Spin Equilibrium Configuration Design And Control Of Four-Satellite Closed Tether System

The tethered satellite system(TSS)is a spacecraft system that connects two or more satellites with flexible and light tethers。 Because of the special structure,it can fulfill special missions that traditional satellite system can’t perform.The TSS based on Golay-3 distribution has high precision of relative position control and can point to the ground stably to realize spatial optics integrated aperture imaging because of the constraint of the tethers.The four-satellite tethered closed system consists of four satellites and six tethers,the kinetics model and control are complicated because of the high degree of coupling between the main satellite and the companion satellites.The main content of this paper includes four scientific problems: the kinetics model,spin equilibrium configurations design,configuration keeping control and configuration change control during the spin process of four-satellite tethered closed system.This paper is divided into four parts:Firstly,the kinetic model of the TSS is established with the Lagrange method.The model analyzes the space geometrical relationship between the main satellite and the three companion satellites and is simplified according to some assumptions.The generalized force is obtained based on the principle of virtual work.Further,the generalized time is introduced to the model and the dimensionless kinetic equation of the TSS is acquired.Secondly,two kinds of spin equilibrium configurations are obtained by analyzing the dimensionless kinetic equation.They are the spin equilibrium configuration in the spatial circular plane and the equilateral triangle configuration in any plane and the stability of two spin equilibrium configurations is further analyzed.However the results show that the two configurations are not stable.Therefore,the additional control force should be added to realize stable control.Then,a control strategy is proposed to keep the configuration by combining the spin velocity with the propeller.The spin velocity is used to keep the convergence of configuration plane and the control force produced by propeller is adopted to keep the pointing of configuration plane.The feed forward control law is designed based on spin velocity.Moreover,four feedback control laws are designed by respectively using Lyapunov function,the Sliding Mode Control(SMC),the State-Dependent Riccati Equation(SDRE)and the Linear Quadratic Regulator(LQR).The simulation results show that the above four methods can keep the TSS configurations well.Finally,the kinetic equations about configuration change are established for configuration change problem of the four-satellite tethered closed system.The guidance law is designed based on Lagrange-Gauss-Lobatto(LGL)pseudo-spectral algorithm.The control law about configuration change is also designed and the influences of control coefficient,tracking function and spin velocity on control effect are analyzed.This paper is aimed at the kinetics model,spin equilibrium configurations design,and control methods of configuration keeping process and tether release during the spin process of four-satellite tethered closed system.This research provides a theoretical and technical basis for space-based distributed synthetic aperture observation.