Relative position and attitude coupling control of Sun–Earth L2 point formation flying by QLTV polynomial eigenstructure assignment

Abstract

A non-linear coupling controller based on polynomial eigenstructure assignment (PEA) is presented for the relative position and attitude control of formation flying around Sun–Earth L2 point. The dynamics of relative position and attitude motion is formulated as a non-linear equation and rewritten into quasi-linear time-varying (QLTV) model in the latter application. In this article, the PEA approach used for linear time-invariant (LTI) and linear parameter-varying (LPV) models is extended to the QLTV model to realize the independence between the closed-loop system and the operating point. With this PEA approach, the eigenstructure assignment for the system can be completed without imposing any particular eigenvalues and 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. The resulting PEA controller is a function of system state and parameters, and produces a closed-loop system with invariant performance over a wide range of conditions. In the application, the corresponding controllers for relative position control and attitude control are designed via each non-linear QLTV equation firstly, and then a combination method for relative position and attitude controllers is presented to consider the coupling effect between these two control systems. Also, the controller is revised by cascade-saturation control logic to limit the maximum values of manoeuvremaneuver rates and inputs of actuator. Finally, a simulation is carried out to validate the performance of the new controller for formation flying.