Methods of precisely positioning a rotor of a machine into one or more service positions for the purpose of servicing the machine. In some embodiments, the machine includes A rotor and a stator segmented into multiple removable stator modules. During servicing, a stator-module replacement tool is precisely located in any one or more of multiple service positions corresponding to the multiple stator modules by selectively energizing the machine. In other embodiments, the machine includes a stator and a rotor having multiple removable permanent magnets corresponding respectively to multiple service positions. During servicing, the rotor is precisely located in any one or more of multiple service positions corresponding to the permanent magnets by selectively energizing the machine. A servicing control system is disclosed for controlling the excitation of a machine stator in a manner that effects precise positioning of the rotor into a selected service position.