I've been trying to find some roughly contemporary examples of a king/prince being captured in battle, thus far without much success. The WotAS had several occasions when kings were almost captured - Frederick at Baumgarten, George at Dettingen, and Carlos at Velletri - but these 18th century royals always seem to get lucky. The closest thing I can think of is the "capture" of the Saxon royal children in 1745, who were still in Dresden when it was occupied by the Prussians, but they weren't really prisoners and I rather doubt that their situation had any bearing on the peace negotiations.
I suspect the example that will be on most people's minds will be the capture of Francis I of France at the Battle of Pavia in 1525 and the humiliating (for France) Treaty of Madrid which followed. On the one hand, it's over 200 years in the past but on the other Pavia is only a short distance up the road from Piacenza. The outcome - holding him prisoner until a treaty imposing massive territorial concessions on France was agreed - may still be a desired end game for Austria.