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电动力绳系卫星的推力幅值较小且方向固定,完成轨道机动任务的周期长,其最优控制问题的求解比较困难。采用在傅里叶空间描述的轨道动力学模型,将控制量电流表示为傅里叶级数的形式,并推导了用傅里叶系数作为参量的椭圆轨道运动的平均轨道根数方程。在此基础上构造了电动力绳系卫星轨道机动的最优控制模型,通过直接配置法将其转化为非线性规划问题,使用序列二次规划法进行了数值求解。固定圈数内最大提升轨道高度和最短时间变轨两个算例表明,该方法可以快速精确地求解椭圆轨道内电动力绳系卫星的最优控制问题。
Electric power rope satellites thrust amplitude smaller and fixed direction to complete the orbital maneuver task cycle length, the optimal control of the problem is more difficult to solve. The orbital dynamics model described in Fourier space is used to represent the control current in the form of Fourier series and to derive the mean orbital equation of elliptic orbit with Fourier coefficients as parameters. Based on this, the optimal control model of orbit maneuvering for electric ropes is constructed, which is transformed into a nonlinear programming problem by direct configuration method. The quadratic programming method is used to solve the problem. Two examples of maximum lifting orbit height and shortest time changing orbit in a fixed number of revolutions show that this method can solve the optimal control problem of the electric power satellites in elliptical orbit quickly and accurately.