基于分数阶微积分理论的新型三维末制导律

Novel 3D terminal guidance law based on the theory of fractional order calculus

针对机动目标拦截问题,设计了一种基于分数阶微积分理论的新型三维末制导律。首先,介绍了分数阶微积分理论的定义及其相关性质,通过分析弹目拦截的空间几何关系,基于传统比例导引律(Proportional Navigation简称PN),设计了分数阶微积分比例制导律(Fractional order calculus proportional navigation简称FOCPN);其次,对设计FOCPN制导律的过载特性及其能量控制特点进行研究,通过分析前置角的变化,研究了FOCPN制导律的弹道平稳度;同时,运用小偏量运动学模型,分析了FOCPN对自动驾驶仪参数变化的鲁棒特性。最后,通过仿真表明,新设计的FOCPN制导律制导精度高,拦截时间短,过载变化较为平稳,解决了传统PN末端视线角速率发散导致的过载激增问题,可有效拦截机动目标。

A novel terminal guidance law based on the fractional calculus was derived aiming at intercepting the maneuvering target.Firstly, the definitions and properties of the fractional order calculus were introduced, the fractional order calculus proportional navigation（FOCPN） was proposed based on the traditional proportional navigation（PN） after analyzing the relative motion relation. Secondly, the characteristic of the load and the control effort of FOCPN were studied, and the trajectory stability of the FOCPN was researched through analyzing the change of leading angle, also the robust of FOCPN against autopilot parameters was analyzed by small deviator kinematics model.At last, simulation result shows that, compared with the traditional PN law, the new designed FO- CPN has the higher guidance precision and the shorter intercept time, and it solves the problem of overload increasing sharply caused by divergence of line of sight rate.The new designed guidance law can intercept maneuvering target effectively.