When starting up, there is an engine shudder

Is the engine missing, or does it feel like a bad motor mount?

You most likely have one of two issues. Balance shafts on pumpe duese engines like to fail. Also, the camshaft and lifters wear out and cause lack of power, smoking, shuddering.

If one of these components are only slightly worn out, it typically won't throw a fault, but it's still a good idea to scan the engine.

Also, one-way pullies on the alternator can also cause a vibration/noise that will be constantly present regardless if the vehicle is warm or cold.