帶有撞擊角度限制的攔截飛彈導引

Abstract

本論文主要目的在探討帶有撞擊角度限制的攔截飛彈導引。帶有撞擊角度限制的導引法則中，最廣為使用的方法為比例導引法則衍生出來的偏置比例導引法則，利用比例導引法則將瞄準線角度變化率遞減至零的性質，設定一個與撞擊角度有關的偏置項，使得瞄準線角度遞減至特定的數值，達到以特定角度撞擊目標的目的。由於科技的進步，目前飛彈的速度已經是早期的數倍，在飛彈飛行速度快又是正面迎擊的情況下，早期以純比例導引法則架構推導出來的純偏置比例導引法則在導引的最後會發生加速度命令暴增的問題，本論文將針對此做改善，建立一個李亞普諾夫函數，藉由其將狀態收斂至平衡點的特性，並且以真比例導引法則的架構為基礎，算出滿足其穩定性條件的偏置項，得到真偏置比例導引法則。模擬中將考慮飛彈飛行控制系統為一個標準二階系統，並且考慮硬體的限制以及重力的影響，模擬結果可以發現真偏置比例導引法則可以改善先前方法的缺點，並且在一定的區間範圍可以以希望的撞擊角度擊中目標。

This thesis investigates missile interceptor guidance with impact angle constraints. The proposed guidance law is a modification of the biased proportional navigation guidance law is reported in the literature. Proportional navigation guidance law forces line of sight rate to zero. By adding a biased term, biased proportional navigation guidance law will force line of sight rate to a specific value which relate to impact angle to impact the target at a particular angle. As the improvement of technology, the current speed of missile is faster than before. Acceleration command of pure biased proportional guidance law tends to blow up as the interceptor approaches target when the speed of interceptor and target is high and flying oppositely. This thesis will improve this problem by establish a Lyapunov function, which will converge the state to the equilibrium point, and base on the structure of true proportional navigation guidance law which called true biased proportional guidance law. The biased term satisfies its stability condition. In simulation, flying control system takes as a second order system and considers some hardware limit and gravity. Simulation results show the proposed true biased proportional guidance law can improve interceptor performance over existing methods and can achieve the goal in certain range of desire impact angle.