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Table of Content

    15 November 2020, Volume 40 Issue 6 Previous Issue    Next Issue
    Research Articles
    Statistical Investigation on the Galactic Cosmic Rays and Solar Wind Variation Based on ACE Observations
    GUO Xiaocheng, CAO Shihao, XIONG Ming
    2020, 40 (6):  969-979.  doi: 10.11728/cjss2020.06.969
    Abstract ( 352 )   PDF (992KB) ( 87 )   Save
    Galactic Cosmic Rays (GCRs) are originated from the interstellar medium and modulated by the heliospheric magnetic field when they enter the heliosphere. Based on the GCR and plasma observations from ACE spacecraft, the relation between the GCR counts and the solar wind parameters during the recent two periods of solar minimum (the years of 2007.0-2009.0 and 2016.5-2019.0) was analyzed by means of the Superposed Epoch Analysis (SEA) method. The results indicate that GCRs are strongly modulated by the Corotating Interaction Regions (CIR) in solar wind, the Stream Interfaces (SI) sandwiched between fast and slow solar wind are closely related with the depression of GCR counts. The mechanism of the GCR variation is investigated through the empirical diffusion coefficients. The so-called "snow-plough" effect of GCR variation prior to the SI crossing appears during the first period, then the GCR counts decrease after the crossing, which corresponds to the sudden drop of diffusion coefficient at the SI. However, this effect is not observed for the second period, the decrease of GCR counts are simply caused by the enhancement of the diffusion coefficient after the SI crossing. Moreover, Heliospheric Current Sheet (HCS) correlate with GCR counts well, the GCRs drift along the current sheet and then accumulate to a pileup structure, which is physically balanced between their diffusion and drift effects. Finally, based on the observation and Parker transport theory, we discuss the physical mechanism of the GCR variation for the crossings of SIs and HCS, and proposed that the interplay between drift and diffusion determines the GCR distribution and variation at a heliocentric distance of 1AU.
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    Simulation of Mean Free Path of Solar Energetic Particles in Three-dimensional MHD Background
    WANG Shangjie, WEI Wenwen, LIU Yousheng, ZHU Yuji, SHEN Fang
    2020, 40 (6):  980-989.  doi: 10.11728/cjss2020.06.980
    Abstract ( 286 )   PDF (1121KB) ( 74 )   Save
    The mean free path of SEP is an important parameter in the study of SEP propagation in space physics, which is determined by the physical properties of SEP and solar wind. In this paper, the MHD-SEP model is used to discuss the mean free path under the three-dimensional MHD background field. The advantage of this model is that it has the solar wind background field tending to the real physical model. Two CRs were selected to simulate the high and low years of solar activity, and the spatial changes were qualitatively analyzed, and the correlation between mean free path and radial solar wind speed was studied. The conclusion of the spatial distribution of the mean free equation obtained by this method can be consistent with that obtained by previous scholars, and can be used to qualitatively establish the parallel mean free equation. The model can reflect the different characteristics of the distribution and value of the parallel mean free path in different events. It shows that the average free path depends on the radial direction and has a good negative correlation with the radial solar wind velocity. This work can be used as a reference for future research on the mean free path of SEP.
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    Comparative Study of Bow Shock Models
    ZHOU Yue, Lü Jianyong, WANG Ming, YUAN Huanzhi
    2020, 40 (6):  990-999.  doi: 10.11728/cjss2020.06.990
    Abstract ( 321 )   PDF (1745KB) ( 53 )   Save
    The Earth's bow shock is created by the interaction of the supersonic solar wind and the magnetospheric obstacle. The bow shock is a very important interface. When the satellites pass through the bow shock, its environment will change significantly. In catastrophic space weather conditions, it will cause great damage to the satellites. Therefore, investigating the shape of the bow shock is of great significance for space weather forecast and the satellite environment monitoring. In the past few decades, many bow shock models have been built to study the relationship between solar wind and bow shock. This paper compares the Peredo model, Merka model, Chao model, and Lu model under both extreme solar wind conditions (including large dipole tilt angle) and quiet solar wind conditions. Results show that during the extreme solar wind conditions and quiet solar wind conditions, the prediction of the Peredo model has a large deviation. Merka model is not accurate during the extreme solar wind conditions. Chao model can accurately describe the bow shock under quiet solar wind conditions but with a large deviation for large dipole tilt angle conditions. Lu model can accurately descry be bow shock under both extreme solar wind conditions and quiet solar wind conditions.
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    Statistical Study on the Geomagnetic Substorm
    LI Shiyou, XIE Rong, XIAO Yang
    2020, 40 (6):  1000-1006.  doi: 10.11728/cjss2020.06.1000
    Abstract ( 235 )   PDF (1156KB) ( 59 )   Save
    The substorm is a process that releases enormous energy in the magnetosphere, including auroral, ionospheric, magnetospheric and thermospheric substorms. The substorm can result in severe disturbances in the whole magnetosphere and ionosphere. In this work, the AL and AE indices are employed to analyze the substorm events in the 24th solar cycle. Statistical analysis is performed on the relationship between the intensity of substorm, the initial value of substorm and the recovery value, the duration of a substorm, the relationship between substorm recovery phase and the duration of the growth phase (including expansion phase) and so on. The statistical results show that: most of the substorm events occurred in the 24th solar activity cycle from 2008 to 2016 are severe, with the peak value of the substorm mostly around 200~1200nT; the duration of most of the substorms ranges from 100 to 400min, the duration of the recovery phase of most of the substorms is between 60 to 300min, and presents the normal distribution characteristics; the recovery phase duration of most substorm events is less than 10 times of the growth phase duration. The statistical results on the substorm are helpful for further understanding of the occurrence and development of substorm in the magnetosphere. Therefore, it is of practical significance to further understand the energy evolution process in the magnetosphere.
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    Analysis of Ionospheric Irregularities and Disturbances at Middle and Low Latitudes in China during the Magnetic Storm
    MEI Dengkui, WEN Debao
    2020, 40 (6):  1007-1013.  doi: 10.11728/cjss2020.06.1007
    Abstract ( 254 )   PDF (1068KB) ( 65 )   Save
    A strong magnetic storm occurred on 8 September 2017 with the Kp index reaching its maximum of 8. The Regional Ionosphere Maps (RIM) were utilized to analyze the ionospheric TEC (Total Electron Content) disturbances over China and its adjacent areas, and the ROTI (Rate of TEC Index) maps were utilized to analyze the ionospheric irregularities in the low-latitude areas of China during the magnetic storm. Furthermore, the dual-frequency GPS observations of three IGS stations at BJFS (39.6°N, 115.9°E), JFNG (30.5°N, 114.5°E) and HKWS (22.4°N, 114.3°E) were used to obtain the trends of ROTI and DROT (standard deviation of differential ROT) indexes for each station. The results showed that during this magnetic storm, the ionospheric positive phase disturbances dominated in the beginning and mainly occurred at middle-and-low latitudes of China, and the dTEC (differential TEC) reached its maximum of 14.9TECU at about 04:00UT. Then the ionospheric positive phase disturbances gradually declined, the ionospheric negative phase disturbances began to occur at low latitudes of China with the dTEC reaching its minimum of -7.2TECU at about 12:00UT. There were obvious ionospheric irregularities observed at lower latitudes in southern China during 12:30UT-13:30UT. Compared with the BJFS and JFNG stations, the ROTI and DROT indexes of HKWS station at low latitude exhibited instability, indicating the latitudinal differences of ionospheric irregularities.
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    Distinguish Small-scale Traveling Ionospheric Disturbances and Equatorial Plasma Bubbles by Clustering Algorithm
    WANG Ling, YIN Fan
    2020, 40 (6):  1014-1023.  doi: 10.11728/cjss2020.06.1014
    Abstract ( 194 )   PDF (1456KB) ( 64 )   Save
    By analyzing the 50Hz high-frequency magnetic field data by Swarm from January 2015 to December 2019, according to the magnetic disturbances above the threshold in the perpendicular direction to the main field, Small-Scale Traveling Ionospheric Disturbances (SSTID) within ±45°N magnetic latitude have been detected. When detecting SSTID, Equatorial Plasma Bubbles (EPB) can be excluded by determining whether there is magnetic disturbance above the threshold in the direction which is parallel to the mean ambient field. However, when the disturbance is weak, the algorithm cannot completely exclude it. According to the different density distribution of SSTID and EPB in parameter space, the EPB can be distinguished by a density-based clustering algorithm. The results demonstrate that the clustering algorithm is very effective on separating EPB and SSTID in different two-dimensional parameter spaces and brings out a clear boundary between the high density region and low density region. The EPB identified by the clustering algorithm shows the strong dependence on solar activity and their statistical features are consistent with the previous study.
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    Assessment of Ionospheric Real-time Data
    ZHAO Jinsheng
    2020, 40 (6):  1024-1029.  doi: 10.11728/cjss2020.06.1024
    Abstract ( 273 )   PDF (949KB) ( 54 )   Save
    Ionospheric delay is one of the major error sources for single-frequency receivers. To improve the accuracy of ionospheric corrections in real-time, some Ionosphere Associate Analysis Centers started to provide real-time global ionospheric data. However, the accuracy of them is unknown. In this sense, this study takes the real-time ionospheric data provided by Aerospace Information Research Institute, Chinese Academy of Sciences (CAS) as an example for assessment. First, the differences between different kinds of ionospheric data are calculated. Meanwhile, positioning accuracy corrected by real-time ionospheric data and ionospheric broadcast ionospheric model over different latitudes for different solar activity periods is presented. The experimental results show that the real-time ionospheric data cannot reflect the spatial variation over the oceanic region for the experimental period. The positioning accuracy corrected by real-time ionospheric data is better than that by ionospheric predicted products and Klobuchar model for high-latitude stations. However, the positioning accuracy corrected by real-time ionospheric data is a bit worse than that of Klobuchar model for mid-latitude stations, while it is better than that corrected by ionospheric predicted products and Klobuchar model for low-latitude stations.
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    Research of Monthly Zonal Winds Derived from Radio Occultation Temperature Data
    DU Xiaoyong, DU Zhitao, GUO Yuening, FU Yang
    2020, 40 (6):  1030-1038.  doi: 10.11728/cjss2020.06.1030
    Abstract ( 255 )   PDF (5918KB) ( 49 )   Save
    In order to make up for the lack of wind data in the middle and upper atmosphere, the gradient wind fields between altitude of 20km to 60km are calculated by interpolating COSMIC temperature data of year 2007 into gridded data. The derived wind fields are compared with ECMWF reanalyzed data and HWM07 model outputs. Results show that the characteristics of wind fields derived from COSMIC temperature data are more similar with that of the reanalyzed data and are similar with HWM07 output as a whole, while are different from HWM07 data in detail. Compared with the ECMWF reanalyzed data, the mean differences of the zonal wind fields are within -1.50~-0.08m·-1, and the RMS are within 1.50~11.95m·-1. Compared with HWM07 outputs, the mean differences of the zonal wind fields are within -0.83~1.21m·-1, and the RMS are within 3.69m~11.14m·-1.
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    Simulation and Analysis on Volume Emission Rate and Limb Radiation Intensity of Airglow at Oxygen A(0, 0) Band
    YANG Xiaojun, WANG Houmao, WANG Yongmei
    2020, 40 (6):  1039-1045.  doi: 10.11728/cjss2020.06.1039
    Abstract ( 209 )   PDF (1295KB) ( 47 )   Save
    Atmospheric parameters in near space (temperature, density, wind field, etc.) have a great influence on the accuracy of the model prediction and the safety of spacecraft operation. Airglow simulation is an indispensable aspect of the inversion of the atmospheric parameter. In this paper, the Volume Emission Rate (VER) and limb radiation intensity of oxygen A(0, 0) band airglow are calculated based on the photochemical model. Firstly, the photochemical model O2 (b1Σg+) was established based on the theory of atmospheric dynamics, photochemical reaction mechanism, and photochemistry. Then, the VER of O2 A-band was calculated, and the limb radiation intensity of airglow is simulated using a geometric path integral along the line of sight. The simulation radiation and its corresponding height are both consistent with the results of AURIC model. Finally, based on the results of the simulation, the influence factors of VER and radiation of oxygen A-band airglow are analyzed.
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    Research on Atmospheric Lidar Signal Simulation Based on HITRAN Database
    CUI Honglu, YAN Zhaoai, ZHANG Bingyan, GUO Wenjie, HU Xiong
    2020, 40 (6):  1046-1051.  doi: 10.11728/cjss2020.06.1046
    Abstract ( 270 )   PDF (611KB) ( 38 )   Save
    Signal simulation is very important for atmospheric lidar research. It provides a basis for the design and development of lidar system. The simulation system in this paper can be used to simulate the lidar echo signal based on the absorption line data in the HITRAN database. It can calculate the absorption spectrum of atmospheric molecules, and the attenuation caused by aerosols. This simulation system can also calculate molecules scatter coefficient with parameters built in LOWTRAN and it can simulate the Signal-to-Noise Ratio (SNR) of the echo signal. The echo signals of 355nm, 532nm and 1064nm are simulated by the simulation system using the lidar equation and these signals agree well with the distribution of aerosols and atmospheric molecules. The simulation results of 532nm are compared with a Rayleigh Doppler lidar measured results and their results are consistent, which shows that the simulation system is reliable. The optical efficiency of this lidar system is roughly evaluated and its value is reasonable. The measured SNR and the simulated SNR are calculated. Their results are similar, so simulated SNR can evaluate the reliability of echo signals.
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    Destratification in Hydrogen Propellant Tank in Space by Jet Injection
    GUO Bin, ZHAO Jianfu, LI Kai, HU Wenrui
    2020, 40 (6):  1052-1065.  doi: 10.11728/cjss2020.06.1052
    Abstract ( 131 )   PDF (4258KB) ( 41 )   Save
    Hydrogen plays a vital role in the future energy system as a space propellant, but it is sensitive to heat leakage from the environment because of low boiling point and low density. On the other hand, the buoyancy convection in the space microgravity environment is weakened and even completely suppressed. When there is local heat leakage on the wall of the propellant tank, temperature stratification will happen around the heat leakage source, causing local overheating. This affects the interfacial heat and mass transfer, causing the tank pressure to rise, and jeopardize the structural safety of the system. To prevent the tank pressure from rising above the design of limits, venting or active pressure control techniques must be implemented. The cryogenic jet mixing is an effective means to suppress temperature stratification. The cryogenic fluid is mixed with the fluid inside the tank through a jet nozzle to reduce the local high temperature and achieve uniform temperature. In this paper, the temperature stratification phenomenon caused by local heat leakage under microgravity condition is numerically simulated by using a fully filled two-dimensional scale tank model, and then the influence of different cryogenic jet mixing conditions on eliminating the temperature stratification effect is analyzed.
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    Liquid-gas Interface Analysis of Propellant Tank Based on Surface Evolver
    JIANG Zhijie, WU Zongyu, LIU Changqing, HUANG Yiyong, HAN Wei
    2020, 40 (6):  1066-1073.  doi: 10.11728/cjss2020.06.1066
    Abstract ( 137 )   PDF (1802KB) ( 39 )   Save
    Propellant tank is an important part of spacecraft system, which is used for the management and transportation of propellant. Under the microgravity condition, the liquid-gas interface inside the propellant tank is curved. The investigation of the liquid-gas interface distribution characteristics is the premise to ensure the normal operation of the propellant tank. In this paper, Surface Evolver, an open-source surface evolution analysis software, is used to study the distribution characteristics of liquid-gas interface in spherical propellant tanks. The influences of filling ratio, contact angle, Bond number and other parameters on the liquid-gas interface are analyzed emphatically, and the variation law of the liquid-gas interface distribution in the propellant tank with each parameter is obtained. The results show that the shape of the liquid-gas interface of the spherical tank is more curved with the increase of the liquid filling ratio, and more flat with the increase of the contact angle or Bond number. Rapid analysis of the liquid-gas interface of the propellant tank is realized, which can provide guidance for the design of the propellant tank and the propellant management device.
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    Statistical Study on the Positive High Potential of Polar Satellite at Low Altitude
    HE Yuxuan, LIU Yong, ZHANG Qiang
    2020, 40 (6):  1074-1083.  doi: 10.11728/cjss2020.06.1074
    Abstract ( 227 )   PDF (2373KB) ( 32 )   Save
    Based on the surface potential data of Polar satellite from 1996 to 2008, a statistical study is presented among the positive high potential of the satellite surface at low altitudes (abnormal events), the solar activity, and the MLT distributions. The main results are as follows. Firstly, the solar radiation positively correlates with the events numbers. The more active the Sun is, the more times abnormal events occur, while the solar radiation does not affect the surface potential of the spacecraft. Secondly, the proportion of abnormal events has seasonal changings. Thirdly, in the high solar activity years, the abnormal events occur more frequently in winter and summer in comparison with spring and autumn. In the low solar activity years, the abnormal events numbers maintain low values in monthly changings, and they have no apparent rules. Fourthly, there are many similarities of abnormal events in hemisphere distributions: the abnormal events do not occur at geomagnetic latitudes between 50° and 60°, but occur more frequently in the polar regions and the dusk sides. However, the abnormal events also have differences in hemispheres distributions: the abnormal events occur more frequently in the southern hemisphere. Lastly, even in the solar maximum year, the abnormal events occurrence rate does not exceed 10%.
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    Research on Image Simulation for Space-based Space Debris Surveillance
    XIA Shengfu, CHEN Junyu, LEI Xiangxu, SANG Jizhang
    2020, 40 (6):  1084-1090.  doi: 10.11728/cjss2020.06.1084
    Abstract ( 185 )   PDF (876KB) ( 60 )   Save
    Space-Based Space Surveillance (SBSS) is an effective mean to complement ground-based system which results in better spatial and temporal coverage. However, the lack of SBSS tracking data has caused inconvenience to the development and validation of the system, algorithm and software. For this, simulation software for generating SBSS images has been developed. In this paper, based on the characteristics of SBSS images, the research of fundamental algorithms is conducted, the simulation process is designed, the example images are given, and the results are analyzed. The instantaneous inertial coordinate system is used in the software system to obtain the high-precision simulation image which conforms to the actual SBSS scenarios. Based on Tycho2 catalog, a fast catalog query method based on the index file was proposed to generate background stars. Simulated observations are generated based on multiple TLE datasets. Finally, we present some examples and analyze the trajectory characteristics of space debris and stars in the images. The simulation results show that the simulation system can obtain more realistic space-based optical images for space debris under different observation conditions and loads, which take accuracy and timeliness into account.
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    Attitude Determination Algorithm for Micro-satellite Based on High-order UKF Using Information Fusion
    ZHANG He, QIN Weiwei, ZHOU Cheng, SONG Hengxin, HUA Yufeng, WANG Yu
    2020, 40 (6):  1091-1101.  doi: 10.11728/cjss2020.06.1091
    Abstract ( 169 )   PDF (1848KB) ( 37 )   Save
    To improve the attitude determination accuracy of miniature low-cost attitude sensors, a micro-satellite attitude determination algorithm that combines magnetometer and solar sensor observations was designed, based on high-order Unscented Kalman Filter (UKF) and the attitude sensor configuration of magnetometer/solar sensor/gyroscope. Firstly, in order to improve the one-step prediction accuracy of the nonlinear system state equation, the high-order UKF algorithm with fifth-order UT transformation was used to increase the number of Sigma sampling points and improve the system state prediction accuracy. Secondly, owing to the shortcoming of the single observation vector filtering algorithm that couldn't coordinate multiple observation data with different dimension simultaneously, an information fusion filtering algorithm using two observation vectors was proposed, which was based on the observations of the magnetometer and the solar sensor. The Kalman gain was obtained by the information corresponding to the geomagnetic vector and the solar vector through the gain calculation of the UKF algorithm. Consequently, the Gaussian probability density criterion was used to fuse the Kalman gain information, and the fused information was used to correct the value of the one-step prediction. Therefore, this algorithm reduced the observation errors of the attitude quaternions. Finally, the simulation results proved the availability of the proposed method.
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    TLE Orbital Determination Based on Simplex Method
    LIU Jinghong, SANG Jizhang, LIU Hongkang
    2020, 40 (6):  1102-1108.  doi: 10.11728/cjss2020.06.1102
    Abstract ( 235 )   PDF (862KB) ( 41 )   Save
    TLE database is the only public source available to orbital information, and many spatial researchers use the database to obtain an accurate orbit determination result. In the future, the number of spatial objects classified by TLE database will continue to increase. Due to the unknown and fluctuation precision of TLE data, it is necessary to use historical TLEs data to determine the orbit of TLE state at reference time. The least square method is often used to get a precise result but has its own shortcomings, such as the need for more accurate initial value, unreliable error evaluation, solution divergence. To overcome the shortcomings of the existing methods, another local search algorithm, i.e., simplex method is proposed to solve the problem of TLE orbit determination. Monto-Caro method is introduced to produce a series of initial simplex to obtain a series of local optimum solutions and avoid the local optimum solution obtained by an initial simplex. The final global optimum solution is obtained by calculating the expectation and variance of the local-optimum solution distribution. The research shows that results obtained by the simplex method can significantly reduce the position and speed errors.
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    Calculation Method of Spacecraft Solar Pressure Area Based on Target Characteristics
    HAN Yi, CHEN Ming, DUAN Chenglin, OUYANG Qi
    2020, 40 (6):  1109-1116.  doi: 10.11728/cjss2020.06.1109
    Abstract ( 136 )   PDF (1204KB) ( 34 )   Save
    Solar Radiation Pressure (SRP) is one the most important forces impacting the precision of spacecraft's orbit determination and prediction in deep space detection. In deep space exploration mission, there is no special solar pressure model for each spacecraft at present. The usual method is to simplify the shape and structure of spacecraft, and estimate the cross-sectional area and SRP area. In order to improve the accuracy of the SRP model, it is necessary to consider not only the occlusion relationship between different parts of the spacecraft in the light direction, but also the reflection characteristics of different materials on the surface of the spacecraft. Aiming at actual mission requirement, the method of calculating solar pressure area based on target characteristics is studied. Based on the information such as target's shape, size, surface materials and their optical characteristics, the analytical model of SRP is built. According to the relevant parameter information, the normal vector of each micro effective plane element, the angle between the plane element and the incident direction of the light, the type of material represented by the plane element, the relationship between mutual occlusion and the reflection characteristics of the material are calculated respectively. The calculation efficiency and precision is increased effectively, and the target's SRP area, the cross section area and the scale factor can be calculated fast. By comparing with theoretical SRP area of rectangular body, the simulated results are proved to be correct. At last one complex spacecraft's SRP areas are calculated and analyzed. This research can provide meaningful and significant references for the SRP modeling solution, orbit determination and forecasting.
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    Flexible Design and Thermal Stability Analysis of Reflector Assembly of Space-based Laser Ranging Load
    LIU Ming, LI Zhenwei, LI Xiang, KANG Zhe, HAN Linchu, LIU Yongzhi
    2020, 40 (6):  1117-1124.  doi: 10.11728/cjss2020.06.1118
    Abstract ( 177 )   PDF (1310KB) ( 36 )   Save
    In this paper, the structure design and thermal stability of the light and small reflector component of laser communication and ranging integration satellite link load are studied. Optimization design of flexible support mechanism of reflector component is carried out. According to the working conditions and in-orbit thermal environment, the optical component integration analysis of the mirror assembly is carried out to evaluate the on-track thermal stability of the opto-mechanical structure. The analysis results show that the surface precision of the mirror with double-layer circular arc slot flexible support structure can be reached at λ/72 after temperature deflection, the fundamental frequency mode is 417.93Hz, meeting the requirements of the index. Furthermore, the dynamic analysis of the mirror assembly is carried out, the results of random vibration analysis show that the root mean square of the acceleration response of the mirror is 11arms and meet the 3σ criterion. Finally, a 0.2g sine sweep test proves that the relative error of the modal analysis is 2.24%, the experimental result show that the analysis results are basically accurate and reliable, that is, flexible support design is reliable to meet the requirements of the use.
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    Influence of Intelligent Hierarchical Control for Flexible-Joint Dual-arm Space Based on Finite Difference Method
    LIANG Jie, QIN Kaiyu
    2020, 40 (6):  1125-1134.  doi: 10.11728/cjss2020.06.1125
    Abstract ( 117 )   PDF (2248KB) ( 23 )   Save
    Because of their unique properties and good performance, some elastic components, such as the harmonic reducers and the torque sensors, are widely used in the joints of the space robots and manipulators, in order to obtain high reduction ratio. Due to the existence of elastic components, joint flexibility is introduced into the space robot system, which makes its stability control more complex. As a result, the intelligent hierarchical control based on finite difference method and elastic vibration suppression for dual-arm flexible space robot with uncertain parameters is discussed. The hierarchical dynamics model of the system is derived by applying the theory of hierarchical systems, the principle of momentum conservation of the system and the Lagrangian method of the second kind. By the aforementioned model, the non-singular terminal sliding mode control algorithms based on Recurrent Fuzzy Neural Network (RFNN) and the sliding mode control algorithm based on finite difference method are designed. It is found that the uncertain parts of the system are approached by RFNN, and at the same time, in order to avoid the complicated derivative calculation and the requirement of measurable angular acceleration, the sliding mode control based on the finite difference method is used to suppress the vibration of flexible joints. The control algorithm has the significant advantage of being suitable for an arbitrarily sized joint flexible rigidity in theory because it does not involve the common singular perturbation two-time-scale decomposition operation. The system comparison and simulation results show that the proposed intelligent hierarchical control algorithm is superior to the traditional control scheme based on singular perturbation.
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