Libration Suppression Of The Three-body Tethered Space Satellite System

Three-body tethered space satellite system generally consists of one main-satellite and two sub-satellites connected by tether,which can be applied to many space missions,such as: artificial microgravity environment,energy or cargo transmission,space exploration,interferometry et al.In its application,orbital eccentricity,Coriolis forces and other external disturbances cause the libration of sub-satellites relative to the main-satellite.This will not only affect the stability of the system,and even lead to the winding and fracture of the tether,which is not conducive to the operation of the system.Therefore,how to suppress the libration of the system is one main issue of three-body tethered space satellite system.To solve the problem,this paper focuses on the libration suppression method of the three-body tethered space satellite system in elliptic orbit and the system with partial space elevator as the application background.The main research contents and results are as follows:(1)Modeling of the general dynamicsIn order to study the libration suppression problem of three-body tethered space satellite system with considering the future expansion of such system and N-body tethered space satellite system including more sub-satellites(N is integer and greater than 2),it is necessary to establish a general dynamics model of N-body tethered space satellite system.At present,the Lagrangian method is widely used in the modeling of three-body or multi-body space tethered satellite systems.Although this method is simple and effective,it is difficult to deduce the dynamic model of multi-body tethered space satellite systems with variable number of sub-satellites.Therefore,the general dynamic model of N-body tethered space satellite system is derived in this paper.This model not only covers the dynamics of the systems studied in this paper,but also can describe the three-dimensional space dynamics of any multi-body tethered space satellite system with the main-satellite moving in the Kepler orbit without disturbance.(2)The libration suppression of a three-body tethered satellite system in elliptic orbit is studied.1)For the liberation suppression of the three-body tethered space satellite system in elliptic orbit,with the thrusters as the control actuator,the existing research on the control input amplitude is too large,which is not conducive to the engineering implementation.Thus,a control strategy based on tracking time-varying solution is proposed by means of dynamics analysis,which realizes the limited thrust stability control of a three-body tethered space satellite system in elliptic orbit.First,based on the general dynamic model,the dynamic equation of the system respects to the true anomaly.Then,by using this equation,the motion characteristics of the system in the true anomaly domain are analyzed,and a class of time-varying solutions of the system liberating angles in elliptic orbits are obtained.The control strategy of tracking the time-varying solution is proposed,and the corresponding sliding mode control law is designed.Simulation results show that the proposed control strategy can effectively suppress the libration of the system in elliptical orbit(including the case of large eccentricity)with a limited thrust amplitude.Compared with the existing studies,this strategy requires less control thrust magnitude.2)At present,no study work on the libration suppression of a three-body tethered satellite system in elliptical orbit without thrusters.In this paper,a control method based on retracting and releasing tether and a control strategy for tracking the periodic solution of liberating angles are proposed,which can suppress the libration of the system with the consumption of only electric energy without the consumption of sub-satellites’ fuel.Firstly,based on the general dynamic model,the dynamic equation of the a three-body tethered space satellite system with variable tether length in elliptic space is derived.Then,by analyzing the dynamic equations of the system,the required tether retrieving/releasing speed when the libration angle is equal to its periodic solution is obtained.Next,the design parameters of the periodic solution for the minimum variation of the length of the tether length are derived.A sliding mode control law is designed to suppress the libration of the system.Finally,the effectiveness of the proposed control method and strategy for libration suppression is verified by numerical simulation.(3)In this paper,the libration suppression of a three-body tethered space satellite system with partial space elevator as its application background is studied.The structure of the system is: "main-satellite-climber(elevator)-end body",which is arranged in the direction of gravity gradient.The climber can move between the main-satellite and end body along the tether.General,the control method is to adjust the tension of the tether or its retrieving/releasing speed.1)In this paper,the problem of system libration suppression caused by Coriolis force is studied.The existing control strategy must restrain the swing by changing the moving speed of the climber along the tether.In this paper,a tension control strategy based on controlling the retracting and end body is proposed for the first time.Based on the control strategy,the sliding mode control method is used to design the control law to verify its effectiveness.The numerical simulation results show that the new control strategy can effectively restrain the swing of the climber when it moves along the tether.The proposed control strategy provides a new idea for solving the problem of three-body tethered space satellite system libration suppression with partial space elevator as the application background.In addition,when the control strategy is adopted,the moving speed of the climber along the tether can be either constant or variable,which makes the operating mode of the system more flexible and diverse.2)The control method of "parallel piecewise optimal state trajectory planning/tracking" was proposed to solve the problem of oscillation suppression of the three-body tethered space satellite system during the tethered motion of the climber.In this method,the entire task flow is divided into several sub-segments,and the optimal state trajectory of the next sub-segment is calculated(generated)while the optimal state trajectory of the current sub-segment is tracked and controlled by the system.In order to verify the effectiveness of the control method,the example of the middle body moving along the tether with constant speed and variable speed is simulated.The simulation results show that the control method proposed in this paper combined with the control strategy of the retractable and retractable end bodies can effectively restrain the libration of the three-body tethered space satellite system in the process of the climber moving along the tether under the premise of satisfying the task constraints.In addition,the control method can also control the moving speed of the climber and the end body along the tether,so as to effectively shorten the task cycle while restraining the swing.Compared with the existing methods,the control method of "parallel piecewise optimal state trajectory planning/tracking" can not only realize the closed-loop control of the three-body tethered space satellite system during the movement of the climber,but also make full use of the parallel computing function of CPUs to improve the computing efficiency.3)The full state stability of the system is studied.The existing research only focuses on the suppression of the libration of the three-body tethered space satellite system in the process of the climber moving along the tether.By the end of the mission,the system is not completely in the state of static equilibrium,that is,the whole state is stable.This situation is not conducive to the stability of the system and the recovery of the middle body after the end of the task.Therefore,in this paper,the reeling speed of tethers are taken as the control inputs,and the reeling speeds of the climber and the end body are jointly controlled to achieve the full state stability of the system.Firstly,the control method of taking the mooring tension instead of the mooring tension as input is put forward,and the dynamic model which can characterize the change of the total tether length of the system is derived.Then,on this basis,the control strategy of simultaneously adjusting the moving speed of the climber along the tether and the retracting speed of the end body along the tether is adopted.The simulation results show that the new control method can make the state variables in the space three-body tethered space satellite system,including the liberating angles,liberating angular velocities and the tethered retracting velocity,converge to zero by the end of the moving of the climber,so as to realize the full state stability of the system.