基于Simulink的鱼雷自动调整提前角导引弹道仿真_英文
第21卷第10期 系
统 仿 真 学 报? V ol. 21 No. 10
2009年5月 Journal of System Simulation May 2009
Torpedo’s Automatically Adjust Lead Angle Guide Trajectory
SimulationBased on Simulink
LI Wen-zhe 1, ZHANG Y u-wen 2, F AN Hui 2, GONG Wei 1
(1. Dalian Naval Academy, Dalian 116018, China; 2. College of Marine Engineering, Northwestern Polytechnical University, Xi’an 710072, China)
Abstract: To overcome such disadvantages as high workload, complexity while debugging and modifying when adopting advanced programming languages such as VC, Delphi, etc. in the torpedo guide trajectory simulatio n, aiming at automatically adjust lead angle guide trajectory of certain torpedo, the torpedo guide trajectory simulation method using Simulink was brought forward, certain torpedo’s guide trajectory mathematic model was constructed, torpedo guide trajectory Simulink simulation model was designed , torpedo’s guide trajectory was simulated , simulation results were got, and simulation curves were drawn. Through the simulation it is indicated that the Matlab/Simulink simulation method makes the dynamic system simulation become easy, visual and quick. The simulation method is of great reference
value for other similar system’s trajectory or guide method simulation .
Key words: Simulink; automatically adjust lead angle guide trajectory; torpedo; simulation
基于Simulink 的鱼雷自动调整提前角导引弹道仿真
李文哲1，张宇文2，范 辉2，龚 潍1
（1.海军大连舰艇学院，大连 116018；2.西北工业大学航海学院，西安 710072）
摘 要：为解决鱼雷武器导引弹道的仿真中采用VC 、Delphi 等高级语言编程工作量大，调试、修改繁琐的问题，针对某型采用自动调整提前角导引弹道的鱼雷，提出了基于Simulink 的鱼雷导引弹道仿真解决方案，建立了该型鱼雷导引弹道数学模型，设计了鱼雷导引弹道Simulink 仿真模型，并通过该模型对该型鱼雷的导引弹道进行了仿真，给出了仿真结果，绘制了仿真曲线；通过仿真表明，采用Simulink 仿真方法使动态系统的仿真变得容易、直观、迅捷，此系统建模与仿真方法，也对其它类似系统的弹道或导引方法仿真具有一定的参考价值。 关键词：Simulink ；自动调整提前角导引弹道；鱼雷；仿真
中图分类号：E925.23 文献标识码：A 文章编号：1004-731X (2009) 10-3003-03
Preface
Torpedo guide system is the most important and complicated part of the torpedo, its dynamic characteristic is generally described by differential equations, and to resolve these differential equations we must recur to modern simulation technique. The MA TLAB software produced by MathWorks company has powerful mathematics calculation functions [1], it has excellent numerical calculation ability and data visualization ability, so it’s broadly used in automatic control, digital signal process, dynamic system simulation, etc. To exactly import control system’s complex model to the computer for analyze and simulate, MathWorks company offers a new control system model graphics input and simulation tool: Simulink, it’s a integrated work environment to realize dynamic system model construction and simulation. As an important part of Matlab,
Received: 2007-09-16 Revised: 2007-12-23
Biographies: LI Wen-zhe (1974-), instructor of Dalian Naval Academy, major in weapon system trajectory and combat efficiency research and teaching work; ZHANG Yu-wen (1946-), professor of Northwestern Polytechnical University, doctor tutor, major in weapon system and exert engineering, firing theory and technology, trajectory and control, etc; FAN Hui (1981-), doctor candidate of Northwestern Polytechnical University, major in weapon system collectivity design theory and method; GONG Wei (1965-), instructor of Dalian Naval Academy, major in weapon system and combat efficiency research work.
Simulink enlarges Matlab’s functions. Simulink has relatively independent function and use method, supplies friendly graphics user interface (GUI). Its model is denoted by frame figures composed of models, and realizes visualization construction. Simulink is a powerful tool for dynamic system model simulation [2-3]. For weapon system’s guide trajectory simulation, we usually use advanced programming language in tradition, and the programming and debugging period is complex, difficult and long. This paper designs and simulates torpedo’s automatically adjust lead angle guide trajectory simulation based on Matlab/Simulink, the programming workload is greatly diminished to compare with traditional programming method.
1 Guide Trajectory Mathematics Model
1.1 Kinematics equations of torpedo
While torpedo does the horizontal movement without transverse rotation, the kinematics relations are:
456123456cos()sin()(1)t t t t t y t r y y r y r
x
v z
v c q c c c c c c c c ψψ?
ωψβσωωβσβωβσ=×??=?×??=??=?×?×?×??=×+×+×?=×+×+×??
2009年5月 系 统 仿 真 学 报 May 2009
Fig.1 Torpedo and target relative relation
In the equations x ，z ，v t ，Фt ，ψt ，β，ωy ，бr are torpedo’s movement in x axis, movement in z axis, velocity, yaw angle, trajectory departure angle, sideslip angle, circular angle speed, vertical rudder angle. coefficient c 1，c 2，c 3，c 4，c 5，c 6 depend on torpedo’s Fig. 1.
1.2 Kinematics equations of target
cos()sin()m m m m m m m my
x v z v ψψψ
ω=×??
=?×??=? In the equations x m ，
z m ，v m ，ψm ，ωmy are target’s movement in x axis, movement in z axis, velocity, trajectory departure angle, circular angle speed.
1.3 The relative movement relation between torpedo
and target
[]cos()cos()sin()sin()/m m t t t t m m r
v q v q q
v q v q r ????=???=???
in the equations r ,q is distance and relative bearing.
1.4 Automatically adjust lead angle trajectory guide
method
Suppose the torpedo use multi-beam gradually changes lead angle method to realize automatically adjust lead angle trajectory. For this guide system, many acoustic beams are lognitudinal axial symmetry at torpedo’s head (Fig. 2), acoustic system approximately measure target bearing angle through
target location at torpedo’s beams, then send guide command.
Fig. 2 Acoustic beams distribute
The basic principle of the guiding method is [4]: record the target beam No and the zero axis beam No, through the change trend of target beam No and zero axis beam No, adjust lead angle, so the torpedo’s course is direct to the encounter point.
1.5 Torpedo automatically adjust lead angle guide
trajectory simulation model
Function 1 is used to calculate target distance(r) and relative bearing(q), Function 2 is used to get torpedo and target’s movement at axis x and z, yaw angle, torpedo and target trajectory departure angle, Function 3 is used to acquire target beam No and zero axis beam No and rudder angle(бr ) according to target distance and relative bearing angle and guiding law, Function 4 is used to get torpedo’s circular angle speed and sideslip angle according to rudder angle and torpedo figure coefficient, Function 5 is used to get target turn around time.
Fig. 3 Torpedo trajectory simulation Simulink model
Target trajecotry
Torpedo trajecotry
2009年5月李文哲，等：基于Simulink的鱼雷自动调整提前角导引弹道仿真May, 2009
2 Simulation Results
2.1 Simulation condition
Suppose that target does the straight run movement with 6m/s velocity, then does the circular movement. Torpedo moves its rudder according to automatically adjust lead angle guide law when torpedo finds target. According the mathematics model stated as before, set initial simulation parameter in the Matlab/Simulink, then do the simulation use the Simulink model.
In the simulation, target velocity is 6m/s, initial distance is 800m, initial torpedo relative bearing angle is -45o, torpedo velocity is 20m/s.
At first target does the straight run movement, when the simulation time is bigger than 50 seconds, target does the circular movement with 0.1 rad/s circular angle speed.
2.2 Torpedo automatic adjust lead angle guide
trajectory simulation curve
Fig. 4 is the Simulink simulation curve.
Fig. 4 Automatic adjust lead angle guide trajectory simulation curve
3 Conclusion
Advanced programming language such as VC, VB, Delphi etc. has the disadvantages as high workload, complexity while debugging and modifying in the complicated torpedo weapon guide system simulation. Using Matlab/Simulink can greatly decrease the programming workload, and has the advantage of visualization, easy to modify the parameters, easy to draw the simulation curves, and the debug time is shorten, we can modify the simulation models, evaluate the results and verify the system behavior at any phase. The system modeling and simulation method of this paper is of great reference value for other similar system’s trajectory or guide method simulation. References:
[1] FAN Ying-le. MATLAB simulation application [M]. Beijing, China:
People’s Post and Telecom Publishing Company, 2001.
[2] JIA Yue, SONG Bao-wei, LIANG Qin-wei, ZHAO Xiang-tao. The
simulation of trail guidance trajectory of a model torpedo based on MATLAB/Simulink [J]. System Engineering Theory and Application, 2006, 26(3): 141-144.
[3] CHEN Gui-ming, ZHANG Min-zhao, QI Hong-yu. Matlab modeling
and simulation [M]. Beijing, China: Science Publishing Company, 2001. [4] YAN Wei-sheng. Torpedo navigation mechanics [M]. Xi’an, China:
Northwestern Polytechnical University Publishing Company, 2005.