How does centre of pressure change with angle of attack?
This Wikipedia article explains that the movement of the center of pressure with changes in angle of attack depends on the airfoil shape.
In summary:


For a symmetric airfoil, as angle of attack and lift coefficient
change, the center of pressure does not move. It remains around the
quarter-chord point for angles of attack below the stalling angle of
attack.  
For a conventionally cambered airfoil, the center of    pressure lies
a little behind the quarter-chord point at maximum lift coefficient (large angle of attack), but as lift coefficient reduces (angle of attack reduces) the center of pressure moves toward the rear.
For a reflex-cambered airfoil, the center of pressure lies a little ahead of the quarter-chord point at maximum lift coefficient (large angle of attack), but as lift coefficient reduces (angle of attack reduces) the center of pressure moves forward.


I do not have a simple expression that can be used to predict this movement of the center of pressure, but I suppose a computational fluid dynamics package can be used to model this for the specific airfoils used on the aircraft.