High Precision Positioning Control to Reference Input Given as Periodic Functions of Rotational Angle to Spindle.

Abstract

In positioning control systems, the reference input is frequently given as periodic functions of the rotational angle of the spindle. To obtain high precision, it is very effective to design a repetitive controller in ‘time domain’ while the spindle is rotating ideally. However, disturbances caused by the spindle structure and machining, which are dependent on the rotational angle, will result in rotational speed fluctuations of the spindle, and this will hinder all efforts to improve the precision of such systems.This paper proposes a systematic approach in ‘angle domain’ to design a control system when the rotational speed of the spindle is fluctuated by the rotational angle dependent disturbances. A model in ‘angle domain’ is obtained as a linear periodic model by introducing a transformation from ‘time domain’ into ‘angle domain’. Focusing on it, a repetitive controller is designed in ‘angle domain’ as to trace a periodic reference input in ‘angle domain’ and eliminate the effects of such rotational speed fluctuations of the spindle. And a repetitive ripple-free deadbeat controller is designed to obtain a desired transient response.