CN108872942A - The real-time keeping method in active primary reflection surface antenna ideal shape face based on datum mark - Google Patents
The real-time keeping method in active primary reflection surface antenna ideal shape face based on datum mark Download PDFInfo
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Abstract
本发明属于雷达天线技术领域,具体是基于基准点的主动主反射面天线理想形面实时保持方法,它利用一套激光测距测角设备即可同时实现反射面天线主反射面和副反射面的位移检测,无需考虑天线形变的形成因素,可适用于静态载荷,如重力载荷、稳态风载荷、雨雪,也适用于缓变载荷,如温度载荷,同时适用于加工安装误差等。实现反射面的闭环实时调整和主动主反射面天线理想形面的实时保持。
The invention belongs to the technical field of radar antennas, and specifically relates to a method for maintaining the ideal shape of an active main reflector antenna in real time based on a reference point, which uses a set of laser ranging and angle measuring equipment to simultaneously realize the main reflector and the secondary reflector of the reflector antenna Displacement detection does not need to consider the factors of antenna deformation. It can be applied to static loads, such as gravity loads, steady-state wind loads, rain and snow, and slowly changing loads, such as temperature loads. It is also suitable for processing and installation errors. Realize the closed-loop real-time adjustment of the reflector and the real-time maintenance of the ideal shape of the active main reflector antenna.
Description
技术领域technical field
本发明属于雷达天线技术领域,具体是基于基准点的主动主反射面天线理想形面实时保持方法,应用于主动主反射面天线在服役过程中理想形面的实时保持。The invention belongs to the technical field of radar antennas, in particular to a reference point-based method for maintaining the ideal shape of an active main reflector antenna in real time, which is applied to the real-time maintenance of the ideal shape of the active main reflector antenna during service.
背景技术Background technique
反射面天线广泛应用于深空探测、射电天文等领域,随着技术的发展,大口径、高频段是其主要发展方向。口径越大,频段越高,反射面天线的性能则越突出。例如,七十年代联邦德国建造的100米全可动射电望远镜,2000年美国建造的格林班克100米射电望远镜,2012年中国建造的65米天马望远镜,工作频段可达毫米波段(30GHz-300GHz)。Reflector antennas are widely used in deep space exploration, radio astronomy and other fields. With the development of technology, large-aperture and high-frequency bands are the main development directions. The larger the aperture, the higher the frequency band, and the more prominent the performance of the reflector antenna. For example, the 100-meter fully movable radio telescope built by the Federal Republic of Germany in the 1970s, the Green Bank 100-meter radio telescope built by the United States in 2000, and the 65-meter Tianma telescope built by China in 2012 can work in the millimeter wave band (30GHz-300GHz ).
反射面天线口径的增大使得外载荷(重力载荷、温度载荷、风荷等)的影响不可忽视,其形面不可避免地将偏离理想形面,导致其精度难以满足高频段对反射面形面的精度要求,进而导致电性能显著恶化。为了降低加工难度同时提高天线电性能,目前大型高频段反射面天线多采用主动主反射面结构,即主反射面面板安装促动器,面板在一定范围内可主动调整,通过实时调整促动器来保持天线形面的高精度。例如上海65米望远镜的主反射面由1008块面板组成,整个天线结构重约2640吨,同时受到风荷载、温度变形的影响,要求在1104台促动器作用下,其形面精度达到0.3毫米,指向精度达到3角秒。The increase of the antenna diameter of the reflector makes the influence of external loads (gravity load, temperature load, wind load, etc.) cannot be ignored, and its shape will inevitably deviate from the ideal shape, which makes it difficult to meet the high-frequency requirements for the reflector shape. Accuracy requirements, which in turn lead to significant deterioration of electrical performance. In order to reduce the difficulty of processing and improve the electrical performance of the antenna, the current large-scale high-frequency reflector antenna mostly adopts an active main reflector structure, that is, the main reflector panel is equipped with an actuator, and the panel can be actively adjusted within a certain range. By adjusting the actuator in real time To maintain the high precision of the antenna shape. For example, the main reflector of the Shanghai 65-meter telescope is composed of 1008 panels, and the entire antenna structure weighs about 2640 tons. At the same time, it is affected by wind load and temperature deformation. It is required that under the action of 1104 actuators, its shape and surface accuracy should reach 0.3 mm. , the pointing accuracy reaches 3 arc seconds.
主动主反射面天线形面调整的关键是形面变形的实时测量,进而实现促动器的实时调整来保证形面精度,但就目前而言,工程上尚未实现反射面理想形面的实时保持。工程上采用的形面测量方法主要包括人工或者无人机摄影测量、激光测距(激光全站仪/激光跟踪仪)和无线电全息法测量。首先,因人工的干预,其实时性难以满足要求,也无法在天线服役状态下实现测量过程。其次,除了主动主反射面的调整之外,副反射面同样在外载荷作用下将偏离理想位置。目前工程上副反射面的调整多采用经验法,通过测量天线远场方向图,根据远场方向图副瓣的对称性能和增益值,根据经验指导副反射面的调整过程,通常调整次数较多且耗时较长。显然,主动主反射面天线的形面调整需同时兼顾主动主反射面的调整和副反射面的调整,目前而言,尚未实现反射面的闭环实时调整。The key to the adjustment of the antenna shape of the active main reflector is the real-time measurement of the deformation of the shape, and then realize the real-time adjustment of the actuator to ensure the accuracy of the shape. However, at present, the real-time maintenance of the ideal shape of the reflector has not been realized in engineering . The shape and surface measurement methods used in engineering mainly include manual or UAV photogrammetry, laser ranging (laser total station/laser tracker) and radio holographic measurement. First of all, due to manual intervention, it is difficult to meet the real-time requirements, and the measurement process cannot be realized when the antenna is in service. Secondly, in addition to the adjustment of the active main reflector, the secondary reflector will also deviate from the ideal position under the action of external load. At present, the adjustment of the sub-reflector in engineering mostly adopts the empirical method. By measuring the far-field pattern of the antenna, according to the symmetry performance and gain value of the sidelobe of the far-field pattern, the adjustment process of the sub-reflector is guided according to experience. Usually, the number of adjustments is large. And it takes a long time. Obviously, the adjustment of the shape and surface of the active main reflector antenna needs to take into account both the adjustment of the active main reflector and the adjustment of the secondary reflector. At present, the closed-loop real-time adjustment of the reflector has not yet been realized.
发明内容Contents of the invention
本发明的目的在于提供一种基于基准点的主动主反射面天线理想形面实时保持方法,以实现反射面的闭环实时调整和主动主反射面天线理想形面的实时保持。The purpose of the present invention is to provide a real-time method for maintaining the ideal shape of the active main reflector antenna based on the reference point, so as to realize the closed-loop real-time adjustment of the reflector and the real-time maintenance of the ideal shape of the active main reflector antenna.
实现本发明目的的技术方案是:基于基准点的主动主反射面天线理想形面实时保持方法,其特征是:至少包括如下步骤:The technical scheme that realizes the object of the present invention is: the real-time maintenance method of the ideal shape surface of the active main reflector antenna based on the reference point, it is characterized in that: at least comprise the following steps:
步骤一,安装激光测量设备及存储副反射面相关数据;Step 1, install laser measuring equipment and store data related to the sub-reflector;
步骤二,建立基准坐标系及存储主反射面相关数据。Step 2, establishing a reference coordinate system and storing relevant data of the main reflecting surface.
步骤三,粘贴靶标点及存储靶标点相关数据。Step 3, paste the target point and store the relevant data of the target point.
步骤四,计算基准坐标系下副反射面相关数据;Step 4, calculating the relevant data of the sub-reflector in the reference coordinate system;
步骤五,计算副反射面坐标系下主反射面促动器靶标点的球坐标;Step 5, calculating the spherical coordinates of the target point of the main reflector actuator in the secondary reflector coordinate system;
步骤六,计算天线服役过程中促动器靶标点在副面坐标系下的坐标值;Step 6, calculating the coordinate value of the actuator target point in the secondary surface coordinate system during the service of the antenna;
步骤七,计算天线服役过程中基准点靶标点在副面坐标系下的坐标值;Step 7, calculate the coordinate value of the reference point target point in the secondary surface coordinate system during the service of the antenna;
步骤八,计算天线服役过程中副面坐标系原点在基准坐标系下的坐标值;Step 8, calculating the coordinate value of the origin of the secondary surface coordinate system in the reference coordinate system during the service of the antenna;
步骤九,计算天线服役过程中副面坐标系到基准坐标系的旋转矩阵;Step 9, calculating the rotation matrix from the sub-surface coordinate system to the reference coordinate system during the service of the antenna;
步骤十,计算天线服役过程中主面促动器的法向调整量;Step 10, calculating the normal adjustment of the main surface actuator during the service of the antenna;
步骤十一,计算天线服役过程中副面位姿调整量;Step 11, calculating the adjustment amount of the secondary surface pose during the service of the antenna;
步骤十二,天线服役过程中不断重复步骤五到步骤十一,实现形面的实时保持。Step 12: Repeat steps 5 to 11 continuously during the service of the antenna to realize real-time maintenance of shape and surface.
所述的步骤一安装激光测量设备及存储副反射面相关数据是在副反射面背面安装激光测距测角仪系统,副反射面顶点位置预留适当尺寸的孔洞,将激光探头移动至副反射面顶点孔洞位置,假定测量坐标系与副面坐标系重合,记为Os-xsyszs,其中Os为坐标原点,位于副反射面顶点位置;在副反射面上标定两个副反射面位姿定位点:Os点和Os-zs轴上一点D,点D在Os-xsyszs坐标系下的坐标为其中,上标s表示Os-xsyszs坐标系下的坐标值。The first step to install the laser measuring equipment and store the related data of the sub-reflector is to install the laser rangefinder goniometer system on the back of the sub-reflector, reserve a hole of appropriate size at the apex of the sub-reflector, and move the laser probe to the sub-reflector. The position of the hole at the vertex of the surface, assuming that the measurement coordinate system coincides with the coordinate system of the secondary surface, is recorded as O s -x s y s z s , where O s is the coordinate origin, located at the vertex of the secondary reflective surface; The positioning point of the sub-reflector’s pose: O s point and a point D on the O s -z s axis, the coordinates of point D in the O s -x s y s z s coordinate system are Wherein, the superscript s represents the coordinate value in the O s -x s y s z s coordinate system.
所述的步骤二建立基准坐标系及存储主反射面相关数据是在主反射面顶点位置建立基准坐标系,记为Or-xryrzr,其中Or为坐标原点,位于主反射面顶点位置,基准坐标系的坐标轴分别与副反射面坐标系的坐标轴平行且同向;在基准坐标系下选择三个基准点A、B和C,其在Or-xryrzr坐标系下的坐标分别记为和且在垂直于Or-zr轴的平面上不共面,其中,上标r表示Or-xryrzr坐标系下的坐标值,该基准点可独立于反射体以避免其发生变形位移,或者该基准点位于反射体中心变形位移较小位置。The second step to establish a reference coordinate system and store relevant data on the main reflector is to establish a reference coordinate system at the apex position of the main reflector, which is recorded as O r -x ry r z r , where O r is the coordinate origin, located at the main reflector The position of the vertex of the surface, the coordinate axes of the reference coordinate system are parallel to and in the same direction as the coordinate axes of the sub-reflector coordinate system; select three reference points A, B and C under the reference coordinate system, which are in O r -x r y r The coordinates in the z r coordinate system are recorded as and and are not coplanar on the plane perpendicular to the O r -z r axis, where the superscript r represents the coordinate value in the O r -x ry r z r coordinate system , the reference point can be independent of the reflector to avoid its Deformation displacement occurs, or the reference point is located at the position where the deformation displacement of the center of the reflector is small.
所述的步骤三粘贴靶标点及存储靶标点相关数据是在主反射面促动器与面板连接位置粘贴靶标点,在Or-xryrzr坐标系下记靶标点坐标为确定促动器靶标点法向单位向量其中,下标a表示第a个靶标点;在步骤二所述三个基准点位置粘贴靶标点,忽略靶标点厚度,其坐标同基准点A、B和C的坐标。The step three of pasting the target point and storing the relevant data of the target point is to paste the target point at the connection position between the main reflector actuator and the panel, and record the coordinates of the target point under the O r -x ry r z r coordinate system as Determining the normal unit vector of the actuator target point Among them, the subscript a represents the a-th target point; paste the target point at the three reference point positions mentioned in step 2, ignoring the thickness of the target point, and its coordinates are the same as the coordinates of the reference points A, B and C.
所述的步骤四计算基准坐标系下副反射面相关数据是根据理想天线设计参数,在基准坐标系Or-xryrzr坐标系下,确定副反射面顶点Os点的坐标确定步骤一中副反射面Os-zs轴上一点D点的坐标其中 The calculation of the relevant data of the secondary reflector in the reference coordinate system in the step 4 is to determine the coordinates of the vertex O s of the secondary reflector in the reference coordinate system O r -x ry r z r coordinate system according to the ideal antenna design parameters Determine the coordinates of a point D on the secondary reflector O s -z s axis in step 1 in
所述的步骤五计算副反射面坐标系下主反射面促动器靶标点的球坐标包括:The step 5 calculating the spherical coordinates of the main reflector actuator target point under the secondary reflector coordinate system includes:
(5a)在副反射面坐标系Os-xsyszs坐标系下,确定主反射面促动器靶标点的坐标值其中 (5a) Under the coordinate system O s -x s y s z s of the secondary reflector, determine the coordinate value of the target point of the main reflector actuator in
(5b)在副反射面坐标系Os-xsyszs坐标系下,将主反射面促动器靶标点的坐标值转换为球坐标其中其中cart2sph为MATLAB数值分析软件中的笛卡尔坐标到球坐标的转换函数。(5b) Under the coordinate system O s -x s y s z s of the secondary reflector, the coordinate value of the target point of the main reflector actuator convert to spherical coordinates in Where cart2sph is the conversion function from Cartesian coordinates to spherical coordinates in MATLAB numerical analysis software.
所述的步骤六计算天线服役过程中促动器靶标点在副面坐标系下的坐标值包括:。The step 6 to calculate the coordinate values of the actuator target point in the secondary surface coordinate system during the service of the antenna includes: .
(6a)利用激光测距测角仪测量促动器靶标点到副反射面坐标系坐标原点的距离及仰角其分别为天线变形后促动器靶标点在副反射面坐标系发生刚体位移后的球坐标的第一分量和第二分量,其中,仰角表示激光束与天线变形后Os-zs轴正向的夹角,上标“′”表示天线变形后的数据;(6a) Measure the distance from the target point of the actuator to the origin of the coordinate system of the sub-reflector using a laser ranging goniometer and elevation angle They are the first component and the second component of the spherical coordinates of the actuator target point after the deformation of the antenna in the sub-reflector coordinate system after the rigid body displacement, where the elevation angle Indicates the angle between the laser beam and the positive direction of the O s -z s axis after the antenna is deformed, and the superscript "'" indicates the data after the antenna is deformed;
(6b)因影响反射面天线电性能的主要因素是反射面的轴向变形,故忽略反射面节点绕轴向的旋转位移,近似认为天线变形后促动器靶标点在副反射面坐标系发生刚体位移后的球坐标的第三分量 (6b) Since the main factor affecting the electrical performance of the reflector antenna is the axial deformation of the reflector, the rotational displacement of the reflector nodes around the axis is ignored, and it is approximately considered that the actuator target point occurs in the secondary reflector coordinate system after the antenna is deformed. Third component of spherical coordinates after rigid body displacement
(6c)计算变形后的促动器靶标点在副反射面坐标系发生刚体位移后的坐标值其中sph2cart为MATLAB数值分析软件中的球坐标到笛卡尔坐标的转换函数。(6c) Calculate the coordinate value of the deformed actuator target point after rigid body displacement in the secondary reflector coordinate system Among them, sph2cart is the conversion function from spherical coordinates to Cartesian coordinates in MATLAB numerical analysis software.
所述的步骤七计算天线服役过程中基准点靶标点在副面坐标系下的坐标值包括:The step 7 to calculate the coordinate values of the reference point target point in the secondary surface coordinate system during the service of the antenna includes:
(7a)利用激光测距测角仪测量基准点靶标点到副反射面坐标系坐标原点的距离及仰角其分别为变形后基准点靶标点在副反射面坐标系发生刚体位移后的球坐标的第一分量和第二分量,其中,下标“b”表示基准点A或者B或者C;(7a) Use the laser ranging goniometer to measure the distance from the reference point target point to the coordinate origin of the sub-reflector coordinate system and elevation angle They are respectively the first component and the second component of the spherical coordinates of the deformed reference point target point after the rigid body displacement occurs in the sub-reflector coordinate system, where the subscript " b " indicates the reference point A or B or C;
(7b)近似认为基准点靶标点在副反射面坐标系发生刚体位移后的球坐标的第三分量其中,符号表示取向量的第三分量,当“b”表示基准点A时,当“b”表示基准点B时,当“b”表示基准点C时, (7b) Approximately consider the third component of the spherical coordinates of the reference point target point after the rigid body displacement occurs in the sub-reflector coordinate system in, symbol Indicates the third component of the vector, when " b " indicates the reference point A, When " b " indicates reference point B, When " b " indicates reference point C,
(7c)计算基准点靶标点在副反射面坐标系发生刚体位移后的坐标值 (7c) Calculate the coordinate value of the reference point target point after the rigid body displacement occurs in the sub-reflector coordinate system
所述的步骤八计算天线服役过程中副面坐标系原点在基准坐标系下的坐标值包括:The step eight of calculating the coordinate values of the origin of the secondary surface coordinate system in the reference coordinate system during the service of the antenna includes:
(8a)在步骤七中令“b”依次表示基准点A、B和C,则依次得到三个基准点的距离和仰角 (8a) In step 7, let " b " denote the reference points A, B and C in turn, then get the distances of the three reference points in turn and elevation
(8b)求解下述方程组并求解得到天线服役过程中副面坐标系原点在基准坐标系下的坐标值 (8b) Solve the following equations and obtain the coordinate values of the origin of the subsurface coordinate system in the reference coordinate system during the service of the antenna
所述的步骤九计算天线服役过程中副面坐标系到基准坐标系的旋转矩阵包括:The calculation of the rotation matrix from the sub-surface coordinate system to the reference coordinate system during the antenna service process in step nine includes:
(9a)在步骤七中令“b”依次表示基准点A、B和C,则依次得到坐标值和 (9a) In step 7, let " b " denote the reference points A, B and C in sequence, then the coordinate values are obtained in sequence and
(9b)建立如下方程组:(9b) Establish the following equations:
其中,T′s2r表示天线服役过程中副面坐标系到基准坐标系的旋转矩阵;Among them, T′ s2r represents the rotation matrix from the sub-surface coordinate system to the reference coordinate system during the service of the antenna;
(9c)将步骤(9b)方程组写成如下矩阵形式:(9c) Write step (9b) system of equations into following matrix form:
(9d)求解步骤(9c)方程组得到旋转矩阵T′s2r:(9d) solving step (9c) system of equations to obtain the rotation matrix T′ s2r :
其中[]-1表示矩阵的逆。where [] -1 means the inverse of the matrix.
所述的步骤十计算天线服役过程中主面促动器的法向调整量包括如下步骤:The step ten calculating the normal adjustment of the main surface actuator during the service of the antenna includes the following steps:
(10a)按如下公式计算促动器靶标点在基准坐标系下的坐标 (10a) Calculate the coordinates of the actuator target point in the reference coordinate system according to the following formula
(10b)按如下公式计算促动器靶标点法向量与反射面轴向夹角的余弦值:(10b) Calculate the cosine value of the angle between the normal vector of the actuator target point and the axial direction of the reflector according to the following formula:
(10c)按如下公式计算促动器法向调整量Δna:(10c) Calculate the normal adjustment amount Δn a of the actuator according to the following formula:
其中Δna>0表示促动器伸长,Δna<0表示促动器收缩。Where Δn a >0 means the actuator is stretched, and Δn a <0 means the actuator is contracted.
所述的步骤十一计算天线服役过程中副面位姿调整量包括:The calculation of the secondary surface pose adjustment amount during the antenna service process in step eleven includes:
(11a)按如下公式确定Os点的调整量 (11a) Determine the adjustment amount of point O s according to the following formula
(11b)计算副反射面发生刚体位移后D点在基准坐标系下的坐标值 (11b) Calculate the coordinate value of point D in the reference coordinate system after the rigid body displacement of the secondary reflector
(11c)按如下公式确定D点的调整量(ΔxD,ΔyD,ΔzD)(11c) Determine the adjustment amount of point D according to the following formula (Δx D , Δy D , Δz D )
所述的步骤十二具体包括:Described step twelve specifically includes:
根据步骤(10c)调整量计算结果依次调整主反射面各个促动器,使主反射面保持理想形状,根据步骤(11a)和(11c)调整量计算结果调整副反射面位姿,使副反射面保持理想位置,并在服役过程中不断重复上述过程,实现主动主反射面天线理想形面的实时保持。According to the calculation result of the adjustment amount in step (10c), each actuator on the main reflector surface is adjusted sequentially to keep the main reflector The ideal position of the active main reflector antenna is maintained, and the above process is repeated continuously during service to realize the real-time maintenance of the ideal shape of the active main reflector antenna.
本发明与现有技术相比,具有如下优点:Compared with the prior art, the present invention has the following advantages:
1、本发明仅仅利用一套激光测距测角设备即可同时实现反射面天线主反射面和副反射面的位移检测,无需考虑天线形变的形成因素,可适用于静态载荷,如重力载荷、稳态风载荷、雨雪,也适用于缓变载荷,如温度载荷,同时适用于加工安装误差等;1. The present invention can realize the displacement detection of the main reflection surface and the secondary reflection surface of the reflective surface antenna at the same time only by using a set of laser ranging and angle measuring equipment, without considering the formation factors of the antenna deformation, and can be applied to static loads, such as gravity loads, Steady-state wind load, rain and snow are also applicable to slow-changing loads, such as temperature loads, and are also applicable to processing and installation errors, etc.;
2、本发明形面检测过程无需人工干预,可实现自动化检测,根据检测结果实时调整主反射面促动器和副反射面可调设备,使主反射面和副反射面同时保持在理想设计位置,实现天线服役过程中理想形面的实时保持。2. The shape and surface detection process of the present invention does not require manual intervention, and automatic detection can be realized. According to the detection results, the actuator of the main reflective surface and the adjustable equipment of the secondary reflective surface can be adjusted in real time, so that the main reflective surface and the secondary reflective surface can be kept at the ideal design position at the same time , to realize the real-time maintenance of the ideal shape of the antenna during service.
下面结合附图及实施案例对本发明做进一步说明。The present invention will be further described below in conjunction with accompanying drawings and examples of implementation.
附图说明Description of drawings
图1为本发明的实现流程图;Fig. 1 is the realization flowchart of the present invention;
图2为理想反射面天线及坐标系示意图;Fig. 2 is a schematic diagram of an ideal reflector antenna and a coordinate system;
图3为变形反射面天线及激光测量示意图;Fig. 3 is a schematic diagram of deformation reflector antenna and laser measurement;
图4为促动器调整量计算过程示意图;Fig. 4 is a schematic diagram of the calculation process of the actuator adjustment amount;
图5为副反射面调整过程示意图;Fig. 5 is a schematic diagram of the adjustment process of the secondary reflector;
图6为本发明使用的35米反射面天线模型图;Fig. 6 is the 35 meters reflector antenna model figure that the present invention uses;
图7为本发明使用的35米反射面天线促动器靶标点调整前后变形对比图;Fig. 7 is the comparison diagram of deformation before and after adjustment of the target point of the 35-meter reflector antenna actuator used in the present invention;
图8为本发明使用的35米反射面天线副反射面调整前后位置对比图。Fig. 8 is a position comparison diagram before and after adjustment of the sub-reflector of the 35-meter reflector antenna used in the present invention.
具体实施方式Detailed ways
如图1所示,基于基准点的主动主反射面天线理想形面实时保持方法,包括如下步骤:As shown in Figure 1, the real-time maintenance method of the ideal shape of the active main reflector antenna based on the reference point includes the following steps:
步骤一,安装激光测量设备及存储副反射面相关数据。Step 1, installing laser measuring equipment and storing relevant data of the sub-reflector.
如图2所示,在副反射面背面安装激光测距测角仪系统,副反射面顶点位置预留适当尺寸的孔洞,将激光探头移动至副反射面顶点孔洞位置,假定测量坐标系与副面坐标系重合,记为Os-xsyszs,其中Os为坐标原点,位于副反射面顶点位置;在副反射面上标定两个副反射面位姿定位点:Os点和Os-zs轴上一点D,点D在Os-xsyszs坐标系下的坐标为其中,上标s表示Os-xsyszs坐标系下的坐标值。As shown in Figure 2, the laser ranging goniometer system is installed on the back of the sub-reflecting surface, and a hole of appropriate size is reserved at the apex of the sub-reflecting surface, and the laser probe is moved to the hole position at the apex of the sub-reflecting surface. The surface coordinate system coincides, recorded as O s -x s y s z s , where O s is the coordinate origin, located at the apex of the sub-reflector; two sub-reflector pose orientation points are calibrated on the sub-reflector: O s point and a point D on the O s -z s axis, the coordinates of point D in the O s -x s y s z s coordinate system are Wherein, the superscript s represents the coordinate value in the O s -x s y s z s coordinate system.
步骤二,建立基准坐标系及存储主反射面相关数据。Step 2, establishing a reference coordinate system and storing relevant data of the main reflecting surface.
如图2所示,在主反射面顶点位置建立基准坐标系,记为Or-xryrzr,其中Or为坐标原点,位于主反射面顶点位置,基准坐标系的坐标轴分别与副反射面坐标系的坐标轴平行且同向;在基准坐标系下选择三个基准点A、B和C,其在Or-xryrzr坐标系下的坐标分别记为和且在垂直于Or-zr轴的平面上不共面,其中,上标r表示Or-xryrzr坐标系下的坐标值,该基准点可独立于反射体以避免其发生变形位移,或者该基准点位于反射体中心变形位移较小位置;As shown in Figure 2, a reference coordinate system is established at the apex position of the main reflection surface, which is denoted as O r -x ry r z r , where O r is the coordinate origin, located at the apex position of the main reflection surface, and the coordinate axes of the reference coordinate system are respectively Parallel to and in the same direction as the coordinate axes of the sub-reflector coordinate system; select three reference points A, B and C in the reference coordinate system, and their coordinates in the O r -x ry r z r coordinate system are respectively recorded as and and are not coplanar on the plane perpendicular to the O r -z r axis, where the superscript r represents the coordinate value in the O r -x ry r z r coordinate system , the reference point can be independent of the reflector to avoid its Deformation displacement occurs, or the reference point is located at the position where the deformation displacement of the center of the reflector is small;
步骤三,粘贴靶标点及存储靶标点相关数据。Step 3, paste the target point and store the relevant data of the target point.
如图2所示,在主反射面促动器与面板连接位置粘贴靶标点,在Or-xryrzr坐标系下记靶标点坐标为确定促动器靶标点法向单位向量其中,下标a表示第a个靶标点;在步骤二所述三个基准点位置粘贴靶标点,忽略靶标点厚度,其坐标同基准点A、B和C的坐标;As shown in Figure 2, the target point is pasted at the position where the main reflector actuator is connected to the panel, and the coordinates of the target point are recorded in the O r -x ry r z r coordinate system as Determining the normal unit vector of the actuator target point Wherein, the subscript a represents the ath target point; paste the target point at the three reference point positions described in step 2, ignore the thickness of the target point, and its coordinates are the same as the coordinates of the reference points A, B and C;
步骤四,计算基准坐标系下副反射面相关数据。Step 4, calculating data related to the sub-reflector in the reference coordinate system.
根据理想天线设计参数,在基准坐标系Or-xryrzr坐标系下,确定副反射面顶点Os点的坐标确定步骤一中副反射面Os-zs轴上一点D点的坐标其中 According to the ideal antenna design parameters, in the reference coordinate system O r -x ry r z r coordinate system , determine the coordinates of the sub-reflector vertex O s point Determine the coordinates of a point D on the secondary reflector O s -z s axis in step 1 in
步骤五,计算副反射面坐标系下主反射面促动器靶标点的球坐标。Step five, calculating the spherical coordinates of the target point of the actuator on the main reflector in the coordinate system of the secondary reflector.
(5a)在副反射面坐标系Os-xsyszs坐标系下,确定主反射面促动器靶标点的坐标值其中 (5a) Under the coordinate system O s -x s y s z s of the secondary reflector, determine the coordinate value of the target point of the main reflector actuator in
(5b)在副反射面坐标系Os-xsyszs坐标系下,将主反射面促动器靶标点的坐标值转换为球坐标其中其中cart2sph为MATLAB数值分析软件中的笛卡尔坐标到球坐标的转换函数;(5b) Under the coordinate system O s -x s y s z s of the secondary reflector, the coordinate value of the target point of the main reflector actuator convert to spherical coordinates in Where cart2sph is the conversion function from Cartesian coordinates to spherical coordinates in MATLAB numerical analysis software;
步骤六,计算天线服役过程中促动器靶标点在副面坐标系下的坐标值。Step six, calculate the coordinate value of the actuator target point in the secondary surface coordinate system during the service of the antenna.
(6a)如图3所示,利用激光测距测角仪测量促动器靶标点到副反射面坐标系坐标原点的距离及仰角其分别为天线变形后促动器靶标点在副反射面坐标系发生刚体位移后的球坐标的第一分量和第二分量,其中,仰角表示激光束与天线变形后Os-zs轴正向的夹角,上标“′”表示天线变形后的数据;(6a) As shown in Figure 3, use the laser ranging goniometer to measure the distance from the target point of the actuator to the origin of the coordinate system of the secondary reflector and elevation angle They are the first component and the second component of the spherical coordinates of the actuator target point after the deformation of the antenna in the sub-reflector coordinate system after the rigid body displacement, where the elevation angle Indicates the angle between the laser beam and the positive direction of the O s -z s axis after the antenna is deformed, and the superscript "'" indicates the data after the antenna is deformed;
(6b)因影响反射面天线电性能的主要因素是反射面的轴向变形,忽略反射面节点绕轴向的旋转位移,近似认为天线变形后促动器靶标点在副反射面坐标系发生刚体位移后的球坐标的第三分量 (6b) Since the main factor affecting the electrical performance of the reflector antenna is the axial deformation of the reflector, ignoring the rotational displacement of the reflector nodes around the axis, it is approximately considered that the actuator target point is a rigid body in the secondary reflector coordinate system after the antenna is deformed the third component of the displaced spherical coordinates
(6c)计算变形后的促动器靶标点在副反射面坐标系发生刚体位移后的坐标值其中sph2cart为MATLAB数值分析软件中的球坐标到笛卡尔坐标的转换函数;(6c) Calculate the coordinate value of the deformed actuator target point after rigid body displacement in the secondary reflector coordinate system Where sph2cart is the conversion function from spherical coordinates to Cartesian coordinates in MATLAB numerical analysis software;
步骤七,计算天线服役过程中基准点靶标点在副面坐标系下的坐标值。Step 7, calculating the coordinate values of the reference point target point in the secondary surface coordinate system during the service of the antenna.
(7a)利用激光测距测角仪测量基准点靶标点到副反射面坐标系坐标原点的距离及仰角其分别为变形后基准点靶标点在副反射面坐标系发生刚体位移后的球坐标的第一分量和第二分量,其中,下标“b”表示基准点A或者B或者C;(7a) Use the laser ranging goniometer to measure the distance from the reference point target point to the coordinate origin of the sub-reflector coordinate system and elevation angle They are respectively the first component and the second component of the spherical coordinates of the deformed reference point target point after the rigid body displacement occurs in the sub-reflector coordinate system, where the subscript " b " indicates the reference point A or B or C;
(7b)近似认为基准点靶标点在副反射面坐标系发生刚体位移后的球坐标的第三分量其中,符号表示取向量的第三分量,当“b”表示基准点A时,当“b”表示基准点B时,当“b”表示基准点C时, (7b) Approximately consider the third component of the spherical coordinates of the reference point target point after the rigid body displacement occurs in the sub-reflector coordinate system in, symbol Indicates the third component of the vector, when " b " indicates the reference point A, When " b " indicates reference point B, When " b " indicates reference point C,
(7c)计算基准点靶标点在副反射面坐标系发生刚体位移后的坐标值 (7c) Calculate the coordinate value of the reference point target point after the rigid body displacement occurs in the sub-reflector coordinate system
步骤八,计算天线服役过程中副面坐标系原点在基准坐标系下的坐标值。Step 8, calculating the coordinate values of the origin of the secondary surface coordinate system in the reference coordinate system during the service of the antenna.
(8a)在步骤七中令“b”依次表示基准点A、B和C,则依次得到距离和仰角 (8a) In step 7, let " b " denote the reference points A, B and C in turn, and then get the distance and elevation
(8b)求解下述方程组并求解得到天线服役过程中副面坐标系原点在基准坐标系下的坐标值 (8b) Solve the following equations and obtain the coordinate values of the origin of the subsurface coordinate system in the reference coordinate system during the service of the antenna
步骤九,计算天线服役过程中副面坐标系到基准坐标系的旋转矩阵。Step 9, calculating the rotation matrix from the sub-surface coordinate system to the reference coordinate system during the service of the antenna.
(9a)在步骤七中令“b”依次表示基准点A、B和C,则依次得到坐标值和 (9a) In step 7, let " b " denote the reference points A, B and C in sequence, then the coordinate values are obtained in sequence and
(9b)建立如下方程组:(9b) Establish the following equations:
其中,T′s2r表示天线服役过程中副面坐标系到基准坐标系的旋转矩阵;Among them, T′ s2r represents the rotation matrix from the sub-surface coordinate system to the reference coordinate system during the service of the antenna;
(9c)将步骤(9b)方程组写成如下矩阵形式:(9c) Write step (9b) system of equations into following matrix form:
(9d)求解步骤(9c)方程组得到旋转矩阵T′s2r:(9d) solving step (9c) system of equations to obtain the rotation matrix T′ s2r :
其中[]-1表示矩阵的逆;Where [] -1 represents the inverse of the matrix;
步骤十,计算天线服役过程中主面促动器的法向调整量。Step 10, calculating the normal adjustment of the main surface actuator during the service of the antenna.
如图4所示,天线服役过程中主面促动器的法向调整量计算过程如下:As shown in Figure 4, the calculation process of the normal adjustment of the main surface actuator during the service of the antenna is as follows:
(10a)按如下公式计算促动器靶标点在基准坐标系下的坐标 (10a) Calculate the coordinates of the actuator target point in the reference coordinate system according to the following formula
(10b)按如下公式计算促动器靶标点法向量与反射面轴向夹角的余弦值:(10b) Calculate the cosine value of the angle between the normal vector of the actuator target point and the axial direction of the reflector according to the following formula:
(10c)按如下公式计算促动器法向调整量Δna:(10c) Calculate the normal adjustment amount Δn a of the actuator according to the following formula:
其中Δna>0表示促动器伸长,Δna<0表示促动器收缩Where Δn a >0 indicates that the actuator is elongated, and Δn a <0 indicates that the actuator contracts
步骤十一,计算天线服役过程中副面位姿调整量。Step 11, calculating the adjustment amount of the secondary surface pose during the service of the antenna.
如图5所示,副反射面位姿可根据标定点Os点和Os-zs轴上一点D点的位置确定,故计算天线服役过程中副反射面位姿可转换为计算点Os和点D的位移,具体步骤如下:As shown in Figure 5, the pose of the sub-reflector can be determined according to the calibration point O s and the position of a point D on the O s -z s axis, so the pose of the sub-reflector can be converted to the calculation point O s and the displacement of point D, the specific steps are as follows:
(11a)按如下公式确定Os点的调整量 (11a) Determine the adjustment amount of point O s according to the following formula
(11b)计算副反射面发生刚体位移后D点在基准坐标系下的坐标值 (11b) Calculate the coordinate value of point D in the reference coordinate system after the rigid body displacement of the secondary reflector
(11c)按如下公式确定D点的调整量(ΔxD,ΔyD,ΔzD)(11c) Determine the adjustment amount of point D according to the following formula (Δx D , Δy D , Δz D )
步骤十二,天线服役过程中不断重复步骤五到步骤十一,实现形面实时保持。Step 12: Repeat steps 5 to 11 continuously during the service of the antenna to achieve real-time maintenance of shape and surface.
根据步骤(10c)调整量计算结果依次调整主反射面各个促动器,使主反射面保持理想形状,根据步骤(11a)和(11c)调整量计算结果调整副反射面位姿,使副反射面保持理想位置,并在服役过程中不断重复上述过程,实现主动主反射面天线理想形面的实时保持。According to the calculation result of the adjustment amount in step (10c), each actuator on the main reflector surface is adjusted sequentially to keep the main reflector The ideal position of the active main reflector antenna is maintained, and the above process is repeated continuously during service to realize the real-time maintenance of the ideal shape of the active main reflector antenna.
本发明的优点可通过以下仿真实验进一步说明:Advantages of the present invention can be further illustrated by following simulation experiments:
1、仿真条件1. Simulation conditions
针对如图6所示的某35米双反射面天线,对本发明方法进行仿真验证。当反射面天线指平时,因重力变形导致主反射面发生变形,且副反射面发生平移和转动。假定副反射面顶点位置安装有测量系统,通过本发明方法给出促动器调整量和副反射面调整过程,以验证本发明方法的正确性。本仿真案例中,基准坐标系下,基准点坐标分别为(1702.5,0,500)、(0,1702.5,900)、(-1474.4,-851.25,0),单位毫米,副反射面位姿定位点坐标分别为(0,0,10882)、(0,0,10482),单位毫米。For a 35-meter double-reflector antenna as shown in Figure 6, the method of the present invention is simulated and verified. When the antenna on the reflecting surface is flat, the main reflecting surface is deformed due to gravity deformation, and the secondary reflecting surface is translated and rotated. Assuming that a measuring system is installed at the apex position of the sub-reflecting surface, the adjustment amount of the actuator and the adjustment process of the sub-reflecting surface are given through the method of the present invention to verify the correctness of the method of the present invention. In this simulation case, under the reference coordinate system, the coordinates of the reference points are (1702.5,0,500), (0,1702.5,900), (-1474.4,-851.25,0), the unit is mm, and the coordinates of the positioning point of the secondary reflector They are (0,0,10882) and (0,0,10482) respectively, in millimeters.
2、仿真结果2. Simulation results
图7给出主反射面天线促动器靶标点调整前后变形对比图。调整前,促动器靶标点变形量较大,变形范围近似为±3毫米,均方根误差1.34毫米。调整后,促动器靶标点变形大幅度减小,逼近理想反射面位置,变形范围近似为±0.5毫米,均方根误差0.28毫米,均方根误差的改善百分比79.1%。Figure 7 shows the comparison diagram of the deformation before and after the adjustment of the target point of the antenna actuator on the main reflector. Before adjustment, the target point of the actuator deformed a lot, the deformation range was approximately ±3 mm, and the root mean square error was 1.34 mm. After adjustment, the deformation of the target point of the actuator is greatly reduced, approaching the position of the ideal reflective surface, the deformation range is approximately ±0.5 mm, the root mean square error is 0.28 mm, and the improvement percentage of the root mean square error is 79.1%.
图8给出副反射面调整前后位置对比图。因反射面天线指平时重力方向为y轴方向,故y轴方向的副反射面位移较大,而x轴方向的副反射面位移较小,图中不予考虑。调整前,副反射面大幅远离理想位置,约6.2毫米,且姿态有一定偏转。调整后,副反射面明显靠近理想位置,且姿态有小幅改善。Fig. 8 shows a comparison diagram of the position of the sub-reflecting surface before and after adjustment. Because the reflector antenna refers to the normal gravity direction as the y-axis direction, the displacement of the sub-reflector in the y-axis direction is relatively large, while the displacement of the sub-reflector in the x-axis direction is small, which is not considered in the figure. Before the adjustment, the sub-reflector is far away from the ideal position by about 6.2 mm, and the posture has a certain deflection. After adjustment, the sub-reflector is significantly closer to the ideal position, and the attitude has improved slightly.
改变仿真条件,将三个基准点分散分布,其坐标分别为(5702.5,0,200)、(0,5702.5,200)、(-5474.4,-2051.25,0),单位毫米,则形面调整结果将更加准确,如图7“基准点分散-调整后”曲线所示,副反射面的调整结果不再给出。Change the simulation conditions and disperse the three reference points, whose coordinates are (5702.5,0,200), (0,5702.5,200), (-5474.4,-2051.25,0), the unit is mm, and the shape adjustment result will be more accurate. Accurately, as shown in the "reference point dispersion-after adjustment" curve in Figure 7, the adjustment result of the sub-reflector is no longer given.
仿真结果表明,本发明的方法可以用于主动主反射面天线形面实时调整过程,可将主反射面和副反射面同时调整到理想位置,服役过程中不断循环上述过程,可实现主动主反射面天线理想形面的实时保持。The simulation results show that the method of the present invention can be used in the real-time adjustment process of the antenna shape of the active main reflector, the main reflector and the secondary reflector can be adjusted to the ideal position at the same time, and the above process is continuously cycled during service to realize the active main reflector The real-time maintenance of the ideal shape of the surface antenna.
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