Libration point orbit maintenance using improved state feedback control based on Floquet theorem

An improved state feedback control (ISFC) scheme is proposed for station-keeping mission of satellite along unstable nonlinear period orbit near collinear libration point. By linearization, collinear libration point orbit maintenance model transforms into linear time-varying differential equations. Based on Floquet theorem and Lyapunov transformation, a state feedback control (SFC) is designed by using characteristic exponent assignment and block controllable form. For accelerating orbit tracking and improving the quality in the process of convergence, an improved state feedback control is proposed by introducing a nonlinear term to replace linear part. Numerical simulation results illustrate the effectiveness of the proposed control scheme in Richardson's third order analytical approximation for a period orbit.