A Master-slave Cross-coupled Iterative Learning Control for Repetitive Tracking of Nonlinear Contours in Multi-axis Precision Motion Systems
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摘要: 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.Abstract: 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.1) 本文责任编委 侯忠生
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图 3 融合反馈PID和前馈PDCCILC的控制结构
Fig. 3 Combined feedback PID and feedforward PDCCILC control structure
图 7 半圆轮廓跟踪均方根轮廓误差的仿真结果(RMS)
Fig. 7 RMS contour error versus iteration for the semi-circle contour in the simulations
图 8 半圆轮廓跟踪的稳态仿真结果
Fig. 8 Steady tracking results of the semi-circle contour in the simulations
图 9 抛物线轮廓跟踪的仿真均方根轮廓误差(RMS)
Fig. 9 RMS contour error versus iteration for the semi-circle contour in the simulations
图 10 抛物线轮廓跟踪的稳态仿真结果
Fig. 10 Steady tracking results of the parabolic contour in the simulations
图 11 螺旋线轮廓跟踪的仿真均方根轮廓误差(RMS)
Fig. 11 RMS contour error versus iteration for the spiral contour in the simulations
图 12 螺旋线轮廓跟踪的稳态仿真结果
Fig. 12 Steady tracking results of the spiral contour in the simulations
图 13 半圆轮廓跟踪的实验均方根轮廓误差(RMS)
Fig. 13 RMS contour error versus iteration for the semi-circle contour in the experiments
图 14 半圆轮廓跟踪的实验结果
Fig. 14 Tracking results of the semi-circle contour in the experiments
图 15 抛物线轮廓跟踪的实验均方根轮廓误差(RMS)
Fig. 15 RMS contour error versus iteration for the parabolic contour in the experiments
图 16 抛物线轮廓跟踪的实验结果
Fig. 16 Tracking results of the parabolic contour in the experiments
图 17 螺旋线轮廓跟踪的实验均方根轮廓误差(RMS)
Fig. 17 RMS contour error versus iteration for the spiral contour in the experiments
表 1 控制器参数
Table 1 Controller parameters
控制器 增益 ${K_p}$ ${K_i}$ ${K_d}$ PID 3 1 0 ILC 0.3 0.1 0.1 CCC 1 0.5 0 
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表 2 单调收敛的计算结果
Table 2 Computational results of monotonic convergence
控制器 $\bar \sigma \left(M \right)$的计算结果 半圆轮廓 抛物线轮廓 螺旋线轮廓 PDCCILC & PID 3 1 0 TDCCILC & PID 0.3 0.1 0.1 PDILC & PID 1 0.5 0 TDILC & PID 1 0.5 0
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表 3 四种控制器下的三种非线性轮廓跟踪结果实验统计数据(${\mu}$m)
Table 3 Experimental statistics of tracking performance (${\mu}$m)
稳态误差 半圆 抛物线 螺旋线 TDILC & PID RMS 3.405 3.637 7.566 MAX 8.501 8.334 17.429 TDCCILC & PID RMS 1.869 1.924 4.897 MAX 5.170 6.001 15.420 PDILC & PID RMS 1.344 1.197 2.992 MAX 4.348 4.696 11.106 PDCCILC & PID RMS 0.821 0.631 1.551 MAX 2.108 2.907 7.240
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