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针对静止轨道上卫星悬停编队问题,考虑空间摄动力及测量误差,建立卫星编队的相对运动模型.根据上述模型,取优化指标函数,将跟踪问题转化为LQR问题,求得最优控制解.综合滑模控制方法,提高最优控制解的鲁棒性,并用Lyapunov第二法证明最优滑模控制器的全局渐近稳定,进行仿真验证.结果表明,所设计的最优滑模控制器对静止轨道卫星编队控制性能优于LQR控制,在200 m的编队距离,相对位置控制精度达到毫米量级.
Considering the space perturbation and measurement error, a relative motion model of satellite formation is established to solve the satellite hovering formation problem in the geostationary orbit. According to the above model, the optimization index function is taken and the tracking problem is transformed into the LQR problem to obtain the optimal control solution. The synthetic sliding mode control method is used to improve the robustness of the optimal control solution. The global asymptotic stability of the optimal sliding mode controller is proved by Lyapunov second method. The simulation results show that the optimal sliding mode controller The control performance of the orbiting satellite formation is superior to that of the LQR control. At a formation distance of 200 m, the relative position control accuracy reaches the order of millimeters.