Research on Optimal Control for Electron Beam Processing Systems and Its Application to Industry

在许多工业领域中，材料的加工，特别是金属的切割和焊接，是非常重要的。近年来，金属的切割和焊接技术取得了很大的进步，并开发了高功率电子束加工技术。本文研究了高功率束流处理系统的数学模型。由于材料的蒸发边界构成自由边界，电子束加工系统将我们引向自由边界问题。作为自由边界问题的典型例子，常引用Stefan问题，然而，电子束加工系统中的自由边界问题不同于Stefan问题。因为自由边界条件中含有与电子束功率密度相对应的功率项。变分不等式是求解自由边界问题的一种强有力的分析方法。利用变分不等式建立了电子束加工系统的数学模型。该模型考虑了材料中杂质的影响，采用随机变分不等式方法建立。在电子束加工过程中，获取被加工材料的状态信息是非常重要的。在本研究中，我们建构了加工状态的估测系统。主要研究成果如下：（1）利用一种新型的随机变分不等式建立了强流束流处理系统的数学模型。并保证了模型的数学安全性。(2)我们构建了边界观察机制来估计加工中材料的状态。(3)提出了一种对加工过程中物料状态进行估计的方法。通过仿真实验验证了该估计器系统的有效性。

In many fields of industry, the processing of materials, specially, the cutting and welding of metals, is very important. Recently, a technique to cut and weld metals has made a considerable progress and the processing technique by the high power electron beam has been developed. In this research, the mathematical formulation of the high power beam processing system has been studied. Since the evaporation boundary of the material constructs a free boundary, the electron beam processing system lead us to the free boundary problem. As a typical example of the free boundary problem, a Stefan problem is often cited, however, the free boundary problem in the electron beam processing system is different from the Stefan problem. Because the condition on the free boundary contains the power term corresponding to the power density of the electron beam. One of the powerful analytical method to solve the free boundary problem is variational inequality. Then, the electron beam processing system was formulated by the variational inequality. Taking the influence of impurities contained in the material into consideration, the model is formulated by the stochastic variational inequality.To obtain the information of the state of the material under processing is very important in the electron beam processing. In this research, we have constructed the estimator system of the state under the processing. Results obtained in this research are as follows :(1) The mathematical model of the high power beam processing system was formulated by the stochastic variational inequality of a new type. And the mathematical security of the proposed model was guaranteed.(2) We construct the boundary observation mechanism to perform the estimation of the state of the material under processing.(3) We had proposed the method to estimatie the state of the material under processing. And the efficiency of the estimator system was guaranteed through the simulation experiments.