外文翻譯原文-滑?？刂茖?duì)攔截器末制導(dǎo)的應(yīng)用

1、The application of Sliding Mode Control on Terminal Guidance of Interceptors Zhu Zhanxia College of Astronautics Northwestern Polytechnical University Xi’an, China e-mail:zhuzhanxia@nwpu.edu.cn XI Feng Northwestern Pol

2、ytechnical University College of Astronautics Xi’an, China e-mail:icefire1014@msn.com Gao Huai Northwestern Polytechnical University College of Astronautics Xi’an, China e-mail:gaohuaihuai@163.com Abstract—In this

3、paper, we discussed the terminal guidance problems of ballistic missile interceptor from dynamical aspect. We assume that the interceptor is equipped with solid propellant system and orbit control engines can provide

4、 stationary continuous thrust or small pulse thrust in the direction vertical to the line of sight(LOS), and the target has some uncertain maneuver. Firstly, we build the relative motion equation between missile and t

5、arget. Then terminal guidance law is designed by use of sliding mode control theory. To realize this terminal guidance law, we also designed the switch law of orbit control engines. Finally, Simulation results show t

6、hat the intercept accuracy with slide mode guidance law in this paper is better than with pure proportional guidance law for targets with maneuverability. They also show that the LOS rate is about to zero in terminal

7、phase for maneuver target and the switch law can ensure to realize the guidance law. Keywords-switch control law; terminal guidance law; sliding mode control; LOS I. INTRODUCTION Ballistic missile is a kind of threaten

8、 weapons and they are difficult to interception because of their fast speed, small size of the radar reflectivity and strong anti-attack ability. In order to realize effective intercept, it is very important to improv

9、e the capability and accuracy of terminal guidance system. Many scholars have studied the guidance and control law design problems of terminal phase extensively. For example, Witsenhausen[1] used variable density func

10、tion to design the ideal control function of terminal guidance section. However, the selection of variable density function is dependent on designer's experience. Liu Shiyong[2], who consider the target maneuver,

11、 designed the orbital control law of interceptor. Chao Tao[3] proposed a fuzzy attitude control law for the interceptor, but it needs build switch logic table and is difficult to realize in engineering. During the int

12、erceptor movement, the relative motion equation is nonlinear because the orbit motion couples with attitude motion. So, the terminal guidance and control belongs to nonlinear system problem. The traditional control me

13、thod has been facing serious challenges, especially when there is outside interference and unknown target maneuver. Recently, as a widely used control method, variable structure control exhibits good performance when

14、dealing with nonlinear system control problems with model uncertainty and external disturbance uncertainties. For example, Jongrae Kirn[4] designed the variable structure control law of missile terminal guidance on th

15、e assumption that attitude and angular velocity were known and target maneuver is ignored. He built the switch surface by using velocity vector. But the application of this method is severely limited because of its a

16、ssumption. So, in this paper, we consider the uncertain maneuver of the target in extra-atmospheric, design the terminal guidance law on the basis of sliding mode variable structure control theory and give the switch

17、law of orbit control engines, try to improve the accuracy of the interceptors and its response speed, to meet the requirements of precision attack. Simulation results verify the effectiveness of the control law and s

18、how that the sliding mode control can be used to deal with this kind of problem. II. DESIGN OF SLIDING MODE GUIDANCE LAW In this paper, we assume that the missile and target move in the same plane, the movement of them

19、 can be decomposed to vertical and horizontal plane. The analysis method is the same for those two plane, so we choose vertical plane as an example. We build the relative motion equation in the line of sight coordina

20、te system. Figure 1 shows the geometry relationship of missile and target. Figure 1. Missile and target relative motion Where, M represents the missile and T represents the target. m V ?? ? , m θ , m η represent the s

21、peed, the trajectory angle and the front angle of the missile respectively. t V ?? , t θ , t η represent the speed, the trajectory angle and the front angle of the target respectively. R is relative distance between mi

22、ssile and target. Then, the relative motion equation is: 2010 Third International Conference on Intelligent Networks and Intelligent Systems978-0-7695-4249-2/10 $26.00 © 2010 IEEE DOI 10.1109/ICINIS.2010.25 144then

23、 τ is delay time, 1 T is the time when the thrust increase to max Ffrom 0, 1 t is the time of the engine beginning shutdown, 2 T is the time when thrust change to 0 from max F . gy Tand gz T represents thrust c

24、omponents along the Oy and Oz axis in body axis coordinate system respectively. From above thrust curve, we can get: ( )( )m ax11m ax 1 1m axm ax 1 1 1 220 0, gy gztF t t T T T T F T t tF F t t t t t T Tττ τ ττ≤ ≤ ? ?

25、 ? ? < ≤ +? =? + < ≤ ? ?? ? < ≤ + ? ?(7) If 0 q ≠ ? , engines work to eliminate q ? and to achieve designed ideal guidance law. So we should design appropriate orbit control law. In vertical plane, we can mak

26、e y q ? tends to zero through control overload y n of missile in order to make missile fly under the designed guidance law. We design the switch instruction in y-axis as: ( )10 10100sgn00gyyy gyy yygyyT n n mn n n T

27、 a n m n nT n n m? ≥ ≥ ? ? ? ≈ ≤ ≤ ? = =? ≤ ? ? ?? ≤? ≤ ? ?(16) In order to avoiding engines on-off frequently and ensuring accuracy of guidance, we choose switching limitation as follows[7]: ( )( )max 1 00 0max 2 01 1F

28、 T t n h TF T t n n h T+ ? = ? ? ? + ? = ? ?(15) Where: 0 1 n n < , T is the sampling period. 0 h and 1 h is coefficient which can be given according to the number of engine switch on-off and the requirements of

29、control accuracy. In horizontal plane, we can make z q ? tends to zero through control overload z n of missile in order to make missile fly under the designed guidance law. Using the same method, we can design the s

30、witch law in z-axis. IV. SIMULATION EXAMPLE Suppose detection distance of the missile seeker is 500km, seeker blind is 200m, initial velocity is 5km/s, pitch angle 0 8 m θ = ? and yaw angle 0 0 m ψ = ? . Suppose maxi

31、mum thrust of orbit control engine max P =4×490N, τ =0.01s, 1 T =0.01s, 2 T =0.01s,0 max 1 max 0.25 , 0.65 n P n P = = .The initial pitch angle of the target 0 5 t θ = ? ? and yaw angle 0 15 t ψ = ? ? ,orbita

32、l height is 200km, target begin to maneuver with 2 ty a g = and 2 tz a g =when R=45km. In order to contrast, we fulfilled the simulation with proportional guidance law(N=4) and with slide mode guidance law respectively

33、. The results are as shown in following. TABLE I. SIMULATION RESULTS TABLE CEP/m Interceptor time/s Proportional guidance law(PGL) 12.583 87.28 Slide mode guidance law(SMGL) 1.857 92.56 Figure 4. Interceptor an