Study of Lonlinear Control of Pecision Positioning Systems

定位机构中存在的库仑摩擦和齿隙严重影响定位单元的精度。由于力或热引起的尺寸变化和变形也会导致定位不准确。本研究旨在探讨克服定位单元中常见的这些阻碍因素的控制方法，使超高精度定位成为可能。研究结果概述如下。预备研究几种控制方案进行了测试，现有的直线定位系统，其中包括一个滚珠丝杠和定位工作台由伺服电机驱动。在所测试的控制方案中，滑模控制在变结构ontol系统中被认为是最有前途的。一种普通的PID反馈控制与脉冲控制相结合的方法也被证明是可行的，其简单且性能良好.高精度定位单元的组装一个新的定位系统被组装在与现有系统相同的结构中，具有更高的精度。定位台的位置通过10nm分辨率的光学线性编码器测量。编码器的阅读值直接反馈给控制回路.控制方案的比较建立了三阶、四阶和五阶数学模型。对于每个模型的状态反馈控制系统和滑模控制系统的设计和性能测试的仿真和实验。在这两种控制方案中，对于三阶模型，忽略高阶模态会导致响应的高频振动。五阶模型在辨识过程中难以确定好的参数值。采用四阶模型设计的滑模控制效果最好。

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.