基于摩擦补偿的两轴直驱伺服进给系统自适应非线性滑模轮廓控制

doi:10.3969/j.issn.1004-132X.2023.11.009

摘要/Abstract

摘要： 为满足两轴直驱伺服进给系统的高精度加工要求，提出一种基于摩擦补偿的自适应非线性滑模轮廓控制(ANSMCC)方法，以兼顾加工精度和响应速度要求。建立适用于大曲率轮廓加工的等效轮廓误差模型，同时考虑系统中存在的不确定性动态的影响，建立准确且能实时补偿的改进LuGre非线性摩擦力动力学模型。为提升两轴直驱伺服进给系统轮廓性能，设计基于非线性滑模面的ANSMCC方法，其中非线性滑模面包含轮廓误差分量，通过改变非线性滑模面中增益矩阵值的大小可实时改变系统的阻尼比，从而协调轮廓误差与系统响应速度的关系。实验结果表明，所提方法可以克服系统运行过程中不确定性动态的影响，准确跟踪大曲率轮廓曲线，提高轮廓加工精度。

关键词: 两轴直驱伺服进给系统, 摩擦补偿, 非线性滑模面, 轮廓误差

Abstract: In order to meet the requirements of high precision for two-axis direct drive servo feed systems, based on friction compensation, an adaptive nonlinear sliding mode contour control(ANSMCC) method was proposed to take into account the requirements of machining precision and response speed. An equivalent contour error model suitable for large curvature contour machining was established, and considering the influences of uncertain dynamics in the system, an improved LuGre nonlinear friction dynamic model with accurate and real-time compensation was established. In order to improve the contour performance of the two-axis direct drive servo feed systems, an ANSMCC method was designed based on the nonlinear sliding mode surface, where the nonlinear sliding mode surface contained the contour error components. By changing the values of the gain matrix in the nonlinear sliding mode surface, the damping ratio of the system might be changed in real time, so as to coordinate the relationship between the contour errors and the system response speeds. The experimental results show that the proposed method may overcome the dynamic influences of uncertainty in the operation of system, accurately track the large curvature contour curves, improve the contour machining accuracy.

Key words: two-axis direct drive servo feed system, friction compensation, nonlinear sliding mode surface, contour error

中图分类号:

TM351

金鸿雁, 王磊, 赵希梅. 基于摩擦补偿的两轴直驱伺服进给系统自适应非线性滑模轮廓控制[J]. 中国机械工程, 2023, 34(11): 1335-1342.

JIN Hongyan, WANG Lei, ZHAO Ximei. Adaptive Nonlinear Sliding Mode Contour Control of Two-axis Direct Drive Servo Feed Systems Based on Friction Compensation[J]. China Mechanical Engineering, 2023, 34(11): 1335-1342.

参考文献

［1］刘艳雄，王根聚，华林，等.采用自适应滑模变结构控制的精冲机双驱动协调控制系统［J］. 中国机械工程，2021，32(18)：2189-2196.
LIU Yangxiong，WANG Genju，HUA Lin，et al.Double-drive Coordinated Control Systems of Fine Stamping Machines Based on Adaptive Sliding Mode Variable Structure Control［J］.China Mechanical Engineering，2021，32(18)：2189-2196.
［2］李超.冗余直驱龙门系统的多输入多输出精密运动控制［D］.杭州：浙江大学，2018.
LI Chao. MIMO Precision Motion Control of Redundantly Driven Gantry Systems with Direct Actuators［D］.Hangzhou：Zhejiang University，2018.
［3］赵希梅，赵久威.精密直驱龙门系统的交叉耦合互补滑模控制［J］.电工技术学报，2015，35(11)：7-12.
ZHAO Ximei，ZHAO Jiuwei. Cross-coupled Complementary Sliding Mode Control for Precision Direct-drive Gantry System［J］. Transactions of China Electrotechnical Society，2015，35(11)：7-12.
［4］KUANG Z A，GAO H J，TOMIZUKA M. Precise Linear-motor Synchronization Control via Cross-coupled Second-order Discrete-time Fractional-order Sliding Mode［J］.IEEE/ASME Transactions on Mechatronics，2019，14(2)：1-11.
［5］LIU Yang，WAN Min，XIAO Qunbao，et al. Combined Predictive and Feedback Contour Error Control with Dynamic Contour Error Estimation for Industrial Five-axis Machine Tools［J］.IEEE Transactions on Industrial Electronics, 2022，69(7)：6668-6677.
［6］原浩，赵希梅.基于全局任务坐标系的直驱XY平台学习互补滑模轮廓控制［J］.电工技术学报，2020，35(10)：2141-2148.
YUAN Hao，ZHAO Ximei.Learning Complementary Sliding Mode Contouring Control Based on Global Task Coordinate Frame for Direct Drive XY Table［J］.Transaction of China Electrotechnical Society，2020，35(10)：2141-2148.
［7］曾子强，曹荣敏，侯忠生，等.二维直线电机的多入多出无模型自适应轮廓控制［J］.控制理论与应用，2020，37(5)：1007-1017.
ZENG Ziqiang，CAO Rongmin，HOU Zhongsheng，et al. Multiple Input Multiple Output Model Free Adaptive Contour Control for Two-dimensional Linear Motor［J］.Control Theory & Applications，2020，37(5)：1007-1017.
［8］武志涛，朱连成.基于滑模轮廓控制器的直线电机精密运动平台轨迹跟踪控制［J］.中国电机工程学报，2015，35(23)：6188-6193.
WU Zhitao，ZHU Liancheng.Trajectory Tracking Control for the Motion Table Driven by Linear Motors Based on Sliding Mode Contour Tracking Controllers［J］.Proceedings of the CSEE，2015，35(23)：6188-6193.
［9］LI Jiangang，WANG Yiming，LI Yanan，et al. Reference Trajectory Modification Based on Spatial Iterative Learning for Contour Control of Two-axis NC Systems［J］.IEEE/ASME Transactions on Mechatronics，2020，25(3)：1266-1275.
［10］HENDRAWAN Y M，FARRAGE A，UCHIYAMA N. Iterative NC Program Modification and Energy Saving for a CNC Machine Tool Feed Drive System with Linear Motors［J］.The International Journal of Advanced Manufacturing Technology，2019，102(3)：3543-3562.
［11］YANG Ming，YANG Jixiang，ZHU Limin，et al.A Novel Curvature Circle Iterative Algorithm for Contour Error Control of Multi-axis CNC Machine Tools［J］.Precision Engineering，2020，65：23-31.
［12］谢东，丁杰雄，霍彦波，等. 数控机床转动轴进给系统轮廓误差分析［J］.中国机械工程，2012，23(12)：1387-1392.
XIE Dong，DING Jiexiong，HUO Yanbo，et al.Contour Error Analysis for Rotation Feed Axis in CNC Machine［J］.China Mechanical Engineering，2012，23(12)：1387-1392.
［13］韦为，耿葵花，耿爱农，等.基于LuGre模型的转子压缩机滑片滑槽运动副摩擦力测试［J］.中国机械工程，2019，30(8)：932-938.
WEI Wei，GENG Kuihua，GENG Ainong，et al.Frictional Force Test of Rotor Compressor Slides-chute Movement Deputy Based on LuGre Model［J］.China Mechanical Engineering，2019，30(8)：932-938.
［14］JIN Hongyan, ZHAO Ximei, WANG Tianhe. Adaptive Backstepping Complementary Sliding Mode Control with Parameter Estimation and Dead-zone Modification for PMLSM Servo System［J］. IET Power Electronics, 2021, 14(4)：785-796.

[1]	李小力, 陈威, 闫蓉. 基于BP神经网络的空间轮廓误差自适应补偿 [J]. J4, 201016, 21(16): 1902-1906.
[2]	倪涛, 徐海远, 李东, 张红彦. 六自由度平台动力学前馈柔顺控制研究[J]. 中国机械工程, 2022, 33(06): 683-689.
[3]	余杭卓1;秦圣峰1,2;丁国富1;江磊1;梁红琴1. 侧铣加工刀具回转轮廓误差预测技术研究[J]. 中国机械工程, 2020, 31(03): 306-313.
[4]	陶浩;何改云;王太勇;董甲甲;张永宾. 一种基于插值拟合的复杂刀具轨迹在线平滑压缩算法[J]. 中国机械工程, 2018, 29(13): 1524-1530,1539.
[5]	陈东宁, 刘一丹, 姚成玉, 蒋栋林, 王可勋, . 基于修正黏性摩擦LuGre模型的比例多路阀摩擦补偿[J]. 中国机械工程, 2017, 28(01): 62-68.
[6]	袁彬, 韩江, 吴路路, 田晓青, 夏链. 基于粒子群算法的滚削齿面综合轮廓误差预测模型与试验研究[J]. 中国机械工程, 2016, 27(20): 2705-2711.
[7]	杨寿智, 邓朝晖, 刘伟, 李建, 彭克立. 凸轮轴数控磨削轮廓误差分析与补偿[J]. 中国机械工程, 2016, 27(16): 2230-2235.
[8]	李学伟, 赵万华, 卢秉恒. 基于误差模型的三轴联动加工轨迹预补偿方法[J]. 中国机械工程, 2014, 25(21): 2918-2924.
[9]	李敏, 王家序, 肖科, 黄超, 徐超. 基于模糊RBF神经网络动态摩擦分块补偿的机器人数字鲁棒滑模控制算法[J]. 中国机械工程, 2012, 23(23): 2792-2796.
[10]	滕福林, 李宏胜, 温秀兰, 黄家才. 电子齿轮比对轮廓误差及加工效率影响的研究[J]. 中国机械工程, 2012, 23(13): 1607-1610.
[11]	谢东1, 2, 丁杰雄1, 霍彦波1, 杜丽1, 王伟1. 数控机床转动轴进给系统轮廓误差分析[J]. 中国机械工程, 2012, 23(12): 1387-1392.
[12]	李培新, 马跃, 于东, 王志成, 韩旭. 一种实时轮廓误差估算方法 [J]. 中国机械工程, 2011, 22(4): 419-423.
[13]	李小力, 陈威, 闫蓉. 基于BP神经网络的空间轮廓误差自适应补偿 [J]. 中国机械工程, 2010, 21(16): 1902-1906.