The high precision spacecraft platform system is an important carrier and plays a significant role in the successful implementation of a space gravitational wave detection mission. In this paper, frontier researches on high-precision spacecraft platform systems were reviewed and summarized. The inertial sensor reference of spacecraft platform, micro-thrust actuator, drag-free attitude control technology of spacecraft platform, formation design and control of spacecraft system were discussed. The recent relevant research progress of spacecraft platform system used for space gravitational wave detection was summarized and discussed, covering both domestic and international frontier research hotspots, focusing on key research issues of space gravitational wave detection spacecraft platform system design. A prospect on the development of spacecraft platform system was proposed, including key payloads, orbit and attitude control strategies, formation configuration design, etc

To observe the frequency in the range of 0.1 Hz to 5 Hz in lunar-based gravitational-wave detection and improve the sensitivity of gravitational-wave detection, a method of lunar-based gravitational-wave detection was proposed. Based on a brief introduction to the mathematical description and properties of gravitational waves, this paper gave a brief introduction to existing gravitational-wave detectors and compared the lunar-based observatories with the space and Earth-based detectors. Lunar-based detectors that have been proposed, such as Gravitational-wave Lunar Observatories for Cosmology (GLOC), Lunar Gravitational-Wave Antenna (LGWA), etc., are briefly introduced. The critical technique is also discussed and alternative solutions are given. The possible main noise sources and corresponding impact magnitudes for lunar-based gravitational wave detection were discussed. Also, the future development of the lunar-based gravitational wave detection is prospected.

To solve the problem of arm length divergence of space gravitational wave detection formation based on CW equation in two-body nonlinear gravitational field, a formation configuration design method based on second-order CW equation was proposed. Firstly, the differential form of the second-order CW equation was derived, and the approximate analytical solution of the second-order CW equation was obtained by perturbation method. Then, the non-existence of circular flying orbit was proved, and the divergence reason of the nominal configuration based on CW equation was analyzed. Secondly, based on second-order CW equation and the energy matching period condition, the formation configuration optimization model was constructed with the phase angles of the spacecraft as optimization variables, and the multi-constraint configuration optimization method based on the global optimization algorithm and the pattern search algorithm was established. Finally, the optimization results were verified by simulation based on the Taiji mission. Simulation results show that the proposed optimization method can reduce the average error of formation arm length to 0.32% and the maximum error to 0.44 %.

To ensure the stability of the orbital configuration of the space gravitational wave detector, the design and optimization method of stable formation configuration of the large-scale spacecraft in space was studied. Considering the influence of the sun-earth-moon gravitational field on the formation configuration, the earth, the moon, and three spacecraft were regarded as a formation for research in the heliocentric coordinate system. Based on dual quaternion, the natural/artificial celestial body dynamics model was established, and the space gravitational wave detection system model with and without a central celestial body was uniformly described. The parameters to be optimized based on genetic algorithm were given, and the optimization objective function was designed. Simulation results show that the detector meets the stability requirements of the orbit configuration within one year without orbit control.

The micro-vibration of ultra-high-static and ultra-high-stable spacecraft was studied. A modeling and simulation method was proposed to introduce the pointing measurement error and additional torque error induced by micro-vibration into the pointing measurement control system. The micro-vibration experiment of the pointing measurement system was carried out based on the quasi-zero stiffness suspension method. The simulation and experimental results show that the pointing measurement error induced by micro-vibration was more significant, and the peak value reached 10e-4°, and the pointing measurement error of the pointing control system caused by micro-vibration was 0.03 pixels. This work can be used for reference in the study of ultra-high-static and ultra-high-stable spacecraft and derivative technologies.

For a kind of adaptive output regulation control that can only obtain the reduced dimension output information of the system, in this paper, a model reference adaptive control method for output regulation based on Kalman filter was proposed, which used the nonlinear estimation ability of Kalman filter to realize the estimation of output measurement information to full dimensional state information, and used the observation state to realize adaptive tracking of the output of closed-loop system to the reference state to ensure the stability of each closed-loop signal. The above method was applied to the control of the drag-free stable platform in the space gravitational wave detection mission, and the stable output tracking ability of the drag-free control system was realized with unknown parameters and additional disturbances. Based on the theoretical analysis of each closed-loop signal stability realized by the Lyapunov method, numerical simulation comparison verifies the effectiveness of the method over the tracking ability of the general output tracking adaptive control method.

Considering low-frequency disturbance of thrust caused by unexpected electrical breakdown and temperature drift in the operation of microwave ion thruster, as well as the ultra-low bandwidth and strong robustness requirements of the drag-free system, which is converted into a frequency domain constraint index, a fractional-order PID was designed as a drag-free controller with perturbation suppression capability as objective function. Simulation study shows that the control had good robustness to various disturbances of the system compared with the classical PID controller, and could suppress the control effects brought by thruster firing and temperature drift, and finally achieved higher control accuracy. The research provides reference for the high-precision control method of gravitational wave detection without dragging satellite considering micro-propulsion system.

Regarding the layout design of micro thrusters for space gravitational wave detection satellites, a feasibility analysis of the layout of micro-thrusters were first presented, and then a robust optimization design method for the layout of micro-thrusters for space gravitational wave detection satellites was proposed. To obtain the robust optimization design results of the micro-thruster group layout of the space gravitational wave detection satellite, taking the condition number of the configuration matrix as evaluation standard, the thruster configuration with the strongest robustness to the configuration error was optimized through numerical simulation. The proposed method was applied to the layout design of micro-thrusters for space gravitational wave detection satellites. Simulation results show that it can improve the robustness of the layout scheme of micro-thrusters.

This paper discussed the attitude and drag-free control of two Earth-orbit drag-free satellites with two test masses. The control schemes of the science mode were designed, and a robust controller capable of resisting disturbances was proposed. First of all, based on the science requirements and the LEO characteristics, the configuration scheme for the science mode was designed, to present a stable observation platform for the detection mission. Secondly, decoupling the complex system dynamics model based on characteristics of dynamic coupling and control time-frequency, three loops—the spacecraft attitude control loop, the drag-free control loop and the suspension control loop—were produced. Control requirements for each loop were specified according to mission requirements. Thirdly, taking into account the control requirements in frequency domain and the spectral models of various external disturbances and sensor noises, constrains for sensitivity functions and complementary sensitivity functions of each control loop were derived utilizing the mixed-sensitivity method of H _∞ robust control theory. By selecting appropriate weight functions, an H _∞ robust controller was designed. Finally, simulation results indicate that not only the inter-satellites pointing error but also the pose errors and residual acceleration of test masses satisfy the control index requirements, which verifies the effectiveness of the designed controller.

Under the control framework of space gravitational wave detection spacecraft platform system, aiming at the high-precision control of nonlinear unmodeled dynamics and performance constraints of space inertial sensor, in this paper, a data-based adaptive control scheme based on data-driven theory was proposed to realize accurate and stable control target of non-affine non-global Lipstchiz space inertial sensor dynamic system. Based on the fuzzy rule, an additional uncertainty estimator is established, and its general approximation characteristics are used to ensure the bounded estimation error. Based on the Control Barrier Function (BLF), an asymmetric performance constraint is constructed, and the BLF-based controller is used to realize the asymmetric constraint control of the closed-loop signal. According to the principle of contraction mapping and the Lyapunov theory of discrete-time system, the boundedness of each closed-loop signal and adaptive estimation is analyzed, and numerical simulation verifies the feasibility and effectiveness of the data-driven adaptive asymmetric constraint control scheme.

To address the sensitivity challenges inherent in gravitational wave detection instruments, this study unequivocally established the paramount indicators for both interferometer measurement noise and the proof mass residual acceleration noise within “Taiji Project” spacecraft. System noise was meticulously decomposed, revealing 26 distinct categories of interferometer measurement noise and 21 categories of residual acceleration noise. A comprehensive modelling approach was undertaken with specific focus on electromagnetic force noise. Through the design of a dedicated simulation system and subsequent calculations, the engineering viability of the spacecraft design proposal was verified. The simulation indicated that total electromagnetic force noise, calculated using parameters attainable with present-day engineering technology or parameters projected from the key technological roadmap, could satisfactorily meet the demanding requirements of gravitational wave detection missions. The findings of this research not only offer a robust framework for simulation and calculation of future noise variables, but also lay the groundwork for refining the indicator system of spacecraft design.