The parametric equations of the desired spindle shaft motion in tool plane are derived and the optimal motions of the shaft in the magnetic bearing planes are calculated. It is assumed that the non-circular orbit of the spindle shaft is a desired operating points set from a control system point of view, and this operation point is a known (i.e., programmed) function of time and angular position. The function is programmed in such a way, that its time constants are much bigger than time constants of the control system that should place the geometrical center of the shaft in the operation point, so dynamics of the programmed motion can be omitted. The parameters of linearized model of the open-loop system are strongly influenced by the position of the operating point. Therefore, the adaptive control system namely gain-scheduling method is designed.

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