This study presents a comprehensive analysis of biased proportional navigation guidance laws with variable gain in the bias command that achieve stationary target interception with a desired impact angle under the restriction of permissible look angle. More specifically, this study investigates the bias shaping approach, which takes the bias gain function given by a product of factors in range and look angle. The linear feedback and fractional power feedback of impact-angle error are considered for command structures. For each command form, this study examines the conditions that should be satisfied by the gain functions to guarantee mission accomplishment without violation of the constraints. The analysis particularly focuses on estimating the set of feasible initial or final conditions that ensure compliance with the constraints along the trajectory. Numerical simulation is performed for a range of initial and final flight-path angles to verify the analytical results. The findings of this study provide a general foundation for the design of a nonswitching guidance law for impact-angle control with limited look angle through shaping of gain profiles.

本研究全面分析了偏置命令中具有可变增益的偏置比例导航制导规律，该规律在允许视角的限制下以所需的撞击角实现静止目标拦截。更具体地说，本研究研究了偏置整形方法，该方法采用由范围和视角因素的乘积给出的偏置增益函数。指令结构考虑了冲击角误差的线性反馈和分数功率反馈。对于每种命令形式，本研究检查了增益函数应满足的条件，以保证在不违反约束的情况下完成任务。该分析特别侧重于估计一组可行的初始或最终条件，以确保符合沿轨迹的约束条件。对一系列初始和最终飞行路径角度进行数值模拟，以验证分析结果。这项研究的结果为通过增益剖面的整形设计用于有限视角的冲击角控制的非切换制导法则提供了一般基础。