基于拟平衡滑翔的横程最大轨迹研究

Maximum cross range trajectory optimization based on quasi-equilibrium glide conditions

求解横程最大弹道问题就是要探求飞行器的最大横程机动能力。将地球看成一圆球,不考虑地球自转,建立三自由度再入滑翔飞行的动力学和运动学方程。用最优控制来描述此问题,控制量为倾侧角和迎角,进一步基于拟平衡滑翔条件推导出由状态变量和倾侧角描述的迎角控制规律的形式,从而使得控制量只有倾侧角。在此模型的基础上采用基于四阶经典Runge-Kutta积分法的配点法来描述此最优控制问题,将其转化为非线性规划问题,优化的性能指标为末端横程最大,用SQP算法优化得到了最优倾侧角控制规律以及相应的飞行轨迹,其结果与直接打靶法计算的结果一致。

The problem of maximum cross range trajectory is to find the maximum of flight vehicle＇s lateral maneuverability.Firstly the 3-DOF equations of motion of a reentry vehicle over a spherical,no-rotating Earth were built.And the aerodynamic coefficient was given by a polynomial equation and it was the function of the attack angle and the Mach number.Then the attack angle formation was concluded with the aid of the quasi-equilibrium glide condition,so that the bank angle become the only control variable.At last the optimal control problem was simplified and the fourth-order Runge-Kutta collocation approach and the SQP algorithm was present for solving the optimal control problem.The numerical example shows the result obtained by the fourth-order Runge-Kutta collocation approach is coincident with the one by a direct shooting method.