基于Koopman算子理论的跨尺度高精度超声驱动温漂补偿方法研究

The significant demands of the aviation, the aerospace, the electronic manufacturing, the national defense equipment constantly challenge the limits of the machining accuracy and the processing scale. The next generation ultraprecision machining technology is required to maintain the high machining accuracy of the submicron or even nanometer scale within the large stroke of meters. Theoretically speaking, the ultrasonic driving technology can meet the new requirement, which can overcome the shortcoming of the existing driving technology, in terms of high precision positioning only within limited scale. In practice, however, the losses inevitably lead to the heat generation within the large stroke and long period, which are caused in the frequently vibrating ceramics and the contact zone of the ultrasonic motor. The temperature dependence of the ultrasonic motor will be subsequently aggravated, which will further limit the positioning accuracy. This project aims at striking a balance between the manufacturing scale and the machining accuracy, which will become ubiquitous in the future. The modeling technology based on the energy variational principle, the linearization technology based on the deep learning and the controller designing technology based on the Passivity theorem will be integrated and optimized within the framework of the Koopman operator theory. A novel driving technology for the ultrasonic motor will be then proposed, after the study on the modeling, the linearization, the controller designing, and the experimental verification of the compensation system of the temperature dependence for the ultrasonic motor. The fast tool servo system will simultaneously maintain a high-precision and long-stroke based on the proposed driving technology. The accumulative positioning error within the large working stroke will be therefore eliminated; subsequently, the ultrasonic motor-based positioning system will maintain the stroke of 1000mm and the accuracy of 50nm during the successive working period.

随着航空航天、电子制造和国防装备等重大需求的推动，下一代超精密加工需要在米级行程实现亚微米甚至纳米级加工精度。超声驱动技术在原理上可弥补现有驱动技术只能在局部高精度定位的不足，满足下一代超精密加工对驱动技术的需求；但实际中大行程连续运行工况下压电陶瓷长时间频繁伸缩以及定动子间频繁接触，将产生较多热量加剧超声驱动单元温度漂移、制约定位精度。本项目将以“未来制造尺度与加工精度难以兼顾”问题为导向，在Koopman算子理论的框架下，整合并优化基于能量变分原理的建模技术、基于深度学习的模型线性化处理技术和基于无源性定理的控制器设计技术，从温漂补偿系统建模、非线性时变温漂补偿模型全局线性化、温漂补偿控制器设计和实验验证等四个层面，研究满足下一代超精密加工需求的高精度大行程型超声驱动技术，旨在消除跨尺度下温度漂移所引起的累计定位误差，实现1000毫米行程下连续往复运动始终保持50纳米定位精度。

针对精密加工领域中大行程与高精度定位难以兼顾的难题，结合电机运行的非理想因素，通过考虑介电损耗、机械损耗与压电损耗，并通过引入温变参数描述了电机的温漂特性，得到改进的交直流超声电机模型，为后文温漂补偿方法的研究提供分析基础；将首先基于Koopman 理论构造全局线性化模型，通过神经网络训练实现迟滞预测模型的辨识与高精度预测；在此基础上，提出增量线性MPC 补偿算法，为减少计算量设计阶梯式控制策略，将目标函数的优化问题转化为有约束的二次线性规划问题；将首先提出驱动电压频率-幅值复合控制策略，以同时解决交流模式下超声电机的温漂特性、调速死区及非线性输出特性问题；一方面，基于改进的最优频率跟踪方案建立温度相关的线性变参数模型，在此基础上设计了非常严格的无源控制器，通过调频补偿电机的温漂特性；另一方面，建立了输出速度的全局线性化Koopman 预测模型，并搭建稀疏型神经网络进行参数辨识， 构造出自适应增量式模型预测控制器来解决交流模式下电机存在的调速死区与非线性输出问题；最终提出双闭环控制策略以实现超声电机的位移轨迹跟踪。与现有建模方法相比，同时考虑了电机的温度依赖性与非线性输出特性，与现有控制方法相比，该控制策略通过调节驱动频率与幅值来解决温度依赖性与非线性输出特性补偿问题，为实际应用中具有温度依赖性的压电执行器的非线性速度输出的改善提供了一种全局线性化建模及补偿基础。输入驱动电压幅值80V，研究温漂特性补偿验证。电机初始温度为23℃，在无控制情况下，导纳相位由59.0°增加至64.85°，电机速度下降了16.37%，有功功率下降了2W。通过调节频率，电机速度稳定在78.1mm/s左右，有功功率保持在9W附近，电机温升也明显减小。可以看出导纳相位的稳定性与电机输出特性的稳定性得到明显改善。在高端装备制造领域中及在非线性控制理论研究领域中具有一定科学意义。

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