姿态角幅值约束下的太阳帆Lissajous轨道保持控制

太阳帆航天器以两姿态角作为轨道控制输入时, 其轨道动力学方程具有非仿射非线性特性. 通过人工平动点处线性化获得的线性系统可完成太阳帆航天器轨道保持控制器的分析与设计. 由于线性近似模型为有误差模型, 存在近似有效范围约束, 表现为轨道高度约束和姿态角幅值约束. 本文研究了姿态角幅值约束对线性近似模型有效性的影响, 通过计算给出满足近似误差要求的姿态角幅值约束. 当控制输入存在幅值约束时, 控制器轨道修正能力受到束缚. 通过研究姿态角幅值约束下的最大允许入轨误差, 设计了最大允许入轨误差下线性二次型调节器(LQR)用于轨道保持控制, 并将控制器应用于太阳帆日地三体系统非线性模型中, 实现了日地人工L₁点Lissajous轨道最大允许入轨误差的控制收敛和良好精度下的轨道保持控制.

Station-keeping Control of Solar Sail Lissajous Orbit with Attitude Angles Amplitude Constraint

The orbital dynamic equations of solar sail spacecraft have non-affine and nonlinear properties with attitude angles as the station-keeping control input. The linearization method has been widely used in settling down station-keeping problem of solar sail spacecraft orbit. However, the linear model, obtained from local linearization around the libration point, inherently has the approximate scope which results in the constraint of the orbit amplitude as well as the constraint of the attitude angles amplitude. In this paper, the model error of solar sail linear dynamic system is presented and the constraint of attitude angles amplitude is calculated. As a result of the controller amplitude constraint, the trajectory control ability is bounded, raising questions about the maximum allowable orbit injection error. Then, the controllability Gramian matrix is used to estimate the maximum allowable orbit injection error. Furthermore, the Linear Quadratic Regulator (LQR) controller considering maximum allowable orbit injection error is designed and applied to solar sail CR3BP nonlinear model. The numerical simulations indicate that Lissajous orbit injection error convergence as well as 20 years' orbit station-keeping with high precision have been realized.