Dynamic equivalence conditions for an air-bearing simulator emulating scaled drag-free control dynamics  

等效模拟无拖曳卫星动力学的地面气浮装置相似设计方法

作　　者：Mingwei Chen Chu Zhang Jianwu He Chao Yang Li Duan Qi Kang 陈明伟;章楚;贺建武;杨超;段俐;康琦

机构地区：[1]Institute of Mechanics,Chinese Academy of Sciences,Beijing 100190,China [2]School of Engineering Science,University of Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Acta Mechanica Sinica》2025年第1期192-210,共19页力学学报(英文版)

基　　金：supported by the National Key Research and Development Program of China (Grant No.2021YFC2202604);the Strategy Priority Research Program of Chinese Academy of Sciences (Grant No.XDA1502110101).

摘　　要：The ground-based experimental tests are crucial to verify the related technologies of the drag-free satellite.This work presents a design method of the ground simulator testbed for emulating the planar dynamics of the space drag-free systems.In this paper,the planar dynamic characteristics of the drag-free satellite with double test masses are analyzed and nondimensionalized.A simulator vehicle composed of an air bearing testbed and two inverted pendulums is devised on the basic of equivalent mass and equivalent stiffness proposed firstly in this paper.And the dynamic model of the simulator equivalent to the sensitive axis motion of the test mass and the planar motion of the satellite is derived from the Euler-Lagrange method.Then,the dynamic equivalence conditions between the space prototype system and the ground model system are derived from Pi theorem.To satisfy these conditions,the scaling laws of two systems and requirements for the inverted pendulum are put forward.Besides,the corresponding control scaling laws and a closed-loop control strategy are deduced and applied to establishing the numerical simulation experiments of underactuated system.Subsequently,the comparative simulation results demonstrate the similarity of dynamical behavior between the scaled-down ground model and the space prototype.As a result,the rationality and effectiveness of the design method are proved,facilitating the ground simulation of future gravitational wave detection satellites.为了设计无拖曳卫星相关技术演示验证的地面仿真平台,本文基于量纲分析和π理论等方法提出了一种与空间无拖曳卫星平面动力学行为相似的地面模型设计方法.该方法从双检验质量无拖曳卫星动力学模型中分析出相似特征,设计了由倒立摆和平面气浮台组成的地面气浮模拟装置.文中利用欧拉-拉格朗日方法推导了等效于检验质量敏感轴平动和卫星平面运动的模拟器动力学模型,得出地面模型系统等效空间原型系统的动力学等效条件.此外,本文首次提出了等效质量和等效刚度的概念,并在此基础上提出了满足等效条件的相似律设计要求以及倒立摆的设计要求.在物理相似性条件下,本文设计了欠驱动系统的闭环控制策略,推导出相应的控制相似律并应用于数值仿真.最后,等效缩放后仿真结果与原型仿真结果的对比验证了二者动力学行为具有相似性,也证明了本文提出的相似性设计方法的合理性和有效性,为未来引力波探测计划的无拖曳卫星地面仿真设计提供了更多依据.

关 键 词：Drag-free satellite Ground simulation Pi theorem Dynamical similarity Scaling law 

分 类 号：V416[航空宇航科学与技术—航空宇航推进理论与工程]