Modeling And Control Of High Precision Postion Keeping For The Sun Earth L₂ Point Formation Flying

Highly precise control of formation flying is one of the most important techniques required to be challenged for the high-resolution interferometry missions in the complex deep-space environment. Focusing on the stringent requirement of these missions, this study addresses the modeling and control of high precision position keeping for the Sun-Earth L₂ point spacecraft formation in the following aspects:Firstly, the modeling of relative motion for the Sun-Earth L₂ point spacecraft formation is developed. A precise relative motion dynamics of the Sun-Earth L₂ point formation is modeled by including the effects of solar radiation pressure and lunar gravity. To be fit for the linear control design, Linear Time-Invariant (LTI) and Linear Parameter-Varying (LPV) model are developed based on the serials expansion of nonlinear equation around its equilibrium point. To reduce the modeling error and avoid the gain scheduling of control strategy, a Quasi-LPV model without approximation is derived from the nonlinear equation with Barbashin method.Secondly, a Linear Quadratic Regulator controller of position keeping for the Sun-Earth L₂ point spacecraft formation is presented. The LQR control theory is applied to design a linear position keeping controller via an LTI model. In order to compensate the disturbances and improve the steady error, an integrator is added into the LQR controller. A position keeping scenario is simulated using a LQR controller to validate the closed-loop system performance.Thirdly, a Polynomial Eigenstructure Assignment controller of position keeping for the Sun-Earth L₂ point spacecraft formation is developed. In this part, a PEA control approach is introduced and further is extended for Quasi-LPV systems to obtain a parameter-varying controller which can ensure a time-invariant performance of the closed-loop system. Based on the Quasi-LPV model of the Sun-Earth L₂ point spacecraft formation, the corresponding position keeping PEA controller is developed. A simulation is carried out to indicate that the resulting Quasi-LPV PEA controller could maintain the high desired system performance over a wide range of conditions.