PA44 instructor pilot reported a safe landing following the shutdown of an engine.

Attributes
ACN	1726394
Time
Date	202002
Local Time Of Day	0601-1200
Place
Locale Reference	ZZZ.Airport
State Reference	US
Environment
Flight Conditions	VMC
Light	Daylight
Aircraft 1
Make Model Name	PA-44 Seminole/Turbo Seminole
Operating Under FAR Part	Part 91
Flight Phase	Cruise
Route In Use	None
Flight Plan	None
Component
Aircraft Component	Engine
Person 1
Function	Pilot Flying Instructor
Qualification	Flight Crew Flight Instructor Flight Crew Instrument Flight Crew Multiengine Flight Crew Commercial
Experience	Flight Crew Last 90 Days 142 Flight Crew Total 1547 Flight Crew Type 60
Events
Anomaly	Aircraft Equipment Problem Critical

Narrative:

After introducing an engine failure in flight to a student; after doing a full shutdown and restart; as I went to cruise the rpm out with the prop lever; the RPM's had no decrease and were above red line. I then used the 'prop overspeed checklist' and completed it and there was little/no change. The left engine was producing strong vibrations and rattling so I made the decision to shut down the engine and secure it. I believe the propeller governor failed which caused the red line RPM which I was unable to reduce properly. To further prevent another occurrence of this situation; it is best for maintenance to check the governor more often to verify its usability.

Original NASA ASRS Text

Title: PA44 instructor pilot reported a safe landing following the shutdown of an engine.

Narrative: After introducing an engine failure in flight to a student; after doing a full shutdown and restart; as I went to cruise the rpm out with the prop lever; the RPM's had no decrease and were above red line. I then used the 'Prop Overspeed Checklist' and completed it and there was little/no change. The left engine was producing strong vibrations and rattling so I made the decision to shut down the engine and secure it. I believe the propeller governor failed which caused the red line RPM which I was unable to reduce properly. To further prevent another occurrence of this situation; it is best for maintenance to check the governor more often to verify its usability.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.