面向不确定度的机床系统正交鲁棒设计方法  

Orthogonal robust design method of machine toolsystem oriented to uncertainty

作　　者：韦进文[1] 郭志俊 李东旭 WEI Jinwen;GUO Zhijun;LI Dongxu(School of Mechanical Engineering,Guangxi University,Nanning 530004,China)

机构地区：[1]广西大学机械工程学院,广西南宁530004

出　　处：《机电工程》2025年第4期780-788,共9页Journal of Mechanical & Electrical Engineering

基　　金：广西自然科学基金资助项目(2023GXNSFAA016717)。

摘　　要：针对数控机床加工中存在不确定度从而影响机床加工精度的问题,依据广义叉积(GCP)鲁棒定理所明确的“叉矩阵(CM)正交则积向量(PV)鲁棒性最强”,提出了一种新的机床控制系统鲁棒设计方法。首先,采用了牛顿法建立了机床的动力学模型,并利用阶跃响应方法分析了不确定度对控制系统性能的影响;其次,详细阐述了GCP鲁棒定理,并将其应用于机床的控制系统设计,即用差分方程系数构造CM、输入输出序列构造PV,得到了系统的GCP形式;然后,在状态空间对系统进行了状态反馈设计,建立了满足CM正交条件的方程组,通过求解该正交方程组确定了控制器参数;最后,采用了蒙特卡洛法(MCM)仿真与加工实验,对该方法的有效性进行了验证。研究结果表明:采用该方法的正交鲁棒系统具有强鲁棒性,对比传统的极点配置系统和滑模控制系统,实验加工误差的期望值分别降低了40.4%和12.3%。该方法能有效抑制不确定度的影响,可为机床控制系统鲁棒设计提供参考。Aiming at the influence of uncertainty on machining accuracy of CNC machine tool,a new robust design method for control system was proposed according to the robustness theorem of generalized cross product(GCP),"the product vector(PV)is the most robust when the cross matrix(CM)is orthogonal".Firstly,the dynamic model of machine tool was established by Newton method,and the influence of uncertainty on the performance of control system was analyzed by step response.Secondly,the robustness theorem of GCP was expounded in detail and applied to the design of the control system of the machine tool:the CM was constructed by the coefficients of the difference equation,the PV was constructed by the input and output sequences,and the GCP form of the system was obtained.Then,the system was designed by state feedback in the state space,and a system of equations satisfying the orthogonal condition of the CM was established.The parameters of the controller were determined by solving the equations.Finally,the effectiveness of the proposed method was verified by Monte Carlo(MCM)simulation and machining experiments.The research results show that the orthogonal robust system designed by this method has strong robustness.Comparing with traditional pole assignment system and sliding mode control system,the expected value of experimental machining error is reduced by 40.4%and 12.3%,respectively.This proves that the proposed method can effectively suppress the influence of uncertainty on machining accuracy,and provides a reference for the robust design of control system.

关 键 词：不确定度 广义叉积 叉矩阵 积向量 正交鲁棒设计 蒙特卡洛法 控制系统性能 

分 类 号：TH161[机械工程—机械制造及自动化] TG659[金属学及工艺—金属切削加工及机床]