多轴运动系统非线性轮廓重复跟踪的主从交叉耦合迭代学习控制

针对多轴运动系统非线性轮廓的重复跟踪，传统时域交叉耦合迭代学习控制器（Cross-coupled iterative learning control，CCILC）的设计，各轴间的耦合算子计算精度要求高，计算效率低.本文提出一种主从交叉耦合迭代学习控制方法.基于主从控制设计方法，主动轴采用时域CCILC，从动轴采用位置域交叉耦合迭代学习控制（Position domain CCILC，PDCCILC）.保证各轴间运动同步性，同时减轻对耦合算子精确性的依赖.因而可以引入轮廓误差矢量法估算耦合算子提高计算效率.采用Lifting的系统时域矩阵展开方法对所提出的算法进行了稳定性分析和性能分析.基于一个两轴毫米级运动平台，三种典型非线性轮廓跟踪（即半圆、抛物线和螺旋线）的数值仿真和实验分析验证了所提出算法的有效性.

A Master-slave Cross-coupled Iterative Learning Control for Repetitive Tracking of Nonlinear Contours in Multi-axis Precision Motion Systems

In traditional time domain cross-coupled iterative learning control (CCILC) design, the requirements of high calculation accuracy of coupling gains between axes and low computational efficiency restrict its application to nonlinear contour tracking in repetitive tasks. This paper presents a master-slave cross-coupled iterative learning control. Based on the master-slave control design concept, the master motion axis applies time domain CCILC, while the slave motion axis adopts position domain CCILC (PDCCILC). The proposed PDCCILC control can improve synchronization between axes as well as relieve the dependence on accuracy of coupling gains, therefore, the efficient contour error vector method can be adopted to estimate the coupling gains. both stability and performance analyses are conducted using the lifted system representation method. Simulation and experimental results of the three typical nonlinear contour tracking cases (i.e., semi-circle, parabola and spiral) with a two-axis micro-motion stage have demonstrated superiority and efficacy of the proposed controller.