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滑翔制导炮弹因体积和成本所限存在控制能力有限的问题,有必要对其方案弹道加以合理的设计,为此提出一种不确定飞行环境下的弹道优化方法以降低方案弹道对各类随机干扰的敏感度。建立了模型偏差、滑翔启控点参数偏差、气动参数偏差及气象偏差等不确定性因素的数学模型,推导出计及随机干扰的滑翔弹动力学系统雅可比矩阵的解析表达式,利用线性协方差分析法,得到了系统误差传播方程,进而建立了不确定飞行环境下的弹道优化模型。利用Chebyshev伪谱法将弹道优化问题转换为非线性规划问题,在此基础上采用内点算法(Ipopt)获得了方案弹道的最优解。仿真结果表明,与不考虑不确定因素的设计方法相比,采用本文方法设计出的方案弹道,纵向和侧向位移散布方差明显减小,显示出对随机干扰更好的抑制效果。
It is necessary to design a reasonable ballistic trajectory for the gliding guided-round projectile because of its limited controllability due to its volume and cost. Therefore, a trajectory optimization method in uncertain flight environment is proposed to reduce the impact of the program trajectory on all kinds of random disturbances Sensitivity. The mathematical model of uncertainties such as model deviation, parameter deviation of gliding control point, aerodynamic parameter deviation and meteorological deviation are established. The analytical expression of Jacobian matrix of gliding missile dynamic system considering random disturbance is derived. Variance analysis method, the system error propagation equation is obtained, and then the trajectory optimization model under uncertain flight environment is established. Using the Chebyshev pseudospectral method, the ballistic optimization problem is transformed into a nonlinear programming problem. Based on this, the optimal solution of the program trajectory is obtained by the Ipopt algorithm. The simulation results show that compared with the design method which does not consider the uncertainties, the dispersion of the ballistic, longitudinal and lateral displacements of the scheme designed by this method is obviously reduced, which shows a better restraining effect on the random disturbance.