The following information came from a Google search:
The 1st Minnesota Heavy Artillery mustered in at St. Paul, and Rochester, Minnesota, between November 1864 and February 1865. Many of the officers were recruited from discharged veteran sergeants of the 1st Minnesota Volunteer Infantry Regiment and corporals from the 3rd Minnesota Volunteer Infantry Regiment, 4th Minnesota Volunteer Infantry Regiment, and 5th Minnesota Volunteer Infantry Regiment. The regiment was assigned as part of the garrison of Chattanooga, Tennessee, for its entire career and saw no combat action. The 1st Minnesota "Heavies" were mustered out of service on September 27, 1865.
The last surviving veteran of the American Civil War from either side, Albert Woolson, was a member of the regiment.
* Lt. Colonel Luther L. Baxter, February 25, 1865 to April 26, 1865.
* Colonel William Colvill, April 26, 1865 to May 6, 1865.
* Colonel Luther L. Baxter, May 7, 1865 to September 27, 1865.
Casualties and total strength
87 enlisted men died of disease. Total fatalities were 87.
Andrews, General Christopher Columbus ed., (1891). Minnesota in the Civil and Indian Wars. Pioneer Press.