The oil pump pushes engine oil through the filter and into the bearings, timing chain, cam phasers and other moving parts. On many newer engines the pump's output is varied by the engine computer through a control solenoid, so it can run at lower pressure when less is needed.
How its codes differ
P06DD means the engine computer commanded the variable oil pump control but oil pressure did not respond as expected (stuck off). Low oil level comes first; then GM and FCA bulletins point at a broken control solenoid, debris jamming the pump, a failed relief valve or a worn pump.
P06DE is the opposite condition (control stuck on). GM groups it with P06DD and P0521 on its 1.2L and 1.3L three-cylinder engines, where debris in the pump is a documented cause.
P0521 is an oil pressure sensor range code. It can come from a real pressure problem caused by the pump, but the sensor itself is also a common cause; a mechanical gauge tells them apart.
On some Jeep engines the pump is built into the timing chain cover, and on many GM V8s it sits behind the timing cover, so pump replacement is a major job.
Oil pump pressure control not responding, as if stuck off
Severity: Inspect soon
Signs it's failing
Check engine light with P06DD, P06DE or P0521
Low oil pressure warning light or message
Engine speed limited (for example to 3,300 rpm on some Jeeps)
Ticking, rattling or knocking from the engine
How to test it
With the engine off on level ground, check the oil level on the dipstick. If the code appeared right after an oil change, mention that to the shop: GM notes that a drained filter and oil gallery can set P06DD. (Low risk)
If the oil pressure warning light comes on or the engine ticks, rattles or knocks, stop driving and switch the engine off. (Low risk)
Ask a dealer whether a bulletin or service update applies to your VIN; GM has an oil pump screening test for some engines. (Low risk)
Confirming oil pressure with a mechanical gauge, commanding the pump control with a scan tool and replacing the pump or timing cover are jobs for a shop. (Best left to a shop)
Warning: Running an engine with low oil pressure can cause serious damage almost immediately, and these tests need the engine running with hot oil. Leave them to a shop.
After the repair
Check the oil level again after the first drive and top up to the full mark with the oil specified for your engine.
Confirm the oil pressure warning stays off at idle and while driving.
Clear codes only after the repair and confirm they do not return after several drives.