Sun–Earth L2 point formation control using polynomial eigenstructure assignment

A nonlinear controller based on polynomial eigenstructure assignment (PEA) is presented for the control of Sun–Earth L2 point formation flying. The relative motion dynamics is formulated as a nonlinear equation and rewritten as a Quasi-Linear Time-Varying (QLTV) model. Using a coprime factorization of the desired closed-loop transfer function, the PEA controller structure is calculated by representing the controller gains as polynomials. During the implementation of spacecraft formation flying, the PEA method is extended from Linear Time-Invariant (LTI) and Linear Parameter-Varying (LPV) models to a QLTV model to produce a closed-loop system with invariant performance over a wide range of conditions. To ensure system performance, the analytic stability analysis of the closed-loop system is developed and a position keeping controller for MIMO formation flying is designed using a decoupling method to achieve the desired performance. Finally, a simulation is carried out to validate the controller performance for the formation flying.

► The dynamics of formation flying is rewritten as a Quasi-Linear Time-Varying model.
► A PEA controller is developed by using QLTV model without approximation.
► The controller produces an invariant performance over a wide range of conditions.
► Comparing to an LQR method, the control performance is improved significantly.