Study Of Nonlinear Orbit Dynamics And Control Near Libration Point

Due to many advantages of libration point orbit in deep-space exploration,it attracts a lot attention from many countries in recent years.However,collinear libration point orbit is unstable according to orbital dynamics.This paper researches the stability of such nonlinear periodic time-varying system,and proposes proper control method aiming at collinear libration point orbit station-keeping with orbital injection errors.The dynamic equations near collinear libration point orbit and orbital error tracking equations under the effect of control inputs are built based on the rotational coordinates of centroid and the model of the Circular restricted three body problem(CR3BP).First,a control method is studied based on the periodicity of libration point orbit.According to Floquet theorem,block controllable form and Lyapunov transition,a state feedback control is proposed based on characteristic exponent assignment for linearization motion equations of periodic orbit.Moreover,the conception of terminal attractor is introduced to accelerate convergence rate,and an improved state feedback control method is designed.This method is employed to the maintenance mission of Halo orbit near L1 point in Sun-Earth barycenter system.Simulation results show the effectiveness of the proposed method.Second,it is proposed that nonsingular fast terminal sliding mode control is associated with extended disturbance observer and improved fast power reaching law.The control method is designed for libration point orbit station-keeping mission influenced by disturbance,especially mismatched disturbance.The extended disturbance observer is utilized to estimate disturbance and its derivative;a novel sliding mode surface is designed by introducing estimation of disturbance into nonsingular fast terminal sliding surface,and the relative control law can accelerate the convergence rate of orbital errors,avoid singular problem during controlling process and reduce the chattering caused by disturbance.Moreover,improved fast power reaching law is considered to eliminate chattering,to accelerate the reaching rate and to guarantee that the control inputs can be adjusted without effecting convergence rate.Lyapunov function is employed to illustrate that the system converges in finite time under the control method.Simulation results show the advantages of the proposed method compared with others.In addition,it is also shown in simulation that the performance of spacecraft moving in libration point orbit under conventional control law with mismatched disturbance.