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首页> 外文期刊>Acta astronautica >Discrete-time LQ optimal control of satellite formations in elliptical orbits based on feedback linearization
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Discrete-time LQ optimal control of satellite formations in elliptical orbits based on feedback linearization

机译：基于反馈线性化的椭圆轨道卫星编队离散LQ最优控制

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摘要

The sampled-data representation of the relative motion is the foundation of the discrete-time LQ optimal control of spacecraft formations. The sampled-data description for the relative motion in circular orbits has been investigated in great detail. However, few are derived for the elliptical orbits. This paper will employ the discrete-time LQ optimal control theory to deal with the problem of relative orbit control of satellites in elliptic orbits. The formation vector is used to express the formation geometry, and nonlinear feedback is utilized to linearize the equations of the relative motion. An analytical state transition matrix is derived from the solutions of the linearized equations. Based on the state transition matrix, a sampled-data representation is presented for the linearized equations. The sampled-data representation is explicitly related to a sampling sequence of the true anomaly of the target satellite with constant length of the sampling intervals. In terms of the discrete-time model, a discrete-time LQ optimal controller is derived for the linearized equations. By combining the discrete-time LQ optimal control with the nonlinear feedback control, a digital controller is obtained for the satellite formations. Simulations are included to demonstrate the performance of the controller.
机译：相对运动的采样数据表示是航天器编队的离散时间LQ最优控制的基础。圆形轨道上相对运动的采样数据描述已被详细研究。但是，很少有关于椭圆轨道的推导。本文将采用离散LQ最优控制理论来解决椭圆轨道上卫星的相对轨道控制问题。地层矢量用于表达地层几何形状，非线性反馈用于线性化相对运动方程。从线性化方程的解导出解析状态转移矩阵。基于状态转移矩阵，为线性化方程式提供了采样数据表示。采样数据表示与具有恒定采样间隔长度的目标卫星真实异常的采样序列明确相关。根据离散时间模型，为线性化方程推导了离散时间LQ最优控制器。通过将离散时间LQ最优控制与非线性反馈控制相结合，可以获得用于卫星编队的数字控制器。包含仿真以演示控制器的性能。

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