CN103868648B

CN103868648B - The centroid measurement method of three axle air supporting emulation experiment platforms

Info

Publication number: CN103868648B
Application number: CN201410128649.1A
Authority: CN
Inventors: 付振宪; 李宗哲; 刘杨; 陈兴林; 周乃新; 强盛; 李欣; 马晔; 陈震宇; 王伟峰
Original assignee: Harbin Institute of Technology Shenzhen
Current assignee: Harbin Institute of Technology Shenzhen
Priority date: 2014-04-01
Filing date: 2014-04-01
Publication date: 2016-06-01
Anticipated expiration: 2034-04-01
Also published as: CN103868648A

Abstract

The invention discloses a method for measuring the center of mass of a three-axis air flotation simulation experiment platform, which belongs to the field of physical simulation. The invention aims to solve the problems existing in the existing technique of measuring the center of mass of an air flotation platform. The method of the present invention comprises the following steps: Step 1, using a dual-axis inclination angle sensor to measure and obtain the X-axis angular velocity ω _x and Y-axis angular velocity ω _y ; adopting an angular acceleration sensor to measure and obtain the Z-axis angular velocity ω _z ; Step 2, listing three The kinematic equation of the axial air flotation simulation experiment platform: Step 3, list the dynamic equations of the three-axis air flotation simulation experiment platform: Step 4, the three formulas of the dynamic equation described in the step 3 are respectively at time t0, t1 and Integrate within t2, and solve it simultaneously with the kinematic equation in step 2 to obtain the centroid position (r _x , _{ry , r z} ₎ of the three-axis air flotation simulation experiment platform.

Description

Centroid measurement method of three-axis air flotation simulation experiment platform

技术领域technical field

本发明涉及三轴气浮仿真实验平台的质心测量方法，属于物理仿真领域。The invention relates to a centroid measurement method of a three-axis air flotation simulation experiment platform, belonging to the field of physical simulation.

背景技术Background technique

随着人们对外太空的探索，将研制的卫星置于气浮仿真平台进行仿真测试，以此降低研究成本，提高卫星执行任务的成功率，已经成为研制发射卫星的必要步骤。三轴仿真实验平台主要用于模拟飞行器等设备在某种环境下的姿态运动。控制技术和计算机技术的发展，以及新型材料的开发运用，使得三轴气浮仿真实验平台体积变小，刚度加大，承载能力更高。此外科学技术的进步还使得三轴气浮仿真实验平台的控制精度以及位资精度都有了极大的提高。因此，三轴气浮仿真实验平台将不再仅限于空间飞行器的实验模拟，也逐渐适用于其他各种方向，如航海时的模拟训练以及某些高精度，高成本的实验设备在投入使用之前的仿真测试。With people's exploration of outer space, it has become a necessary step to develop and launch satellites by placing the developed satellites on the air flotation simulation platform for simulation tests, so as to reduce research costs and improve the success rate of satellite missions. The three-axis simulation experiment platform is mainly used to simulate the attitude movement of aircraft and other equipment in a certain environment. The development of control technology and computer technology, as well as the development and application of new materials, have made the three-axis air flotation simulation experiment platform smaller in size, stronger in stiffness, and higher in carrying capacity. In addition, the progress of science and technology has also greatly improved the control accuracy and position accuracy of the three-axis air flotation simulation experiment platform. Therefore, the three-axis air flotation simulation experimental platform will no longer be limited to the experimental simulation of space vehicles, but will gradually be applicable to various other directions, such as simulation training during navigation and some high-precision, high-cost experimental equipment before they are put into use. simulation test.

在三轴气浮仿真实验平台中工作台是气浮台的本体，它用来安装姿态控制系统的测试部件。由于卫星在空间飞行时所须的驱动力矩很小，所以在进行地面模拟试验时，必须将干扰力矩控制到很小的数值。当各项干扰力矩控制到规定数值后，工作台便可浮在球轴承上在任意姿态角达随迁平衡，以实现稳定，此时卫星就像飘浮在空间飞行轨道上一样，再通过遥测、遥控装置，姿控系统就可在模拟台上进行各种试验了。传统人工调平费时费力，且往往达不到良好的调节效果。通过此调平机构，使旋转中心与整体质心重合，研制出的工作台具有很高的平衡精度，以满足地面仿真实验的使用要求。In the three-axis air flotation simulation experiment platform, the workbench is the body of the air flotation platform, which is used to install the test components of the attitude control system. Since the driving torque required by satellites in space flight is very small, it is necessary to control the disturbance torque to a small value when carrying out ground simulation tests. When the disturbance torques are controlled to the prescribed values, the workbench can float on the ball bearings at any attitude angle to achieve a dynamic balance to achieve stability. At this time, the satellite is like floating on a space flight orbit, and then through telemetry, The remote control device and the attitude control system can carry out various tests on the simulation platform. Traditional manual leveling is time-consuming and laborious, and often fails to achieve good adjustment results. Through this leveling mechanism, the center of rotation coincides with the center of mass of the whole, and the developed workbench has high balance accuracy to meet the requirements of ground simulation experiments.

中国专利《一种三维姿态角的测量方法和系统》，其公开号为CN102135421A，公开日为2011年10月12日，该专利提出了通过分析两路平行光线经孔光阑在图像传感器上形成的光斑，求解出平台三维空间的运动信息的方案。但是上述装置未考虑仿真实验时实验环境可能不够理想化，如灰尘，线缆等对光线的遮挡以及机械台体的震动带动光线的震荡，都会影响测量的准确性。Chinese patent "A Method and System for Measuring Three-Dimensional Attitude Angle", its publication number is CN102135421A, and its publication date is October 12, 2011. The solution to solve the motion information of the three-dimensional space of the platform. However, the above-mentioned device does not consider that the experimental environment may not be ideal when the simulation experiment is carried out. For example, dust, cables, etc., which block the light and the vibration of the mechanical platform drive the vibration of the light, which will affect the accuracy of the measurement.

中国专利《一种适用于光纤陀螺观测系统的质心测量装置》，其公开号为CN201138270，公开日为2009年1月14日，该专利用于测量陀螺敏感轴上的速度。然而光纤陀螺属于电子陀螺，无转动部分，易受电磁干扰，使用场合受限制。其漂移非常大，在实际应用中，如果用于精确的导航、制导，需要进行非常复杂的解算和补偿。Chinese patent "A Centroid Measuring Device Applicable to Fiber Optic Gyro Observation System", its publication number is CN201138270, and its publication date is January 14, 2009. This patent is used to measure the speed on the sensitive axis of the gyroscope. However, fiber optic gyroscopes are electronic gyroscopes, which have no rotating parts, are susceptible to electromagnetic interference, and are limited in use. Its drift is very large. In practical applications, if it is used for precise navigation and guidance, very complicated calculation and compensation are required.

中国专利《一种只用单个电子水平仪的质心调节装置》，其公开号为CN101900627A，公开日为2011年9月14日，该专利虽然可以直接得到一个平面即X、Y平面上的姿态角信息，但是在调节Z向时其方法采用了电机带动质量块上升，直至电子水平仪输出非零信号，即三轴气浮台台面处于临界状态。此种临界状态较难判断，需要丰富的工程经验，最后偏差较大，并且在Z向调解过程中难以求解质心具体位置。Chinese patent "A Centroid Adjusting Device Using Only a Single Electronic Level", its publication number is CN101900627A, and the publication date is September 14, 2011. Although this patent can directly obtain the attitude angle information on a plane, that is, the X and Y planes , but when adjusting the Z direction, the method uses the motor to drive the mass to rise until the electronic level outputs a non-zero signal, that is, the three-axis air bearing table is in a critical state. This kind of critical state is difficult to judge and requires rich engineering experience. In the end, the deviation is relatively large, and it is difficult to solve the specific position of the center of mass during the Z-direction adjustment process.

发明内容Contents of the invention

本发明目的是为了解决现有测量气浮台质心技术存在的问题，提供了一种三轴气浮仿真实验平台的质心测量方法。The object of the invention is to solve the problems existing in the existing technique of measuring the center of mass of an air flotation platform, and to provide a method for measuring the center of mass of a three-axis air flotation simulation experiment platform.

本发明所述三轴气浮仿真实验平台的质心测量方法，该方法包括以下步骤：The method for measuring the center of mass of the three-axis air flotation simulation experiment platform of the present invention comprises the following steps:

步骤一、采用双轴倾斜角传感器测量三轴气浮仿真实验平台的X轴角度信息和Y轴角度信息，进而获取X轴角速度ω_x和Y轴角速度ω_y；Step 1. Measure the X-axis angle information and the Y-axis angle information of the three-axis air flotation simulation experiment platform by using a dual-axis tilt angle sensor, and then obtain the X-axis angular velocity ω _x and the Y-axis angular velocity ω _y ;

采用角加速度传感器测量三轴气浮仿真实验平台的Z轴旋转角的角加速度，进而获取Z轴角速度ω_z；Use the angular acceleration sensor to measure the angular acceleration of the Z-axis rotation angle of the three-axis air flotation simulation experiment platform, and then obtain the Z-axis angular velocity ω _z ;

步骤二、根据步骤一获取的X轴角速度ω_x、Y轴角速度ω_y和Z轴角速度ω_z列出三轴气浮仿真实验平台的运动学方程：Step 2. According to the X-axis angular velocity ω _x , Y-axis angular velocity ω _y and Z-axis angular velocity ω _z obtained in step 1, list the kinematic equations of the three-axis air flotation simulation experiment platform:

$[\begin{matrix} \overset{\cdot \cdot}{φ φ} \\ \overset{\cdot \cdot}{θ θ} \\ \overset{\cdot \cdot}{ψ ψ} \end{matrix}] = = {((cos cos))}^{- - 11} \cdot \cdot [\begin{matrix} cos cos θ θ & sin sin θ θ sin sin φ φ & sin sin θ θ cos cos φ φ \\ 00 & cos cos φ φ cos cos θ θ & - - cos cos θ θ sin sin φ φ \\ 00 & sin sin φ φ & cos cos φ φ \end{matrix}] \cdot \cdot [\begin{matrix} {ω ω}_{x x} \\ {ω ω}_{y the y} \\ {ω ω}_{z z} \end{matrix}]$

其中，φ为横滚角，为横滚角的微分；θ为俯仰角，为俯仰角的微分；ψ为偏航角，为偏航角的微分；Among them, φ is the roll angle, is the differential of the roll angle; θ is the pitch angle, is the differential of the pitch angle; ψ is the yaw angle, is the differential of the yaw angle;

步骤三、将步骤一获取的X轴角速度ω_x、Y轴角速度ω_y和Z轴角速度ω_z微分，列出三轴气浮仿真实验平台的动力学方程：Step 3. Differentiate the X-axis angular velocity ω _x , Y-axis angular velocity ω _y and Z-axis angular velocity ω _z obtained in step 1, and list the dynamic equation of the three-axis air flotation simulation experiment platform:

$[\begin{matrix} {\overset{\cdot \cdot}{ω ω}}_{x x} \\ {\overset{\cdot \cdot}{ω ω}}_{y the y} \\ {\overset{\cdot \cdot}{ω ω}}_{z z} \end{matrix}] = = [\begin{matrix} \frac{(({I I}_{y the y} - - {I I}_{z z})) \cdot &Center Dot; {ω ω}_{y the y} \cdot \cdot {ω ω}_{z z} + + m m g g \cdot \cdot ((- - c c o o s the s φ φ \cdot \cdot c c o o s the s θ θ \cdot \cdot {r r}_{y the y} + + s the s i i n no φ φ \cdot \cdot c c o o s the s θ θ \cdot \cdot {r r}_{z z}))}{{I I}_{x x}} \\ \frac{(({I I}_{z z} - - {I I}_{x x})) \cdot \cdot {ω ω}_{x x} \cdot &Center Dot; {ω ω}_{z z} + + m m g g \cdot &Center Dot; ((cos cos φ φ \cdot &Center Dot; c c o o s the s θ θ \cdot &Center Dot; {r r}_{x x} + + s the s i i n no θ θ \cdot &Center Dot; {r r}_{z z}))}{{I I}_{y the y}} \\ \frac{(({I I}_{x x} - - {I I}_{y the y})) \cdot &Center Dot; {ω ω}_{x x} \cdot \cdot {ω ω}_{y the y} + + m m g g \cdot &Center Dot; ((- - s the s i i n no φ φ \cdot &Center Dot; c c o o s the s θ θ \cdot &Center Dot; {r r}_{x x} - - s the s i i n no θ θ \cdot &Center Dot; {r r}_{y the y}))}{{I I}_{z z}} \end{matrix}]$

其中：I_x表示X轴的转动惯量，I_y表示Y轴的转动惯量，I_z表示Z轴的转动惯量；Wherein: I _x represents the moment of inertia of the X axis, I _y represents the moment of inertia of the Y axis, and I _z represents the moment of inertia of the Z axis;

m表示三轴气浮仿真实验平台及仿真部件总质量；m represents the total mass of the three-axis air flotation simulation experiment platform and simulation components;

g为重力加速度；g is the acceleration due to gravity;

(r_x，r_y，r_z)表示三轴气浮仿真实验平台的质心位置；(r _x , _{ry , r z} ₎ represent the position of the center of mass of the three-axis air flotation simulation experiment platform;

步骤四、对步骤三所述动力学方程的三个公式分别在时间t0、t1和t2内进行积分，并与步骤二的运动学方程联立求解，获取三轴气浮仿真实验平台的质心位置(r_x，r_y，r_z)：Step 4. Integrate the three formulas of the dynamic equations described in step 3 respectively within time t0, t1 and t2, and solve them simultaneously with the kinematic equations in step 2 to obtain the position of the center of mass of the three-axis air flotation simulation experiment platform (r _x , r _y , r _z ):

$[\begin{matrix} {r r}_{x x} \\ {r r}_{y the y} \\ {r r}_{z z} \end{matrix}] = = \frac{11}{m m g g} \cdot \cdot [\begin{matrix} - - {I I}_{y the y} \cdot &Center Dot; \underset{t t 00}{&Integral; &Integral;} c c o o s the s φ φ c c o o s the s θ θ \cdot &Center Dot; \underset{t t 11}{&Integral; &Integral;} + + {I I}_{z z} \cdot &Center Dot; \underset{t t 00}{&Integral; &Integral;} s the s i i n no φ φ c c o o s the s θ θ \cdot &Center Dot; \underset{t t 22}{&Integral; &Integral;} {ω ω}_{z z} \\ {I I}_{x x} \cdot &Center Dot; \underset{t t 11}{&Integral; &Integral;} c c o o s the s φ φ c c o o s the s θ θ \cdot &Center Dot; \underset{t t 00}{&Integral; &Integral;} {ω ω}_{x x} + + {I I}_{z z} \cdot \cdot \underset{t t 11}{&Integral; &Integral;} s the s i i n no θ θ \cdot \cdot \underset{t t 22}{&Integral; &Integral;} {ω ω}_{z z} \\ - - {I I}_{x x} \cdot \cdot \underset{t t 22}{&Integral; &Integral;} sin sin φ φ c c o o s the s θ θ \cdot \cdot \underset{t t 00}{&Integral; &Integral;} {ω ω}_{x x} - - {I I}_{z z} \cdot \cdot \underset{t t 22}{&Integral; &Integral;} s the s i i n no θ θ \cdot \cdot \underset{t t 22}{&Integral; &Integral;} {ω ω}_{z z} \end{matrix}] . .$

本发明的优点：本发明所述三轴气浮仿真实验平台的质心测量方法调节方案较为便捷，受环境影响较小且具有较高的测量精度。The advantages of the present invention: the adjustment scheme of the centroid measurement method of the three-axis air flotation simulation experiment platform in the present invention is relatively convenient, less affected by the environment and has high measurement accuracy.

附图说明Description of drawings

图1是本发明所述三轴气浮仿真实验平台的质心测量方法的控制原理框图；Fig. 1 is the control principle block diagram of the centroid measurement method of three-axis air flotation simulation experiment platform of the present invention;

图2是本发明所述三轴气浮仿真实验平台的质心测量方法的流程图。Fig. 2 is a flow chart of the centroid measurement method of the three-axis air flotation simulation experiment platform of the present invention.

具体实施方式detailed description

具体实施方式一：下面结合图1和图2说明本实施方式，本实施方式所述三轴气浮仿真实验平台的质心测量方法，该方法包括以下步骤：Specific embodiment one: below in conjunction with Fig. 1 and Fig. 2 illustrate this embodiment, the centroid measurement method of three-axis air flotation simulation experiment platform described in this embodiment, this method comprises the following steps:

$[\begin{matrix} \overset{\cdot \cdot}{φ φ} \\ \overset{\cdot \cdot}{θ θ} \\ \overset{\cdot &Center Dot;}{ψ ψ} \end{matrix}] = = {((cos cos))}^{- - 11} \cdot \cdot [\begin{matrix} cos cos θ θ & sin sin θ θ sin sin φ φ & sin sin θ θ cos cos φ φ \\ 00 & cos cos φ φ cos cos θ θ & - - cos cos θ θ sin sin φ φ \\ 00 & sin sin φ φ & cos cos φ φ \end{matrix}] \cdot &Center Dot; [\begin{matrix} {ω ω}_{x x} \\ {ω ω}_{y the y} \\ {ω ω}_{z z} \end{matrix}]$

$[\begin{matrix} {\overset{\cdot \cdot}{ω ω}}_{x x} \\ {\overset{\cdot &Center Dot;}{ω ω}}_{y the y} \\ {\overset{\cdot \cdot}{ω ω}}_{z z} \end{matrix}] = = [\begin{matrix} \frac{(({I I}_{y the y} - - {I I}_{z z})) \cdot &Center Dot; {ω ω}_{y the y} \cdot &Center Dot; {ω ω}_{z z} + + m m g g \cdot \cdot ((- - c c o o s the s φ φ \cdot &Center Dot; c c o o s the s θ θ \cdot \cdot {r r}_{y the y} + + s the s i i n no φ φ \cdot \cdot c c o o s the s θ θ \cdot \cdot {r r}_{z z}))}{{I I}_{x x}} \\ \frac{(({I I}_{z z} - - {I I}_{x x})) \cdot \cdot {ω ω}_{x x} \cdot &Center Dot; {ω ω}_{z z} + + m m g g \cdot \cdot ((cos cos φ φ \cdot &Center Dot; c c o o s the s θ θ \cdot &Center Dot; {r r}_{x x} + + s the s i i n no θ θ \cdot &Center Dot; {r r}_{z z}))}{{I I}_{y the y}} \\ \frac{(({I I}_{x x} - - {I I}_{y the y})) \cdot &Center Dot; {ω ω}_{x x} \cdot \cdot {ω ω}_{y the y} + + m m g g \cdot &Center Dot; ((- - s the s i i n no φ φ \cdot &Center Dot; c c o o s the s θ θ \cdot &Center Dot; {r r}_{x x} - - s the s i i n no θ θ \cdot &Center Dot; {r r}_{y the y}))}{{I I}_{z z}} \end{matrix}]$

g为重力加速度；g is the acceleration due to gravity;

该方法涉及的控制原理框图如图1所示，The block diagram of the control principle involved in this method is shown in Figure 1.

双轴倾角传感器采用陀螺仪来实现。角加速度传感器采用电子倾角仪来实现。The dual-axis inclination sensor is implemented using a gyroscope. The angular acceleration sensor is realized by an electronic inclinometer.

当三轴气浮仿真实验平台质心与气浮球轴承旋转中心不重合时，气浮球轴承上的载物平台会呈现出一种周期震荡的运动状态。该三轴气浮仿真实验平台运动时即可看作是本体坐标系相对于参考坐标系的定点旋转运动。根据欧拉定理，以原点为旋转中心，绕Z轴旋转偏航角ψ，然后绕Y轴旋转俯仰角θ，最后，以X轴为旋转轴旋转横滚角φ。此时这三个欧拉角ψ，θ，φ就可以确定本体坐标系中平台旋转的任何一个姿态。When the center of mass of the three-axis air flotation simulation experiment platform does not coincide with the rotation center of the air flotation ball bearing, the loading platform on the air flotation ball bearing will show a state of periodic oscillation motion. When the three-axis air flotation simulation experiment platform moves, it can be regarded as a fixed-point rotational movement of the body coordinate system relative to the reference coordinate system. According to Euler's theorem, with the origin as the center of rotation, rotate the yaw angle ψ around the Z axis, then rotate the pitch angle θ around the Y axis, and finally rotate the roll angle φ around the X axis. At this time, the three Euler angles ψ, θ, φ can determine any posture of the platform rotation in the body coordinate system.

三个欧拉角ψ，θ，φ为中间变量，代表欧拉角的微分，即三个欧拉角的角速度。I_x，I_y，I_z为已知量，在三轴气浮仿真实验平台制作时就确定了。The three Euler angles ψ, θ, φ are intermediate variables, Represents the differential of the Euler angles, that is, the angular velocity of the three Euler angles. I _x , I _y , and I _z are known quantities, which are determined when the three-axis air flotation simulation experiment platform is made.

步骤四中对步骤三所述动力学方程的三个公式分别在时间t0、t1和t2内进行积分，此法既可以保证等式成立，又可解决解算过程中欧拉角矩阵不可逆的情况。联立平台运动学公式及动力学公式，将质心位置(r_x，r_y，r_z)作为未知量，即可反解出三轴气浮仿真实验平台当前质心位置。In Step 4, the three formulas of the kinetic equation described in Step 3 are respectively integrated within time t0, t1 and t2. This method can not only ensure the establishment of the equation, but also solve the situation that the Euler angle matrix is irreversible during the solution process. _Combining the platform kinematics formula and dynamics formula, taking the position of the center of mass (r _x , ry , r _z ) as the unknown quantity, the current position of the center of mass of the three-axis air flotation simulation experimental platform can be inversely solved.

具体实施方式二：下面结合图1说明本实施方式，本实施方式对实施方式一作进一步说明，步骤一中获取X轴角速度ω_x和Y轴角速度ω_y的获取过程为：Specific embodiment two: the present embodiment is described below in conjunction with Fig. 1, and present embodiment is further described to embodiment one, obtains the acquisition process of X-axis angular velocity ω _x and Y-axis angular velocity ω _y in step 1:

双轴倾斜角传感器测量三轴气浮仿真实验平台的X轴角度信息和Y轴角度信息，所述X轴角度信息经串行通信接口电路输出给工控机，工控机对X轴角度信息进行微分处理，获取X轴角速度ω_x；The dual-axis inclination angle sensor measures the X-axis angle information and the Y-axis angle information of the three-axis air flotation simulation experiment platform, and the X-axis angle information is output to the industrial computer through the serial communication interface circuit, and the industrial computer differentiates the X-axis angle information Processing, to obtain the X-axis angular velocity ω _x ;

所述Y轴角度信息经RS485接口电路输出给工控机，工控机对Y轴角度信息进行微分处理，获取Y轴角速度ω_y。The Y-axis angle information is output to the industrial computer through the RS485 interface circuit, and the industrial computer performs differential processing on the Y-axis angle information to obtain the Y-axis angular velocity ω _y .

串行通信接口电路采用RS485或RS232串行接口电路。The serial communication interface circuit adopts RS485 or RS232 serial interface circuit.

具体实施方式三：下面结合图1说明本实施方式，本实施方式对实施方式一作进一步说明，步骤一中Z轴角速度ω_z的获取过程：Specific embodiment three: the present embodiment is described below in conjunction with Fig. 1, and the embodiment one is further described in this embodiment, the acquisition process of the Z-axis angular velocity ω _z in the step 1:

角加速度传感器测量三轴气浮仿真实验平台的Z轴旋转角的角加速度，所述Z轴旋转角的角加速度由A/D转换电路转换成数字信号的角加速度，所述数字信号的角加速度被工控机进行积分处理，获取Z轴角速度ω_z。The angular acceleration sensor measures the angular acceleration of the Z-axis rotation angle of the three-axis air flotation simulation experiment platform, and the angular acceleration of the Z-axis rotation angle is converted into the angular acceleration of the digital signal by the A/D conversion circuit, and the angular acceleration of the digital signal is Integral processing is carried out by the industrial computer to obtain the Z-axis angular velocity ω _z .

具体实施方式四：本实施方式对实施方式一作进一步说明，t0＝8ms～12ms；t1＝16ms～25ms；t2＝25ms～35ms。Embodiment 4: In this embodiment, Embodiment 1 is further explained, t0=8ms˜12ms; t1=16ms˜25ms; t2=25ms˜35ms.

具体实施方式五：本实施方式对实施方式一作进一步说明，t0＝10ms；t1＝20ms；t2＝30ms。Embodiment 5: In this embodiment, Embodiment 1 is further explained, t0=10ms; t1=20ms; t2=30ms.

Claims

1. The method for measuring the center of mass of the three-axis air flotation simulation experiment platform is characterized in that the method comprises the following steps:

Step 1. Measure the X-axis angle information and the Y-axis angle information of the three-axis air flotation simulation experiment platform by using a dual-axis tilt angle sensor, and then obtain the X-axis angular velocity ω _x and the Y-axis angular velocity ω _y ;

Use the angular acceleration sensor to measure the angular acceleration of the Z-axis rotation angle of the three-axis air flotation simulation experiment platform, and then obtain the Z-axis angular velocity ω _z ;

Step 2. According to the X-axis angular velocity ω _x , Y-axis angular velocity ω _y and Z-axis angular velocity ω _z obtained in step 1, list the kinematic equations of the three-axis air flotation simulation experiment platform:

[\begin{matrix} \overset{\cdot &Center Dot;}{φ φ} \\ \overset{\cdot &Center Dot;}{θ θ} \\ \overset{\cdot &Center Dot;}{ψ ψ} \end{matrix}] = = {((c c o o s the s))}^{- - 11} \cdot \cdot [\begin{matrix} c c o o s the s θ θ & s the s i i n no θ θ s the s i i n no φ φ & s the s i i n no θ θ c c o o s the s φ φ \\ 00 & c c o o s the s φ φ cos cos θ θ & - - c c o o s the s θ θ s the s i i n no φ φ \\ 00 & sin sin φ φ & cos cos φ φ \end{matrix}] \cdot &Center Dot; [\begin{matrix} {ω ω}_{x x} \\ {ω ω}_{y the y} \\ {ω ω}_{z z} \end{matrix}]

Among them, φ is the roll angle, is the differential of the roll angle; θ is the pitch angle, is the differential of the pitch angle; ψ is the yaw angle, is the differential of the yaw angle;

Step 3. Differentiate the X-axis angular velocity ω _x , Y-axis angular velocity ω _y and Z-axis angular velocity ω _z obtained in step 1, and list the dynamic equation of the three-axis air flotation simulation experiment platform:

[\begin{matrix} {\overset{\cdot &Center Dot;}{ω ω}}_{x x} \\ {\overset{\cdot &Center Dot;}{ω ω}}_{y the y} \\ {\overset{\cdot \cdot}{ω ω}}_{z z} \end{matrix}] = = [\begin{matrix} \frac{(({I I}_{y the y} - - {I I}_{z z})) \cdot \cdot {ω ω}_{y the y} \cdot \cdot {ω ω}_{z z} + + m m g g \cdot \cdot ((- - c c o o s the s φ φ \cdot \cdot c c o o s the s θ θ \cdot &Center Dot; {r r}_{y the y} + + s the s i i n no φ φ \cdot \cdot c c o o s the s θ θ \cdot \cdot {r r}_{z z}))}{{I I}_{x x}} \\ \frac{(({I I}_{z z} - - {I I}_{x x})) \cdot \cdot {ω ω}_{x x} \cdot &Center Dot; {ω ω}_{z z} + + m m g g \cdot \cdot ((cos cos φ φ \cdot &Center Dot; c c o o s the s θ θ \cdot \cdot {r r}_{x x} + + s the s i i n no θ θ \cdot \cdot {r r}_{z z}))}{{I I}_{y the y}} \\ \frac{(({I I}_{x x} - - {I I}_{y the y})) \cdot &Center Dot; {ω ω}_{x x} \cdot &Center Dot; {ω ω}_{y the y} + + m m g g \cdot &Center Dot; ((- - s the s i i n no φ φ \cdot &Center Dot; c c o o s the s θ θ \cdot \cdot {r r}_{x x} - - s the s i i n no θ θ \cdot \cdot {r r}_{y the y}))}{{I I}_{z z}} \end{matrix}]

Wherein: I _x represents the moment of inertia of the X axis, I _y represents the moment of inertia of the Y axis, and I _z represents the moment of inertia of the Z axis;

m represents the total mass of the three-axis air flotation simulation experiment platform and simulation components;

g is the acceleration due to gravity;

(r _x , _{ry , r z} ₎ represent the position of the center of mass of the three-axis air flotation simulation experiment platform;

Step 4. Integrate the three formulas of the dynamic equations described in step 3 respectively within time t0, t1 and t2, and solve them simultaneously with the kinematic equations in step 2 to obtain the position of the center of mass of the three-axis air flotation simulation experiment platform (r _x , r _y , r _z ):

[\begin{matrix} {r r}_{x x} \\ {r r}_{y the y} \\ {r r}_{z z} \end{matrix}] = = \frac{11}{m m g g} \cdot &Center Dot; [\begin{matrix} - - {I I}_{y the y} \cdot &Center Dot; \underset{t t 00}{&Integral; &Integral;} cos cos φ φ cos cos θ θ \cdot &Center Dot; \underset{t t 11}{&Integral; &Integral;} {ω ω}_{y the y} + + {I I}_{z z} \cdot \cdot \underset{t t 00}{&Integral; &Integral;} sin sin φ φ cos cos θ θ \cdot \cdot \underset{t t 22}{&Integral; &Integral;} {ω ω}_{z z} \\ {I I}_{x x} \cdot &Center Dot; \underset{t t 11}{&Integral; &Integral;} cos cos φ φ cos cos θ θ \cdot &Center Dot; \underset{t t 00}{&Integral; &Integral;} {ω ω}_{x x} + + {I I}_{z z} \cdot &Center Dot; \underset{t t 11}{&Integral; &Integral;} sin sin θ θ \cdot &Center Dot; \underset{t t 22}{&Integral; &Integral;} {ω ω}_{z z} \\ - - {I I}_{x x} \cdot &Center Dot; \underset{t t 22}{&Integral; &Integral;} sin sin φ φ cos cos θ θ \cdot &Center Dot; \underset{t t 00}{&Integral; &Integral;} {ω ω}_{x x} - - {I I}_{y the y} \cdot &Center Dot; \underset{t t 22}{&Integral; &Integral;} sin sin θ θ \cdot &Center Dot; \underset{t t 22}{&Integral; &Integral;} {ω ω}_{z z} \end{matrix}] . .

2. according to the centroid measuring method of three-axis air flotation simulation experiment platform described in claim 1, it is characterized in that, in the step 1, obtain the acquisition process of X-axis angular velocity ω _x and Y-axis angular velocity ω _y as:

The dual-axis inclination angle sensor measures the X-axis angle information and the Y-axis angle information of the three-axis air flotation simulation experiment platform, and the X-axis angle information is output to the industrial computer through the serial communication interface circuit, and the industrial computer differentiates the X-axis angle information Processing, to obtain the X-axis angular velocity ω _x ;

The Y-axis angle information is output to the industrial computer through the RS485 interface circuit, and the industrial computer performs differential processing on the Y-axis angle information to obtain the Y-axis angular velocity ω _y .

3. The method for measuring the centroid of the three-axis air flotation simulation experiment platform according to claim 2, wherein the serial communication interface circuit adopts RS485 or RS232 serial interface circuit.

4. according to the centroid measuring method of three-axis air flotation simulation experiment platform described in claim 1, it is characterized in that, the acquisition process of Z-axis angular velocity ω _z in the step 1:

The angular acceleration sensor measures the angular acceleration of the Z-axis rotation angle of the three-axis air flotation simulation experiment platform, and the angular acceleration of the Z-axis rotation angle is converted into the angular acceleration of the digital signal by the A/D conversion circuit, and the angular acceleration of the digital signal is Integral processing is carried out by the industrial computer to obtain the Z-axis angular velocity ω _z .

5. The centroid measurement method of the three-axis air flotation simulation experiment platform according to claim 1, characterized in that t0=8ms～12ms; t1=16ms～25ms; t2=25ms～35ms.

6. The method for measuring the center of mass of the three-axis air flotation simulation experiment platform according to claim 1, wherein t0=10ms; t1=20ms; t2=30ms.