Many have discussed that in old prayer books Psalm 30 is not printed before Barukh Sheamar, and some have claimed that its addition in Nusach Ashkenaz to that point is probably a mistake, a possible misunderstanding of a Kabbalistic practice, especially in light of Tur Orach Chayim 281:
ויותר נכון מנהג אשכנז לומר כל המזמורים בין ברוך שאמר לישתבח כדי שיהא לכולם ברכה לפניהם וברכה לאחריהם.
And the Ashkenazi custom of saying all the psalms between Barukh Sheamar and Yishtabach is more appropriate, because for all of them there would be a blessing before and after.
It is also related that the Vilna Gaon was against this addition (Maaseh Rav 26). However, since the 19th century in almost all Nusach Ashkenaz prayer books we find Psalm 30 there. Which authorities argued that it should be still said and how did they reason?