卡氏天线副面补偿技术中副面焦点坐标调整量的高精度数据拟合
收稿日期: 2013-12-19
修回日期: 2014-02-17
网络出版日期: 2014-02-26
基金资助
中国探月工程三期资助项目;国家"973"计划(2013CB837900);国家自然科学基金(11103056,10778703,11153002);中科院"西部之光"项目(XBBS201122)
Accurate Data Fitting for Adjustments of Focus Position Coordinates Applied to Cassegrain Antenna's Sub-reflector Compensation
Received date: 2013-12-19
Revised date: 2014-02-17
Online published: 2014-02-26
Supported by
China Lunar Exploration Project Ⅲ; National Basic Research Program of China (2013CB837900); National Natural Science Foundation of China (11103056,10778703,11153002); "Westen Light" Project of Chinese Academy of Sciences (XBBS201122)
基于新疆110 m射电望远镜预研项目、南山天线改造计划和国家对航天领域的战略需求,对大型卡氏天线主面板变形的副面实时补偿作了深入研究.简单介绍了副面补偿的理论模型并用静力分析法得出若干特殊仰角下的调整量,进而运用MATLAB对调整量进行了高精度的数据拟合.给出了线性最小二乘法和正交多项式最小二乘法2种拟合方法拟合模型方程,通过误差分析从不同方面对比了拟合方法的效果,在阶数为4、精确至小数点后15位时,2种拟合方法的误差差值数量级为10-13 mm,且小于零.最终选择并应用精度更高的正交多项式最小二乘拟合方法在特定的俯仰角度范围内生成了部分调整量数据,为副反射面在任意俯仰角下的补偿过程创造了条件,满足了天文观测和航天深空探测对数据准确性和系统可靠性的要求,具有一定的实用性.
胡开宇, 艾力·玉苏甫, 徐雪林, 项斌斌, 刘奇 . 卡氏天线副面补偿技术中副面焦点坐标调整量的高精度数据拟合[J]. 航空学报, 2014 , 35(12) : 3425 -3437 . DOI: 10.7527/S1000-6893.2013.0542
Based on the rapidly progress of the Xinjiang 110 m radio telescope project, Nanshan antenna reform programme and national strategic demand for aerospace development, this paper makes a thorough study for the real-time compensation of the sub-reflector for the deformation of the large antenna's main panel. First, it presents a brief introduction to the theoretical model of sub-reflector compensation and an analysis of adjustments under certain special elevations. Then it realizes high-precision data fit using MATLAB because of its powerful numerical calculation. This paper gives two different data fit methods and model equations and compares the effects of the two fit methods from different aspects by detailed error analysis. When the fit order is 4 and computing to 15 decimal places, it calculates the error of the difference between these two data fit methods: the value is negative and the magnitude is 10-13 mm. Finally, the paper chooses the higher precision fitting method whose absolute error is minuend and uses this method to generate a partial adjustment database in the range of some special angels in order to create conditions for the entire sub-reflector compensation process which satisfies the requirements for astronomical observations and deep-space exploration for data accuracy and system reliability. The specific technology is believed to possess certain general value for applicability.
Key words： antenna; sub-reflector; data fit; error compensation; error analysis
[1] Leng G J. Homology design on reflector and electromechanical optimization of large antenna[D]. Xi'an: Xidian University, 2012. (in Chinese) 冷国俊. 大型天线反射面保型与机电综合优化设计[D]. 西安: 西安电子科技大学, 2012.
[2] Castleberg P A,Xilouris K M. The arecibo observatory[J]. IEEE Potentials, 1997, 16(3): 33-35.
[3] Prestage R M, Constantiks K T, Hunter T R, et al. The green bank telescope[J]. Proceedings of the IEEE, 2009, 97(8): 1382-1390.
[4] Wielebinski R. The effelsberg 100-m radio telescope[J]. Naturwissenschaften, 1971, 58(3): 109-116.
[5] Qi J C. The research on antenna sub-reflecter parallel mechanism control system[D]. Qinhuangdao: Yanshan University, 2012. (in Chinese) 戚金超. 天线副反射面并联机构控制系统的研究[D].秦皇岛: 燕山大学, 2012.
[6] Duan Y B, Li J J, Hou Y L, et al. Configuration design of the adjusting parallel mechanism for sub-reflector of antenna of radio telescope antenna[J]. Machinery Design & Manufacture, 2013(8): 222-225. (in Chinese) 段艳宾, 李建军, 侯雨雷, 等. 射电望远镜天线副反射面并联调整机构设计[J]. 机械设计与制造, 2013(8): 222-225.
[7] Dou Y C, Yao J T, Hou Y L, et al. Orientation precision monitoring and homing strategy of the sub-reflector adjusting system for 65 meters radio telescope[J]. Robot, 2012, 34(4): 399-405. (in Chinese) 窦玉超, 姚建涛, 侯雨雷, 等. 65米射电望远镜副面调整系统姿态精度监测与回零策略[J]. 机器人, 2012, 34(4): 399-405.
[8] Li Y J, Lu Q P, Peng Z Q, et al. Exact solutions and applications of the inverse kinematics of six-bar parallel mechanism in synchrotron radiation beam-line[J]. Nuclear Techniques, 2008, 31(7): 485-488. (in Chinese) 李勇军, 卢启鹏, 彭忠琦, 等. 同步辐射光束线六杆并联机构的逆运动学精确求解及应用[J]. 核技术, 2008, 31(7): 485-488.
[9] Shi H L, Cai X X. Best match and adjustment of sub-reflector and best realistic description for main surface deformation[J]. Electro-Mechanical Engineering, 1988(2): 45-50. (in Chinese) 施浒立, 蔡显新.变形主面的最佳逼真描述和副面最佳匹配调整[J]. 电子机械工程, 1988(2): 45-50.
[10] Nocedal J, Wright S. Numerical optimization[M]. New York: Springer-Verlag, 1999: 1-11.
[11] Duan B Y, Qiu Y H, Xu G H, et al. Study on optimization of mechanical and electronic synthesis for the antenna structure system[J]. Mechatronics, 1994, 4(6): 553-564.
[12] Levy R. Optimization of antenna structure design, N84-32622[R]. Washington D.C.: NASA, 1984.
[13] Cheng J Q. The ptinciples of astronomical telescope design[M]. New York: Springer, 2009: 1-27.
[14] Liang Z F, Suonan J L, Kang X N, et al. Permanent faults identification using least squares fitting algorithm for three-phase reclosure in transmission lines with shunt reactors[J]. Journal of Xi'an Jiaotong University, 2013, 47(6): 85-96. (in Chinese) 梁振锋, 索南加乐, 康小宁, 等. 利用最小二乘拟合算法的三相重合闸永久性故障判别[J].西安交通大学学报, 2013, 47(6): 85-96.
[15] Huang Z, Li S J, Guo B. General reliability life data fit method based on mixture of Garmma distribution[J]. Acta Aeronautica et Astronautica Sinica, 2008, 29(2): 379-386. (in Chinese) 黄卓, 李苏军, 郭波. 基于混合Garmma分布的通用可靠性寿命数据拟合方法[J]. 航空学报, 2008, 29(2): 379-386.
[16] Lopes A M, Almeida F. The generalized momentum approach to the dynamic modeling of a 6-dof parallel manipulator[J]. Multibody System Dynnamics, 2009, 21(2): 123-146.
[17] Duan B Y, Wang C S. Reflector antenna distortion using MEFCM[J]. IEEE Transactions on Antennas Propagation, 2009, 57(10): 3409-3413.
[18] Rahmat-Samii Y. An efficient computational method for characterizing the effects of random surface errors on the average power pattern of reflectors[J]. IEEE Transactions on Antennas and Propagation, 1983, 31(1): 92-98.
/
| 〈 |
|
〉 |
CJA