqrt{\theta}_{idle}$. It means that the engine is probably NOT at idle. So in that situation, if you move the throttle, you probably do want to increase thrust, but not from idle.  The EEC may have different control schedules for idle vs above idle operation.