A controller controls precession of a gyroscope that oscillates about a precession axis perpendicular to a spin axis and a roll axis of the gyroscope. To do so, the controller detects a deviation of a center of the oscillation away from a nominal center. The precession is caused by roll of the gyroscope about the roll axis and imposes decreasing amounts of damping upon the roll as the precession moves away from the nominal center. The controller reduces the deviation of the center of the oscillation by applying an asymmetric amount of braking to the precession when the precession and the deviation are in a same direction relative to when the precession and the deviation are in opposing directions.