DA40 Flight Instructor reported malfunction of Engine Control Unit (ECU) during climbout and returned to the departure airport.

Narrative

Aircraft was written up yesterday for similar problem. On run up ensured that ECU (Engine Control Unit) test was good as well as running up engine to 100%. On takeoff; indications normal; slight overspeed of prop but this is normal; climb out noticed rpm did not reduce upon pulling power to 92%. Advised ATC that we needed to return to ZZZ; also at this point ZZZ had gone IFR; so we filed IFR with departure to come back. ATC vectored us across the Runway XXL localizer at 2500 ft. for sequence; at this point we could hold 88 kias and altitude without overspeeding prop to red (45% load max) in accordance with the QRH. ATC gave us a vector a little far from the field so I asked for them to keep us close in case even though the situation was stable. I (Instructor Pilot) took over flying after first vector back to ZZZ. Vectored for ILS XXL right around joining the localizer had dual ECU fail and advised Tower we would be unable to go around; [the student] ran QRH; annunciations persisted. Elected to land flaps up so we could maintain speed with as little power as possible. Landed and taxied back uneventfully. Followed up with TRACON once on the ground.This issue was written up day prior and taken care of by Maintenance but as far as I can tell was not flown. On the ground all of our indications were good. Problem did not replicate until we were in the air. Suggest maintenance flight next time when a prop governor jam is involved.