Abstract: Thermal error mechanism modeling or identification modeling methods based on modern control theory face bottlenecks in both theoretical bases and practical applications.Combining Cuckoo Search (CS) and Model-free adaptive control (MFAC),a data-driven global dynamic adaptive prediction method named the thermal error CS-MFAC prediction method was proposed under the digital twin architecture.The digital twin structure of thermal error of CNC machine tool was put forward to realize the visualization,real-time update and mapping of thermal error status and large data of operation.Then,a data-driven MFAC prediction method was proposed,which converted the non-linear time-varying thermal error system into a linear system described by pseudo partial derivative using the compact format linearization method,and the adaptive prediction of thermal error was realized only using twin system I/O data.The global optimization algorithm of parameters based on CS was further proposed to realize dynamic optimization of prediction parameters driven by twin data,which greatly improved the accuracy and robustness of thermal error prediction under different conditions.Experiments on the XK-L540 CNC milling machine showed that under unmodeled conditions,the maximum residual of the CS-MFAC prediction method was reduced by 58.82~91.73% and 67.46~96.55% respectively compared with traditional model and MFAC method,which verified the feasibility and validity of the proposed method.

Key words: CNC machine tools, thermal error, digital twin, model-free adaptive control, cuckoo search

摘要： 基于现代控制理论的热误差机理建模或者辨识建模的方法在理论基础和实际应用上都面临着瓶颈,将布谷鸟算法(CS)与无模型自适应控制(MFAC)相结合,提出一种数字孪生架构下基于数据驱动的全局动态自适应预测方法,即热误差CS-MFAC预测方法。首先,提出数控机床热误差数字孪生架构,实现热误差状态及工况大数据的可视化及实时更新、映射;然后提出基于数据驱动的MFAC预测方法,利用紧格式线性化方法把非线性时变热误差系统转化为由伪梯度向量描述的线性系统,仅用孪生系统I/O数据实现热误差的自适应预测;进一步提出基于CS的参数全局优化算法,实现孪生数据驱动下的预测参数动态优化,大幅提高在不同工况下热误差预测的准确性和鲁棒性。在XK-L540型数控铣床上进行的实验表明,在未建模工况条件下,CS-MFAC预测方法与传统模型、MFAC方法相比,最大残差分别降低了58.82%~91.73%和67.46%~96.55%,从而验证了该方法的可行性和有效性。

关键词: 数控机床, 热误差, 数字孪生, 无模型自适应控制, 布谷鸟算法