I think the wobbly prop on the DA 40 (Tdi models) is electronic and you push a button which exercises the CSU. (hope im right there...)
Not quite correct, but close. The prop is hydraulically controlled variable pitch, but the hydraulics are controlled by the ECU (also known as FADEC) and the DA-40 TDI has two of those.
It is not a constant speed in the traditional sense where the RPMs are kept constant regardless of the throttle position. Instead, it has a load lever (0-100%) which controls both the throttle (actually manifold pressure and injected fuel) and the RPMs. It works generally fine and hassle-free, but at 50% load (typical downwind setting) the prop "hunts" a bit.