Study of Lonlinear Control of Pecision Positioning Systems

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Precision of a positioning unit is heavily influenced by coulomb friction and backlash which exist in the mechanism of the positioning system. Dimension variation and deformation due to force or heat also cause inaccuracy of positioning. This study is to investigate control methods which overcome these obstructing factors commonly found in positioning units and make posible an ultra-high precision positioning. The outline of the study results is given below.1. Preparatory StudySeveral schemes of control were tested on an existing linear positioning system which consists of a ball screw and positioning table driven by a servo-motor. Among the tested control schemes the sliding mode control in the variable structure ontol system was found most promising. An ordinary PID feedback control combined with a pulse mainipulating input was also found practical in its simplicity and good performance.2. Assemblage of a High Precision Positioning UnitA new positioning system was assembled in the same construction as the existing system with a much higher precision. The position of the positioning table was measured by an optical linear encoder of 10nm resolution. The reading of the encoder was directly fed back to the control loop.3. Comparison of Control SchemesMathematical models of the third order, the fourth order and the fifth order were constructed. For each model a state feedback control system and a sliding mode control system were designed and tested for performance by both simulations and experiments. In either control scheme, for the third order model neglected higher order modes caused high frequency vibration in responses. The fifth order model had a difficulty in determining good parameter values in identification process. The sliding mode control designed with the fourth order model gave the best results.