数学建模 飞机管理模型

Air Traffic Control

Abstract

本文讨论了如何对新进入区域内的飞机是否会与区域内原有的飞机碰撞的问题，和如若碰撞，调整各架飞机方向角，使得飞机均能安全飞出正方形区域的问题。

针对判断飞行的飞机之间是否发生碰撞亦即可碰撞问题，把各架飞机的运动轨迹端点坐标用时间表示后，就可以写出第六架飞机与其它五架飞机的距离表达式，判断这个最小距离是否小于8km，如果小于，则碰撞，否则不碰撞。这一过程的实现可通过MATLAB编程动态模拟飞机在区域内的飞行过程。在时间轴上连续取样，最后得出第六架飞机和第五架相碰，碰撞时事件飞机的坐标位（），相碰时刻为？

针对检测到碰撞的存在并采取措施进行规避，即碰撞规避问题。需要对各架飞机的方向角进行调整，并且使得飞机方向角调整幅度最小。建立非线性规划模型，利用MATLAB求得第i架飞机)6,5,4,3,2,1

i调整的角度分别为：

(

关键字:飞机碰撞方向角最优解非线性规划

Contents

I. Introduction

Grow inside 160 kilometers of exact square districts in the about 10,000 meters high empty some side, usually how many the airplane make level flight.Position and speed vector of each airplane inside the district are recorded its data by the calculator, so that they carry on a flight management.When desire gets into the airplane of the district to arrive a district edge, after recording its data, immediately compute and judge whether meeting and airplane occurrence in the district collision.If will collide, then should compute how to adjust each(including is lately ingoing) direction Cape that the airplane flies.To avoid collision.Now suppose a condition as follows:

1)The standard that don't collide is more than 8 kilometers for the distance of arbitrarily two airplanes.

2)The airplane flies the range that the direction Cape adjusts to be higher than 30 degrees.

3)All airplane airspeeds are all per hours are 800 kilometers.

4)The airplane that gets into the district while arriving a district edge, with the distance of airplane inside the district in response to above 60 kilometers.

5)At most need to consider 6 airplanes.

6)Need not consider that the airplane leaves the condition of this empress in the district.

Please to the problem establishment mathematics model of the flight management that avoid collision.List to compute a step, carry on a calculation to the following data.(direction Cape the error margin isn't higher than 0.01 degrees)Requesting airplane to fly the range that the direction Cape adjusts is as far as possible small.

The coordinates that establishes the district's 4 tops (0,0),(160,0) , (160,160) , (0,160)

Airplane serial number Abscissa x Ordinate y

Direction

Cape

（degree）

1 150 140 243

2 85 85 236

3 150 155 220.5

4 14

5 50 159

5 130 150 230 New 0 0 52

Note:The direction Cape points to fly direction and X stalk just to of clip Cape. Try to carry on evaluation and expansion to your model according to the actual application background.

II. The Description of the Problem

2.1The analysis of the problem background

在一个确切的广场区，每架飞机的位置和速度矢量飞机到达区的边缘.其数据记录，计算器立即计算和判断飞机发生碰撞的区域.如果发生碰撞然后计算如何调整各方向开普敦的飞机飞以避免碰撞，.程序如下：

In an exact square district, position and speed vector of each airplane are recorded its data by the calculator.When the airplane arrives the edge of district, the calculator immediately computes and judge whether meeting and airplane occurrence in the district collision.If the occurrence collides and computes then how adjust each direction Cape that the airplane flies to avoid collision.Process such as figure a show:

access

leave

2.2 on the analysis to problem 1

由于模型假设飞机是在同一高度飞行，故可以认为飞机是在同一水平面上，这样只需讨论二维平面管理飞机不相碰撞的管理和调节问题。

首先要判断各架飞机之间是否会碰撞。可以在二维坐标上找出各个飞机的点坐标，以此确定飞机的相对位置。图1中虚线框代表整个正方形区域。左下角处为刚进入区域边缘的第6架。再可由题目中给出的飞机的坐标和飞行角度，借助MATLAB 编程及图像输出的方法确定初始运行轨道，由此可写出在t 时刻各个飞机

Square area

airplane Calculate and

determine

Adjustment flight path