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Single Event Upsets Fault Tolerance of Convolutional Neural Networks Based on Adaptive Boosting
LUO Xi, ZHOU Qing, JIANG Yuanyuan
, Available online  , doi: 10.11728/cjss2026.02.2025-0025
Abstract(331) FullText HTML (46) PDF 3965KB(18)
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Single-Event Upsets (SEUs) in the space radiation environment pose a serious threat to the reliability of satellite-borne intelligent systems. Traditional fault-tolerance methods such as Triple Modular Redundancy (TMR) and periodic scrubbing face challenges including excessive resource overhead and high power consumption. This paper presents a lightweight fault-tolerance method based on Adaptive Boosting-based Fault-Tolerance Method (AB-FTM) to address SEU vulnerabilities in convolutional neural networks. The proposed approach constructs a heterogeneous ensemble architecture comprising three weak models (ResNet20, ResNet32, ResNet44) and integrated with a dynamic weight adjustment mechanism. By integrating a dynamic weight adjustment mechanism, the method not only significantly reduces the parameter scale (achieving an 18.2% reduction compared to ResNet110) but also enhances classification accuracy, robustness, and fault tolerance. Experimental validation on datasets including CIFAR-10, MNIST, EuroSAT, and Galaxy10 DECals demonstrates that when 0.032‰ of parameters are affected by single-event upsets, the proposed method improves classification accuracy by 53.25%, 63.49%, 57.67%, and 47.43% respectively compared to the TMR-based ResNet110, significantly outperforming traditional triple modular redundancy solutions. This approach provides a novel solution for future space science satellites employing satellite-borne intelligent systems, balancing reliability, lightweight design, and computational efficiency.
Design and Ground Calibration of the Low-energy Ion Analyzer and Low-energy Electron Analyzer onboard the Chang’E-7 Mission
SU Bin, KONG Linggao, GAO Jun, LIU Chao, ZHANG Aibing, LYU Yulong, WANG Wenjing, MA Liyuan
, Available online  , doi: 10.11728/cjss2026.02.2025-0095
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The Low-Energy Ion Analyzer (LEIA) and Low-Energy Electron Analyzer (LEEA), integral components of the Chang’E-7 (CE-7) lander’s lunar surface environment detection system, conduct in-situ measurements of low-energy charged particles (0.001～30 keV) to elucidate solar wind-regolith interaction mechanisms, investigate microstructure evolution in the lunar near-surface plasma environment, and support space-environment assessment for future lunar research stations. Employing identical hemispherical electrostatic analyzers with asymmetric electrostatic deflectors, both analyzers achieve wide-field detection (90° × 360° FOV), broad energy coverage, and voltage-controlled variable geometric factors. Ground calibration using standard plasma beam sources confirmed compliance with mission requirements: energy resolution <15% (ΔE/E), dynamic flux range spanning seven orders of magnitude, and angular resolution <15° × 22.5°, collectively enabling comprehensive characterization of lunar surface plasma phenomena.
Response of Thermospheric Winds at Mid-latitudes in the Northern and Southern Hemispheres to the Geomagnetic Storm on 18 March 2018
XIA Xinmiao, JIANG Guoying, NEL Amoré Elsje, ZHU Yajun, XU Jiyao, YUAN Wei
, Available online  , doi: 10.11728/cjss2026.02.2025-0039
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The responses of thermospheric winds at middle latitudes to the moderate geomagnetic storm of 18－19 March 2018, are examined using two ground-based Fabry-Perot Interferometer (FPI) observations from the Xinglong (XLON, 40.2°N, 117.6°E; magnetic latitude 35°N) and the Sutherland Astronomical Observatory (SAAO, 32.4°S, 20.8°E; magnetic latitude 40.7°S), combined with simulations from the Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIEGCM). The storm reached a maximum Kp index of 6, classifying it as a moderate storm. Ground-based FPI measurements provided high-resolution wind data at both stations, capturing the temporal evolution of zonal (east-west) and meridional (north-south) wind components. Meanwhile, the TIEGCM simulations offered a theoretical framework to interpret the observed disturbances and assess the model’s capability in reproducing storm-induced thermospheric dynamics. The results reveal that the response of thermospheric winds to the geomagnetic storm is more pronounced in the southern hemisphere than that in the northern hemisphere. Significant enhancements in equatorward and westward winds are observed at the SAAO station, with maximum meridional wind speeds reaching 128.4 m·s–1 (equatorward) and maximum zonal wind speeds reaching –165.6 m·s–1 (westward). Comparative analysis with TIEGCM simulations indicates that the model can reasonably reproduce the disturbance trends in observations, particularly in the variations of meridional winds at SAAO and zonal winds at XLON. The model successfully captured the transition from quiet-time wind patterns to storm-driven disturbances, including the shift toward westward and equatorward. However, certain quantitative discrepancies remain in the model's predictions: the model underestimates the eastward zonal winds at SAAO and overestimates the equatorward meridional winds at XLON. Future studies could consider using multiple ground-based stations and a variety of observations, such as temperature, density, chemical composition for the study. Furthermore, investigating the role of seasonal and local time effects in modulating hemispheric asymmetries could provide deeper insights into thermospheric storm responses. Overall, this study contributes to a better understanding of the storm impacts on thermospheric winds and hemispheric differences, as well as their potential physical causes.
Case Comparative of Simultaneous Observations of Large-scale Traveling Thermospheric and Ionospheric Disturbances
PAN Jianhong, CAI Hongtao, YAN Xu, HU Kun, YANG Lubing, QIN Haiyin, ZHANG Shiwei
, Available online  , doi: 10.11728/cjss2026.02.2025-0069
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To compare the propagation characteristics of Large-Scale Traveling Atmospheric Disturbances (LSTAD) and Large-Scale Traveling Ionospheric Disturbances (LSTID) that propagate in tandem in the thermosphere-ionosphere, this paper takes advantage of the CHAMP satellite’s ability to simultaneously observe atmospheric mass density and electron density across latitudes, studying a pair of LSTAD and LSTID events that propagated in tandem over long distances on 19 March 2002. Around 04:00-06:00 UT on 19 March, with a sudden and significant increase in the AE index, the CHAMP satellite observed the LSTAD and LSTID propagating in tandem in the Northern Hemisphere. Over the next approximately 6 h after 04:00 UT, these disturbances in atmospheric mass density and electron density propagated southward, crossed the equator, and entered the Southern Hemisphere, eventually dissipating there. On the other hand, the ground-based GNSS chain observations also confirmed the existence of the LSTID observed by the satellite. Through comparative analysis, it was found that due to the highly controlled movement of electrons by the Lorentz force while neutral particles are not constrained by it, the horizontal propagation speeds of LSTAD and LSTID along the meridian direction show significant differences. Therefore, at the same time and position on the same orbit, their phases are not the same and may even differ significantly.
Ground Calibration Method and Experiments of Lunar Surface Dust Sensor in Chang’E-7 Mission
LI Cunhui, ZHUANG Jianhong, WANG Hu, CUI Zecheng, WANG Jiajie, ZONG Chao, WEI Yongqiang, ZHANG Haiyan
, Available online  , doi: 10.11728/cjss2026.02.2025-0116
Abstract(183) FullText HTML (40) PDF 2834KB(14)
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The Chang’E-7 spacecraft is scheduled to be landed in the Aitken Basin region of the lunar South Pole to conduct comprehensive exploration and research on the lunar surface environment. As one of the main detectors onboard the Chang’E-7 spacecraft, a lunar dust detector is developed for in-situ measurements of naturally suspended dust in the polar region, key parameters such as the particle size, velocity, and cumulative mass flux will be obtained. To achieve high-precision scientific detection, systematic ground calibration experiments were conducted. For particle size calibration, a single-particle free-fall method combined with an equivalent test scheme using neutral density filters was employed, achieving coverage of the particle size range from 1 µm to 5000 µm. Experimental results demonstrate that the particle size retrieval error does not exceed 17%. Velocity calibration was performed by measuring the time-of-flight of free-falling particles from different heights, yielding a velocity measurement error within 13%. For mass flux calibration, the solution titration method was used to obtain the sensitivity of the Quartz Crystal Microbalances, with sensitivities in three orthogonal directions all on the order of 10–9 g·Hz–1·cm–2 and exhibiting good linearity. Furthermore, temperature-frequency correction curves were established to support the normalization of in-orbit data. The calibration results indicate that the performance indicators of the dust detector meet the requirements for detection in the extreme environment of the lunar South Pole. The established calibration methods and retrieval models provide a reliable foundation for the interpretation of subsequent in-orbit scientific data.
Retrieval of the Imaginary Part of the Dielectric Constant in Mountain Glaciers Using Airborne Radar Based on a Dual Rough Interface Numerical Simulation Model
SHA Ziyi, ZHU Di, BAI DongJin, XU Guoqing, MA Jianying, LIU Tianao
, Available online  , doi: 10.11728/cjss2026.02.2025-0052
Abstract(320) FullText HTML (31) PDF 4646KB(14)
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As a key indicator of global climate change and an essential freshwater resource, the accurate acquisition of multiple physical parameters of glaciers holds significant importance for global climate change research, ecological conservation, and water resource planning. In China, glaciers are predominantly mountain glaciers distributed in high-altitude regions. Constrained by harsh environments and complex terrain, traditional in-situ detection methods fail to achieve large-scale continuous monitoring of internal glacier parameters. Satellite-borne glacier remote sensing, meanwhile, faces limitations in resolution and interference from complex ground clutter in mountainous glacier regions, and thus has yet to be operationalized. Airborne radar, with its superior spatial resolution and flexible detection capabilities, has become a critical technical tool for glacier monitoring and research. However, airborne detection of mountain glaciers still confronts challenges posed by undulating ice surfaces and complex subglacial topography: scattering clutter from the uneven ice surface interferes with radar signal interpretation and precise inversion of key parameters, while the intricate subglacial structure and scattering losses caused by ice surface topography interact with dielectric losses within the ice, impeding accurate inversion of glacier dielectric constants. To address these challenges, this study integrates airborne ultra-wideband radar detection data from mountain glaciers with the Pseudo-Spectral Time Domain (PSTD) numerical simulation method. A coupled model of ice surface-subglacial dual interface topography and dielectric parameters is established. Through two-dimensional PSTD electromagnetic simulations, the interaction mechanism between topographic scattering and ice dielectric loss is elucidated. Furthermore, an inversion method for the imaginary part of the ice layer dielectric constant in measured regions is proposed based on dynamic range analysis. For the measured data from Laohugou Glacier No. 12, iterative optimization converges the estimated imaginary part value to 6.0×10–4. The relative error between the estimated imaginary part and the theoretical mean is 21%. Cross-validation between simulation results and theoretical models demonstrates that this method effectively improves the inversion accuracy of glacier dielectric parameters in complex terrain by decoupling the synergistic interference between topographic relief and dielectric parameters, thereby offering a viable solution for studying internal dielectric properties of glaciers.
Design and Simulation Results Analysis of a Spaceborne Fabry–Perot Interferometer for the Near-Space Atmospheric Wind Field
SUN Yiran, WANG Houmao, LI Pengda, LIU Jiu, WANG Yongmei, FU Liping, HUANG Cong, ZONG Weiguo
, Available online  , doi: 10.11728/cjss2026.02.2025-0041
Abstract(322) FullText HTML (48) PDF 4830KB(26)
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Currently, there are relatively few spaceborne methods for detecting near-space atmospheric wind fields, and the Fabry–Perot Interferometer (FPI) is one of the more important and widely used detection techniques. To address the gap in China’s space-based FPI wind sensing capabilities, the National Space Science Center developed a spaceborne FPI wind interferometer. This paper mainly introduces this instrument’s optical design, structural design, thermal control design, optical simulation, and result analysis. First, the optical design is discussed based on the wideband detection requirements, and the imaging system’s image quality is evaluated. Then, based on optical simulation data, wind speed inversion and accuracy analysis of the spaceborne FPI instrument are conducted. The wind speed errors at the 557.7 nm and 762.0 nm bands are –1.722 m·s–1 and –2.3672 m·s–1, respectively, indicating that the spaceborne instrument design meets the wind measurement requirements. Then, the key points of the instrument's structural design and the thermal control solution for the imaging part are presented, along with a translational filter switching device driven by a trapezoidal lead screw and a micro gear stepping motor or micro linear motor. The paper also explores the relationship between the temperature control accuracy of the instrument’s core components (the etalon) and wind measurement errors. A combined active and passive design is adopted to minimize the impact of temperature fluctuations on the results, which is verified with simulation results.
Simulation and Experimental Study on the Influence of Cables on the Performance of Search Coil Magnetometers
ZHU Linshan, ZHOU Bin, ZHANG Tianyu, XUE Yongliang, CHENG Bingjun, TAO Ran, XIE Yujing, WENG Chenghan
, Available online  , doi: 10.11728/cjss2026.02.2025-0037
Abstract(329) FullText HTML (71) PDF 5872KB(17)
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In response to the performance impact of long cable signal transmission between the search coil and the preamplifier circuit, this paper establishes for the first time a circuit equivalent model of Search Coil - Cable - Preamplifier Circuit. Through simulation analysis and experimental verification, the influence of cable length on the frequency distribution of sensor noise is revealed. Theoretical analysis indicates that cable length has limited impact on sensor sensitivity, but significantly increases the noise level in the high-frequency band (>1 kHz). Based on a prototype search coil magnetometer with a target specification of 10～1000 Hz bandwidth and 30 fT·Hz1/2 (1 kHz) noise, the variation law of noise with cable length is validated. Experimental results show that as the cable length increases from 3 m to 39 m, the noise corner frequency shifts forward from 7.5 kHz to 2 kHz, while the high-frequency noise at 10 kHz increases by a factor of six. The study finds that an increase in cable length has a significant impact on the noise of inductive magnetometers, specifically manifested as a slight improvement in low-frequency noise and a sharp deterioration in high-frequency noise. Although cable length has a notable effect on inductive magnetometers, its influence can be predicted and mitigated through theoretical modeling incorporating cable parameters. This research provides critical parameter basis for the engineering implementation of search coil magnetometers in space exploration scenarios requiring long-cable applications.
High Wind Speed Correction of HY-2 Satellite Microwave Scatterometer Based on Broad Learning System
SU Yue, ZHANG Jinxin, LIU Guihong, MA Wentao, YU Yang, WU Zhiheng, WANG Sheng, YANG Xiaofeng, GUANG Jie
, Available online  , doi: 10.11728/cjss2026.02.2025-0023
Abstract(448) FullText HTML (123) PDF 5214KB(16)
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Accurate observation of sea surface wind fields is essential for tropical cyclone forecasting and meteorological hazard mitigation. The HY-2 series microwave scatterometer continuously measures Ku-band ocean surface winds. However, its current wind speed retrieval algorithm struggles in high wind conditions and systematically underestimates speeds during extreme events such as typhoons. To address this bias, this study utilized the HY-2 wind speed data of nine tropical cyclones between 2021 and 2022 as the data source. The Stepped Frequency Microwave Radiometer (SFMR) wind speed measurements served as the ground truth. A modeling dataset was constructed by resampling the SFMR reference data to match the 25 km spatial resolution of the HY-2 scatterometer, followed by spatiotemporal matching within a two-hour time window. The matched dataset was then randomly divided into a training set and a testing set at a 7︰3 ratio. Subsequently, the Broad Learning System (BLS) was employed to conduct the regression analysis and develop a high-wind-speed correction model. BLS employs a shallow, flat architecture in which input features are expanded into “enhanced nodes,” avoiding the deep stacks typical of conventional neural networks. This structure reduces computational cost and accelerates convergence while maintaining predictive performance. Validation results demonstrate that the corrected HY-2 wind speeds achieved a Root Mean Square Error (RMSE) of 4.47 m·s–1, representing a 35% improvement compared to the uncorrected data. For wind speeds exceeding 25 m·s–1, the corrected RMSE reached 6.76 m·s–1, marking significant enhancements over the original values of 13.27 m·s–1. Additionally, a comparative analysis using Typhoon Chanthu (in 2021) as a case study revealed that the corrected HY-2C maximum wind speed increased from 22.09 m·s–1 to 32.73 m·s–1, closely matching wind fields retrieved by Synthetic Aperture Radar (SAR). Further validation through wind speed profile comparisons confirmed the effectiveness of the proposed model. These results demonstrate that our correction framework markedly improves extreme-wind retrieval accuracy, yielding bias-corrected HY-2 products that are more reliable for applications, such as storm surge simulation and typhoon track forecasting.
Evolution Prediction Model of Equatorial Plasma Bubbles Based on SimVP
ZHONG Jia, ZOU ZiMing, WU Kun, XU JiYao, LU Yang, SUN Longcang, YUAN Wei
, Available online  , doi: 10.11728/cjss2026.02.2025-0046
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Equatorial Plasma Bubbles (EPBs) are large-scale depletion structures characterized by significantly reduced electron density, which frequently emerge in the low-latitude ionosphere during post-sunset hours. These dynamic plasma irregularities play a crucial role in space weather phenomena, as their evolution can induce severe amplitude and phase scintillations in radio signals, leading to disruptions in satellite communications, global navigation systems, and radar operations. Given their substantial impact on technological systems, accurate prediction of EPB evolution has become a critical challenge in both space physics research and operational space weather forecasting.. To address this challenge, this study introduces a novel data-driven approach for EPB evolution prediction by leveraging the SimVP (Simpler yet Better Video Prediction) framework, an advanced deep learning architecture designed for spatiotemporal sequence forecasting. The proposed model learns the complex nonlinear dynamics of EPB structures from historical airglow image sequences, capturing both their morphological transformations and drift patterns. Through extensive experimentation, we systematically evaluate the influence of key parameters—including time resolution, input/output sequence length, and environmental noise—on prediction performance. Our findings demonstrate that an optimal configuration with a 3 min temporal resolution and a 6-frame input/output structure achieves superior predictive accuracy, as evidenced by high Structural Similarity (SSIM=0.989) and Peak Signal-to-Noise Ratio (PSNR=34.704) metrics. Further analysis reveals that the spatial complexity of EPB structures, such as bifurcation events and irregular boundary deformations, significantly affects prediction fidelity, whereas the impact of light pollution—a common issue in ground-based airglow observations—is comparatively minor. The model proposed in this paper demonstrates robust cross-station applicability. Beyond forecasting, the model also exhibits potential for reconstructing corrupted airglow data, offering a computational solution to enhance observational datasets affected by atmospheric or instrumental noise. This work not only establishes a robust, machine learning-based tool for EPB evolution analysis but also contributes to the broader development of Artificial Intelligence (AI) applications in space weather modeling and ionospheric research.
A Dataset of Geomagnetic Kpest Index from Individual Stations (2022－2024)
WANG Jing, ZHONG Qiuzhen, LUO Bingxian, WANG Xiao, ZHAO Mingliang, CHENG Yonghong, SHEN Hua
, Available online  , doi: 10.11728/cjss2026.02.2025-0131
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The Kp index is a parameter designed to indicate the level of global geomagnetic disturbances originating from the interaction of the solar wind with the magnetosphere. The index is defined at 3-hour intervals and has 28 levels. Kp is a global version of the local K index, which was conceived by Bartels and is commonly used in scientific research of the solar-terrestrial relationship. The continuity of the index over 50 year makes it particularly valuable in studies of solar-cycle variations and other long-term effects on interplanetary and magnetospheric phenomena. For example, Kp has been used in studies of solar wind shock waves, the interplanetary magnetic field, plasma density variations in the magnetosphere, and magnetospheric ULF waves. In addition, the index is widely used as an input to magnetospheric/ionospheric models. For example, the plasmapause is modeled to move closer to the Earth with increasing Kp. The location of substorm injection is modeled to have a similar Kp dependence. The magnetic field model of Tsyganenko has an explicit Kp dependence, and the magnetotail becomes more stretched for higher Kp. These models are used both in scientific research and in monitoring and predicting space weather. In 2011, the National Space Science Center of the Chinese Academy of Sciences established the Chinese Academy of Sciences Space Environment Monitoring Network, which included Mohe, Beijing, Langfang, Sanya, and Fuke stations. A geomagnetic Kpest index, which can effectively identify the day-to-day variation characteristics of the geomagnetic regular daily variation, reflect the seasonal and local time effects of geomagnetic disturbances, and is suitable for the distribution characteristics of China’s geomagnetic observatory network, has been developed through the integration and processing of the H-component monitoring data from fluxgate magnetometers at these five geomagnetic observatory stations. This dataset contains the geomagnetic Kpest indices for the five geomagnetic observatory stations from 2022 to 2024. It addresses the current situation where the official Kp index is released with a two-week delay, failing to meet operational requirements, and can provide data support for space weather forecasting services.
Cosmic Ray Muon Count Dataset from Siziwang Station in Inner Mongolia (2023－2025)
CHENG Yonghong, ZHONG Qiuzhen, ZHUANG Chunbo, SHI Liqin, SONG Xiaochao, WANG Jing, SHEN Hua, WEI Lihang
, Available online  , doi: 10.11728/cjss2026.02.2025-0133
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The Muon Telescope at Siziwang Station in Inner Mongolia is used to detect the secondary cosmic ray muons reaching the ground. The Muon Telescope began construction in November 2019, was completed in April 2023, and produced scientific data. The muon telescope consists of a scintillator observation stack, an electronics recorder, a monitoring platform, and a power supply. The scintillator observation stack is composed of 48 detector units, divided into upper and lower layers with 24 units in each layer, arranged in a 6×4 array. In each detector unit, the plastic scintillator has dimensions of 50 cm × 50 cm × 5 cm. The distance between the upper and lower layers is 89 cm. A 5cm-thick layer of lead bricks is laid between the upper and lower layers to filter out low-energy cosmic rays and low-energy particles in the surrounding environment. The detectors have a total area of 6 m2. Muon signals generated by the 48 detector units of the Muon Telescope are processed through front-end circuits for amplification, discrimination, and shaping, then sent to the FPGA logic circuit for directional coincidence calculation. This produces raw muon counts in 15 directions. After undergoing barometric correction calculation, a dataset of corrected muon counts in 15 directions is formed, with a temporal resolution of 1 hour. The count rate in the vertical direction is the highest, with the 1-hour count rate being around 600,000 counts and the relative statistical error approximately 0.13%. The muon data can sensitively reflect diurnal variations, long-term variations of cosmic rays, and short-term Forbush decrease perturbations induced by coronal mass ejections. Spanning from May 2023 to April 2025, this dataset covers the high-activity phase of the 25th solar activity cycle. It provides valuable data resources for research on solar eruptions, their interplanetary disturbance propagation, and geomagnetic response processes, while also supporting space weather early warning efforts.
Design and Implementation of a High-performance Image Compression Core for Spaceborne Applications
FU Zhiyu, ZHANG Xuequan
, Available online  , doi: 10.11728/cjss2026.01.2025-0021
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To address the critical need for efficient image storage and transmission in aerospace applications, this study presents a CCSDS 122.0-B-1-compliant compression core implemented on FPGA. The design incorporates innovative encoding control logic and optimized data organization through co-optimization of algorithmic features and hardware constraints. A segment-based architecture with 256-pixel blocks achieves superior compression efficiency among existing solutions, while effectively containing error propagation through segmented compression. The architecture further enables continuous quality adaptation and progressive image transmission. To resolve performance bottlenecks in scanning and encoding processes, fully parallelized scanning with adaptive parallel encoding was developed, and a 50% efficiency improvement was demonstrated in validation tests. Supporting images up to 4096×4096 pixel with 16-bit depth, the core delivers 90.64×106sample·s–1 throughput, meeting operational requirements for diverse space missions.
Design of Finite Frequency Domain Disturbance Rejection Controller for the Drag-free Spacecraft in Space-borne Gravitational Wave Detection
XU Qianjiao, CUI Bing, WANG Pengcheng, XIA Yuanqing, ZHANG Yonghe
, Available online  , doi: 10.11728/cjss2024.05.2024-0022
Abstract(1112) FullText HTML (421) PDF 5881KB(77)
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In space-borne gravitational wave detection, there are technical challenges in designing the controller for the drag-free spacecraft with dual test masses. These difficulties arise from constraints within the limited measurement frequency domain and the necessity for a high-precision control index. In this paper, a design method of disturbance rejection controller in the finite frequency domain based on the generalized Kalman-Yakubovich-Popov (GKYP) lemma is proposed. Firstly, to address the performance constraints within the designated frequency band of the detection mission, a finite frequency domain control performance index in the form of a frequency response function is constructed. This index is meticulously developed by amalgamating the sensitivity and complementary sensitivity control indexes. Then, a control structure with fixed-order characteristics for output feedback is proposed, and a method for selecting controller parameters based on the GKYP lemma is established. By this, a finite frequency domain disturbance-resistant controller design method is constructed. In contrast to current drag-free controller design methods, the proposed approach significantly diminishes the conservatism in the control index. This realizes the precise design of the controller in the specified frequency band, ultimately resulting in a reduction in the order of the controller. Finally, numerical simulations demonstrate that the proposed method successfully meets the control performance index for each loop of the drag-free system even in the presence of complex disturbances and noises.

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