It is Paul's spirit and he can restrain it
This is part of Paul's argument, so it is worth looking at the verse before:
For if I pray in a tongue, my spirit prays, but my mind is unfruitful.
We see mind being contrasted with spirit here, as we do in verse 15. However (just proceeding), here we are told explicitly it is Paul's spirit and Paul's mind. We can only think of it as the Holy Spirit in 15, if we also think it refers to a Holy Mind. The parallelism demands that of a good reader.
Is this voluntary?
Yes, and that is what the entire chapter is about. It is about Paul urging the Corinthians to behave orderly by controlling themselves.
In verse 12 we read:
So you too, since you are eager to possess spiritual gifts, strive to excel for the edification of the church.
That is the Corinthians are to put in effort to edify the church. Verses 13-25 (which include 25) explain that this effort involves praying less exclusively in the spirit, and more with the mind.
Verses 27-28, demonstrate that Paul is calling on them to restrain themselves.
27 If anyone speaks in a tongue, it must be by two or at the most three, and each one in turn, and one is to interpret; 28 but if there is no interpreter, he is to keep silent in church; and have him speak to himself and to God.
Indeed, the book of Corinthians is about Paul giving instructions to defeat divisions. In Chapter Five, sexual morality. In chapter Six, lawsuits discouraged. Closer to fourteen, chapter Eleven: hair covering and the Lord's Supper
In Chapter Thirteen Paul talks about love, and in Chapter Fourteen they are to restrain themselves out of love, it being more important to demonstrate love for others than tongues speaking.
In conclusion, Paul is writing to the Corinthians about real divisions and he is giving them a real standard that he expects them to adopt. Much of this standard is about praying and singing in the spirit (the person's spirit) in contrast with the mind (the person's mind) and Paul's standards are adoptable and he gives them to be adopted.