The Robust D-stability Analysis Of Relative Position-keeping Control For The Sun-earth L₂ Libration Point Formation Flying Spacecrafts

Highly precise keeping of formation flying of Sun-Earth L₂ point spacecraft formation is one of the most significant and challenging techniques for deep space exploration.This dissertation is focused on the mathematical modeling,related position keeping,robust stability analysis and distubance-attenuation control,the detail content of which is as follows:Based on the polynomial eigenstructure assignment approach（PEA）,the formation flying keeping control problem for Sun-Earth L₂ point is studied.After establishing the mathematical model,that is,a quasi-linear parameter varying（Quasi-LPV）system based on the Barbashin approach,the polynomial eigenstructure assignment controller is designed for formation maneuver and position keeping.Furthermore,considering the constraints of control output and maneuver velocity,a hierarchical saturation method is developed to obtain the PEA controller with those constraints taken into consideration.The D-stability is investigated for Sun-Earth L₂ point spacecraft flying control systems with parameters uncertainty.The single-input single-output（SISO）formation closed-loop system is first designed for both autonomous and uncertainty cases.Then,the characterization equation is established with a multiple affine approach.Furthermore,the finite inclusion theorem is employed to obtain the varying domain for controller gains and dynamical parameters under the D-stability.Finally,the D-stability condition is derived for the overall formation systems.The D-stability analysis strategy is proposed for multi-input and multi-output（MIMO）closed-loop control systems based on linear matrix inequality approach with consideration of coupled factors.For the model for Sun-Earth L₂ formation flying,the MIMO closed-loop control model is designed for six types of typical uncertainty parameters.A linear matrix inequality solving approach is developed for a class of approaches based on polynomial matrices convex,which is used to solve D-stability problem for MIMO systems with parameter uncertainty,and is extended to intersection D domain.At last,for the MIMO formation systems,the exact varying scope for uncertainty parameters is analyzed.The obtained results are more ideal compared to the SISO analysis results.The time-domain D-stability analysis method is developed for MIMO system based on parameter-dependent Lyapunov function approaches.The proposed methods first establish a matrix multi-convex functions,and then the stability analysis is performed for the MIMO systems by solving the LMI in the D domain.Finally,the designed approaches are applied to D-stability analysis for Sun-Earth L₂ point.Compared with frequency domain strategies,the designed approaches have a higher efficiency with the same simulation conditions.