keep up vs keep on

Keep up the good work.
Keep on good working.

If a person is doing a good job and you appreciate it (like it) which of these two will you use?

What are the differences between these two phrases?

In my opinion the first phrase is a bit wrong.
Why?
One can keep up with some other one but can one (a person) keep up with something?

Thanks

The first phrase is correct. It is the second one which is incorrect.

Keep up the good work.
Keep working well.

Now I consider both original phrases

Keep up the good work.
Keep on good working.

incorrect for the situation.

Keep working well! This one is now my favorite one. (for the situation)

Thanks