Robust control for a quasi-linear parameter varying Sun-Earth L2 formation flying

A nonlinear controller is designed for a L₂ formation flying control system, and robust stability is investigated for the closed-loop system with uncertainties. The L₂ formation flying is modeled as a second-order quasi-linear parameter-varying model, which is obtain from the nonlinear formation flying model with Barbashin method by including explicit dependence of the dynamic derivatives on states and external parameters. Base on this QLPV model, a polynomial eigenstructure assignment approach is applied to complete the controller design for the system. As function of state and external parameters, the controller realize the independence between the closed-loop system and the operating point to ensure the performance of the closed-loop system is independent with every operating equilibrium. Simulation is carried out to validate the control performance. Considering the uncertainties in the controller parameters and dynamic derivatives, parametric stability margins of system are analyzed by using Kharitonov´s approach. Analysis results show the controller is fairly robust with respect to these uncertainties.