无奇点三维攻击时间控制滑模导引律

为研究导弹在视场角约束下的三维攻击时间控制问题,提出一种三维非线性滑模导引律。利用攻击时间误差设计滑模面,推导出三维形式的俯仰和偏航加速度指令;通过对所设计制导律进行简单修正,解决了零初始前置角引起的奇点问题;从数学上证明了该导引律的稳定性和收敛性,讨论了导引律相关参数的取值范围,分析了与纯比例导引法、解耦三维导引律之间的关系。仿真结果表明,所设计导引律能够在视场角约束条件下有效实现攻击时间增大或减小的控制;俯仰和偏航平面的耦合程度越强,该导引律控制能耗小的优势越为明显。

Nonsingular sliding mode guidance law for impact time control in three-dimensional space

To study the problem of impact time control for missiles in three-dimensional space with field-of-view constraint, a three-dimensional nonlinear sliding mode guidance law was proposed. The sliding mode surface was designed by using the impact time error and then the acceleration commands in pitch and yaw were derived. By making a simple correction to the proposed guidance, the singular issue driven by zero-initial-heading-error was overcome. The stability and convergence of the proposed guidance law was proved in a rigorous mathematical manner. The value range of some certain parameters and the relationship with the pure proportional navigation guidance law and the decoupled three-dimensional guidance law were analyzed. Simulation results indicate that control of the increasing or reducing impact time can be achieved effectively with the field-of-view constraint by using the proposed guidance law. The stronger the degree of coupling between the pitch and yaw planes is, the more advantageous the proposed guidance law in control energy is.