The Research On Drag-free Control Technology For Deep Space Gravitational Wave Detection

Gravitational waves are ripples in space-time that carry the basic degrees of freedom of gravitational interaction.Gravitational waves cover a wide frequency range from 10^-18Hz to 10⁴Hz,among which the space gravitational wave detections mainly focus on the origin of gravitational waves within the range of 10^-4Hz to 10⁰Hz.By placing two free-floating test masses inside the satellite,the distance between them can be accurately measured,and the variation of the distance between the test masses directly reflects the space-time propagation effect of gravitational waves.The drag-free control system is one of the most important technologies in gravitational wave detection because it can provide an ultra-static,ultra-precise and ultra-stable platform for quality measurement.In the context of the Taiji program,this paper mainly studies the drag-free control and inter-satellite link pointing technology in the process of gravitational wave detection mission.Firstly,the gravitational wave detection mission requires a formation of three satellites,each of which consists of a satellite body,two test masses and two telescopes,forming a complex system with 19 dimensional degrees of freedom.The orbit and attitude dynamics equations of the satellite body and the test mass and their perturbation factors are described.The relative dynamics of the space circle formation are analyzed.The relative dynamics and electrostatic coupling between satellites and test masses are analyzed.Secondly,according to the configuration and mission objectives of the gravitational wave detection satellite,the control problem were divided into four interconnected control problems,including drag-free control,suspension control,spacecraft attitude control and inter-satellite laser pointing control.Aiming at these four control problems,the control principles were introduced,and the control model of the whole system loop is established through the analysis of its input source and its design driver.A controller design method based on Input decoupling was adopted to decompose the complex MIMO（Multi Input Multi Output）problem into multiple SISO（Single Input Single Output）problems,which simplifies the controller design.Then,the drag-free control loop was selected to be designed of which the design constraints were analyzed.A series of constraints were converted into sensitivity function requirements,and a robust control method called H∞control in frequency domain was selected to design the drag-free control controller.The controller was designed and performed to achieve the desired performance.Finally,the laser link alignment technology in the gravitational wave detection constellation was studied to solve the problems caused by constraints such as 3million kilometers of ultra-distant distance between stars and limited accuracy of attitude sensors.Considering the propagation delay of laser between satellites,the point ahead angle adjustment was calculated according to the orbit characteristics of formation satellites to ensure the coverage of laser link to the receiving stars.According to the characteristics of the field of view and resolution of STR（Star Tracker）,CCD（Charge Coupled Device）and QPD（Quadrant Photodiode）three kind of attitude sensors,a three-level acquisition strategy was designed to establish the inter-satellite laser link,that is,to determine the switching process of the sensor,the attitude movement process of the satellite-telescope system and the opening and closing process of the laser path.Based on the pointing error,stability requirements,the characteristics of sensor and actuator and the dynamics model of satellite-telescope system,a PID controller was designed to drive the micro thruster and the telescope joint angle actuator,so that the telescope can be aligned to the designed pointing.In this paper,the drag-free controller,laser acquisition strategy and inter-satellite laser pointing controller were designed which provide the technical basis for the laser interferometry of the gravitational wave detection.However,there are still many shortcomings.In the future research,it’s better to concentrate on the design of the suspension control loop and the attitude determination method in the acquisition process.