无阻力双星编队的满系数矩阵MIMO定量反馈控制

研究由两颗无阻力卫星构成的、用于重力场测量的松散式编队相对位置控制方法，主要解决编队控制所产生的非重力加速度在重力场测量频带内的干扰抑制问题。首先，选取双星位置中点作为编队系统质心，建立了考虑J2摄动项的双星相对动力学模型。然后，根据定量反馈理论（QFT）确定系统在频域内的跟踪性能、鲁棒稳定性、输入干扰抑制等约束。与当前常规的对角型QFT控制器设计方法不同，本文针对编队系统的多输入多输出（MIMO）通道强耦合特性，设计了更具一般性的满系数矩阵鲁棒控制器，不但实现了闭环控制回路整定、通道解耦和稳态收敛，还有效抑制了编队控制量功率谱在科学测量频带内的干扰。最后，通过在时域中的数字仿真校验了该方法控制器的有效性和鲁棒性。

Full Matrix MIMO QFT Controller Design for Drag Free Satellites in Dual Formation

In order to suppress the non-gravitational acceleration interference generated by formation control in the gravity measurement band, relative position control method for loose formation flying drag-free satellites applied to Earth gravimetry mission is investigated. Firstly, a relative dynamic model with J2 perturbation effect is derived based on a formation center of mass, which is located at the middle position of the two satellites. Then, the frequency domain constraints for tracking performance, robust stability and input disturbance suppression are specified based on the quantitative feedback theory (QFT). Different from the general diagonal matrix QFT controller, a fully populated robust controller matrix is designed through taking the highly-coupled multiple-input-multiple-output (MIMO) system characteristics into account. Not only loop-shaping, channel decoupling and steady convergence for closed control loop are realized, but also the power spectral density of disturbance generated by formation control is suppressed in scientific measurement band. Finally, the time domain numerical simulation is carried out to illustrate the effectiveness and robustness of the proposed controller.