【运动学】导弹姿态控制含Matlab源码

1 简介

从1945年V自2枚导弹推出以来，70多年来，从防空导弹到反舰导弹，从弹道导弹到巡航导弹，从亚音速导弹到超音速导弹。在大气中，这些导弹可以按照目标轨迹移动，其姿态控制系统至关重要。导弹姿态控制系统关系到导弹飞行的成败。导弹姿态控制系统主要有以下两个功能:在大气层复杂干扰条件下，确保导弹姿态角偏差始终稳定在系统允许的范围内；根据制导控制指令改变导弹的姿态角，从而改变导弹的运动状态，从而纠正飞行路线，使导弹能够准确命中目标。由于导弹在大气层中的运动非常复杂，为了简化问题，导弹的运动总是分解为铅锤表面的纵向运动和水平表面的横向运动，导弹在空间中的角运动分解为三个方向：俯仰、偏航和滚动。由于导弹的姿态变化主要由角运动引起,所以导弹的姿态控制系统主要目的就是对导弹的角运动进行控制[1]。

目前，大气层导弹的姿态控制主要采用以下三种方法：气动控制、推力矢量控制和喷气反应控制。它们也可以相互使用，形成复合控制。喷气反作用控制通过喷气发动机将导弹携带的气源或燃料燃烧或分解产生的高压气体喷射到弹体外，产生反作用力和反作用扭矩，从而控制导弹的姿态。但直接侧向喷流的应用会使侧喷发动机产生的高压气流与来流气体碰撞，形成激波干扰[2]。导致弹体表面的气动压力分布重置，会改变导弹设计之初的假设条件，导致导弹姿态发生变化，导致导弹姿态发生变化。推力矢量控制是通过改变导弹主发动机喷射气流的方向来控制导弹姿态。对于未采用推力矢量技术的导弹，主发动机的气流喷射方向始终与导弹的中轴一致，发动机产生的推力方向也沿导弹轴向前。此时，导弹发动机的推力作用是抵消导弹的阻力或为导弹提供加速动力。使用推力矢量技术的导弹改变了发动机的推力方向，产生侧向控制力和控制扭矩，从而达到控制导弹姿态的目的。其优点是导弹姿态的变化不会影响其控制扭矩，但矢量发动机结构过于复杂，成本高，不适用于普通导弹[3]。根据气动力的基本定律和相对性原，当导弹在大气中飞行时，气动力的作用是不可避免的。气动力可分解为铅垂面内的升力、水平面内的侧向力和与导弹前进方向相反的阻力。这三种作用分别在导弹上产生滚动扭矩、偏航扭矩和俯仰扭矩，从而改变导弹势。基于气动控制的导弹姿态控制方法具有控制连续、控制能耗低、结构简单等优点，广泛应用于大气层飞行导弹[4]。

本文的研究对象是大气中的飞行导弹。通过设计基于气动控制的姿态控制定律，导弹具有较高的动态响应特性，使导弹能够在允许的时间内以较高的精度达到预期的姿态。执行机构是安装在弹体尾部的四个空气舵面。通过姿态控制规则计算控制指令，控制舵面的偏转角度，改变空气动力矩，进一步改变姿势，实现准确控制导弹姿势的目的。

2 部分代码

clc;clear;定义导弹、大气、地球等固定参数-%Jx=2.95;Jy=168.2;Jz=168.2;m=300;S=0.0616;L=0.3;rho=1.2;g=9.8;i=10000;ii=i/10;t=zeros(1,ii-1);dt=0.001;H=pi/180;K=180/pi;定义初始位置参数-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%x=zeros(1,i);y=zeros(1,i);z=zeros(1,i);y(1)=30000;定义初始速度参数-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%V=zeros(1,i);Vx=zeros(1,i);Vy=zeros(1,i);Vz=zeros(1,i);V(1)=2275;Vx(1)=2275;定义初始弹道参数-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%theta=zeros(1,i);psiv=zeros(1,i);gammav=zeros(1,i);theta(1)=(40*pi)/180;定义初始姿态参数-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%htheta=zeros(1,i);psi=zeros(1,i);gamma=zeros(1,i);htheta(1)=40*H;psi(1)=0*H;gamma(1)=5*H;htheta0=50*H;psi0=10*H;gamma0=0*H;%-定义初始舵偏角-%-deltax=zeros(1,i);deltay=zeros(1,i);deltaz=zeros(1,i);%--------------------------定义初始姿态角速度参数---------------------------%omegax=zeros(1,i);omegay=zeros(1,i);omegaz=zeros(1,i);定义攻角/侧滑角-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%alpha=zeros(1,i);beta=zeros(1,i);dalpha=0;dbeta=0;定义空气动力和空气动力矩-%-X=zeros(1,i);Y=zeros(1,i);Z=zeros(1,i);Mx=zeros(1,i);My=zeros(1,i);Mz=zeros(1,i);定义控制律参数-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-Kpx=-1.5;   Kdx=-0.018;Kpy=-1.5;   Kdy=-0.05;Kpz=-1.8;   Kdz=-0.05;定义绘图用数组-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-hthetat=zeros(1,ii-1);psit=zeros(1,ii-1);gammat=zeros(1,ii-1);omegaxt=zeros(1,ii-1);omegayt=zeros(1,ii-1);omegazt=zeros(1,ii-1);xt=zeros(1,ii-1);yt=zeros(1,ii-1);zt=zeros(1,ii-1);Mxt=zeros(1,ii-1);Myt=zeros(1,ii-1);Mzt=zeros(1,ii-1);deltaxt=zeros(1,ii-1);deltayt=zeros(1,ii-1);deltazt=zeros(1,ii-1);定义气动力和气动力矩的插值矩阵-%B = [-6，-4，-2，0，2，4，6]；A = [-6；-4；-2；0；2；3；4；6；8；10]CX = [0.926,0.750,0.636,0.583,0.614,0.722,0.888;0.758,0.596,0.511,0.468,0.489,0.570,0.726;      0.644,0.504,0.426,0.398,0.411,0.487,0.614;0.602,0.477,0.399,0.367,0.390,0.458,0.574;      0.650,0.508,0.428,0.410,0.415,0.502,0.627;0.699,0.547,0.463,0.434,0.449,0.533,0.674;      0.762,0.601,0.512,0.471,0.497,0.585,0.739;0.921,0.749,0.628,0.578,0.613,0.735,0.902;      1.136,0.949,0.817,0.763,0.800,0.934,1.115;1.405,1.212,1.080,1.029,1.067,1.200,1.388];CY = [-2.694,-2.563,-2.426,-2.351,-2.427,-2.605,-2.686;-1.854,-1.710,-1.642,-1.593,-1.618,-1.711,-1.800;      -0.920,-0.818,-0.802,-0.794,-0.797,-0.798,-0.873;0.034,0.036,0.015,0.033,0.009,0.004,0.031;      0.930,0.894,0.868,0.808,0.802,0.836,0.928;1.373,1.331,1.275,1.190,1.233,1.257,1.340;      1.825,1.751,1.685,1.566,1.633,1.715,1.787;2.704,2.647,2.460,2.344,2.428,2.583,2.677;      3.411,3.458,3.365,3.276,3.312,3.397,3.392;4.175,4.292,4.283,4.241,4.218,4.263,4.181];

3 仿真结果

4 参考文献

[1]黄金阳, 辛长范, 马云建,等. 基于Matlab/FlightGear的导弹飞行姿态与轨迹可视化系统[J]. 导航与控制, 2016, 15(6):5.

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