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The first abnormality id a rapid decrease and a slow recovery but the second one is a slow decrease and a rapid recovery. 2 very different events.
Can You use Serial monitor and do some Serial printouts of strategic data? That could help You get closer to the reason for the disturbances.
Sorry. I got it wrong but my comment about Serial still stands.
The event appears quite repeatable with respect to time so I would expect it has nothing to do with the actual PID loop, more likely an issue with the input signal.
Anything in the project have a time based event, like turning on a motor?