基于保辛算法的绳系卫星系统闭环反馈控制问题求解

应用非线性系统滚动时域控制的保辛算法求解绳系卫星系统子星释放和回收过程的闭环反馈控制问题.通过第二类Lagrange方程推导出二体绳系卫星系统的动力学方程;通过拟线性化方法将绳系卫星系统闭环反馈控制问题转化为线性非齐次Hamilton系统两端边值问题的迭代求解;通过保辛算法将线性非齐次Hamilton两端边值问题转化为线性方程组的求解;通过递进更新时间步的状态变量和控制变量,完成绳系卫星系统的闭环反馈控制.数值仿真表明:相对于Legendre伪谱方法,用保辛算法求解绳系卫星系统的闭环反馈控制问题的计算速度和收敛速度较快.绳系卫星系统的开环控制和闭环反馈控制问题数值仿真结果表明:在绳系卫星的初始状态存在偏差的情况下,使用开环控制会导致系统在终端无法达到稳定状态,而使用闭环反馈控制则能在一段时间内抵消初始状态向量偏差对系统产生的影响,最终达到稳定状态.

Solution on closed-loop feedback control problems of tethered satellite system based on symplectic preservation algorithm

The closed-loop feedback control problems of the subsatellite deployment and retrieval process of tethered satellite system is solved by sympleetic preservation algorithm with nonlinear receding horizon control. The dynamics equations of two-body tethered satellite system are deduced by Lagrange equations of the second kind ; the closed-loop feedback control problems of tethered satellite system are transformed into the iteration solution on linear nonhomogeneous Hamilton system＇s two-point boundary value problems by quasilinearization method; the two-point boundary value problems of linear nonhomogeneous Hamilton system are transformed into the solution of a set of linear equations by symplectic preservation algorithm; the closed-loop feedback control of tethered satellite system is achieved by progressively updating the state and control variables on each time step. The numerical simulation shows that,compared with the Legendre pseudospeetral method, the computation and iteration speed is faster for solving closed-loop feedhaek control problems of tethered satellite system hy sympleetic preservation method, The numerical simulation results of the open-loop control and closed-loop feedback control problems of tethered satellite system show that, under the situation that the initial state of tethered satellite is with errors, the open-loop control can not lead to a stable state system in the terminal, and the closed-loop feedback control can eliminate the effect of initial errors on the svstetn within a certain period of time and the system reaches the stable state finally.