Nano scale dynamic track control in multidimensional space

Yong-min Jiang
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Abstract

According to the experimental and theoretical derivation, we present the first study of the CNC machine tool control theory based on the relation between geometry and motion. By studying the trajectory characteristics in both multidimensional space and time space, the displacement and its derivatives are designed as a motion vector space. With this vector space, the relationship among geometric parameters, dynamic parameters, function and its derivatives, can be studied all together. They can also be studied respectively according to its geometric and physical meanings. The time-derivative can increase the middle variables as a reference time for the control technology process. If the variation ratio of real time to reference time is known or measurable, the trajectory differential equation can be completely solved. We put forward a new method: to control the track realization process is the way to control the trajectory movement parameter. Through experiment and simulation, it has been proven that this method can realize geometry and integrated control, reduce motion trajectory calculation, and while improving precision, it increases path planning adaptability to the environment. It is therefore a good method to control tracks for machine tools.
多维空间纳米尺度动态轨迹控制
在实验和理论推导的基础上,首次提出了基于几何与运动关系的数控机床控制理论。通过研究在多维空间和时间空间中的轨迹特征,将位移及其导数设计为一个运动向量空间。有了这个向量空间,就可以综合研究几何参数、动态参数、函数及其导数之间的关系。也可以根据其几何意义和物理意义分别进行研究。时间导数可以增加中间变量作为控制工艺过程的参考时间。如果实时时间与参考时间的变化率已知或可测量,则可以完全求解轨迹微分方程。提出了一种新的控制轨迹实现过程的方法,即控制轨迹运动参数的方法。通过实验和仿真,证明该方法能够实现几何化和一体化控制,减少运动轨迹计算,在提高精度的同时,增加了路径规划对环境的适应性。因此,对机床进行轨迹控制是一种很好的方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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