Quasi-LTV Polynomial Eigenstructure Assignment Control for Formation Flying Around Sun-Earth L2 Point *

A nonlinear controller based on polynomial eigenstructure assignment (PEA) is presented for the control of formation flying around Sun-Earth L2 point. The dynamics of relative motion is formulated as a nonlinear equation firstly and rewritten into QLTV model in latter application. With PEA method, the eigenstructure assignment for the controller can be completed without imposing any particular eigenvalues. Using a polynomial matrix eigenspace of the system and a coprime factorization of the desired closed-loop transfer function which can determine different control performance, the designer is only left to choose the controller structure and calculate the controller gains by several simple formulas to produce a flexible design method. To implement for nonlinear system, the PEA method used for LTI and LPV model is extended to the QLTV model to realize the independence between the closed-loop system and the operating point. To ensure the system performance, the analytic stability analysis of closed-loop system is also developed. With such PEA method, a position keeping controller for MIMO formation flying is designed with a decoupling method to complete the desired performance design. Finally, a simulation is carried out to validate the controller performance for the formation flying.