Ubiquitous Computing and Communication Journal (ISSN 1992-8424)

AIR-TO-GROUND INTEGRATED FUZZY GUIDANCE SYSTEM Mohamed Rizk, SM IEEE

Ahmed ElSayed

Faculty of Engineering, Alexandria University, Alexandria, Egypt. mrmrizk@ieee.org

Department of Computer Science and Engineering, University of Bridgeport, Bridgeport, CT, USA. eng_ahmedabdelsalam@yahoo.co.uk

ABSTRACT In this paper we consider the problem of air to ground missile guidance system using fuzzy controller. The missile model is assumed as three degree of freedom (3DOF) (assuming the analysis in the vertical plane only).The homing guidance method is used. This paper presents numerical results for applying the fuzzy controller to the missile in different situations of control parameters in different positions. Keywords: Fuzzy Control, Missile Guidance.

1

INTRODUCTION

In the last few years there has been an increasing interest in the applications of the fuzzy set theory in practical control problems. Fuzzy control is applied to processes that are too complex to be analyzed by conventional techniques. The missile guidance system is one of these systems which are complex system to analyze. There are many ways to design the guidance system such as homing guidance, command guidanceâ€Śetc. In this paper we present the problem of ground to air integrated missile guidance system, which mean that the controller works direct to the missile dynamics without the autopilot and the actuator, using fuzzy controller. First, the used guidance method, homing guidance, will be explained; then a scenario of the missile mission will be explained. 1.1.

Homing Guidance Systems:

A homing guidance system is defined as a guidance system by which a missile steer itself toward a target by an internal mechanism without the need of external source for tracking the target or itself. The homing guidance systems are classified into three general types: a. b. c.

Active homing Semi active homing Passive homing

In this paper we consider the active homing guidance system, which in its simplest form consists of a transmitter and receiver of energy. The guidance system enables the missile to detect the presence of the target, and a control system computes and

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analyzes the received data to get a control command suitable for the position of target. Missiles which use an active homing guidance are completely independent; the missile does not require any signal from any external source or any guidance intelligence [1]. The advantage of an active homing guidance method is that it does not need any external guidance equipment which makes the missile works in any place without the need of building any fixed structure, except a launcher. The main disadvantage of the active homing guidance system is the destruction of the tracking and guidance equipment when the missile hits the target and destroys itself, which increases the cost and the price of the missile. 1.2.

Missile mission description :

The missile mission presented in this paper is an air-to-ground missile mission, which means that an aircraft will launch a missile on a stationary target (such as a Tank, Artillery positionâ€Ś). Typically the launching occurs far from the target and the consequence of aligning the missile's flight path with the target early in flight causes the missile to fly in at a shallow angle. For targets which the fronts and the sides are more strongly protected than the top this is a clearly disadvantage. In this paper the primary objective is to design guidance controller against stationary targets with low final miss distance and increases the final attitude of the missile to overcome the previous disadvantage.

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where

2

MISSILE MODEL

θ is attitude in radian

From the analysis of the forces of aerodynamics around the missile shown in Fig. (1), we can get the following equations which describe the motion of the missile [2] [3] [4]

q is budy rotation rate in rad/sec m is missile mass in kg. g is the accelerati on of gravity in m/s

2

I yy is the moment of inertia about y axis in Kg.m

2

2 W& is the accelerati on in the Z body axis in m/s 2 q& is the change in body rotation rate in rad/s

T is the thrust in the X body axis in N

ρ is the air density in Kg/m

3

S ref is the reference area in m Figure 1: Forces and variables around the missile airframe

U& =

T + Fx m

q& =

M I yy

C X is the coefficien t of aerodynami c force in t he X axis

− qW − g sin θ .......... ...( 1)

Fz + qU + g cos θ .......... .........( 2 ) W& = m .......... .......... .......... .......... ..( 3 )

θ& = q .......... .......... .......... .......... .........( 4 ) U e = U cos (θ ) + W sin (θ ).......... .......( 5 )

2

C Z is the coefficien t of aerodynami c force in t he Z axis C M is the coefficien t of aerodynami c moment about the Y axis d ref is the reference length in m

W e = −U sin (θ ) + W cos (θ ).......... .....( 6 )

δ

is the fin angle in radians

X& me = U e .......... .......... .......... .......... ( 7 ) Z& me = W e .......... .......... .......... .......... .( 8 )

FX

is the aerodynami c force in the X body

where Fx = q S ref C x (Mach, α )

Fz = q S ref C z (Mach, α, δ )

M = q S ref d ref C M (Mach, α, δ, q ) q=

1 2

ρV

V = U

2

2 +W

axis in N FZ

is the aerodynami c force in the Z body axis in N

M

is the aerodynami c moment along the Y body axis

q

is the dynamic pressure in Pa

V 2

−1 ⎛ W ⎞ α = tan ⎜ ⎟ ⎝U ⎠

is the airspeed in m/s α is the incidence in radians

U is the velocity in the X body axis in m/s W is the velocity in the Z body axis in m/s U e is the velocity in the X earth axis in m/s We is the velocity in the Z earth axis in m/s X me is the X position of the missile in the X

earth axis in m

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830

4

Z me is the Z position of the missile in the Z earth axis in m

3

FUZZY CONTROLLER DESIGN

This section presents the design of the integrated fuzzy guidance system using homing guidance. The controller will get the starting altitude of the missile with respect to the earth coordinate Z me0 and the instantaneous earth X axis position of the missile X me , and will produce the elevator deviation angle (fin deflection angle) as an output.

Table 1: Fuzzy controller rules table

X me

N

Z

Z meo

PV S

PS

PM

PB

PV B

NE

PL

PM B

PV B

PV B

PV B

PV B

Z

NM

PL

PS

PL

PL

PV B

PV B

Z

FM

PL

PV S

PV B

PL

PL

PV B

Z

FV

PL

PV S

PM B

PV B

PL

PL

Z

As known from the missile dynamics that the fin deflection angle will change the acceleration normal to the missile body and the moment about the missile Y axis, which will change the position of the missile in space [2]. First let us consider the membership function of the two inputs and the output [5], [6] as shown in Fig. 2. Second, from the logic of the missile dynamics and the distribution of the forces and velocities we can consider the following rule table (Table 1). The value of the maxima and the minima of the universe of discourse for each input and output are obtained from the maximum and the minimum of the coordinate of the space of the missile motion, and the value of maximum and minimum of the output is the safe limit of the elevation angle which the missile can have.

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NUMERICAL RESULTS

The controller is tested with simulation [7] for numerical example with a missile with the previous model and the following numerical configurations: U0 = 900 m/s, W0 = 0 m/s, q0 = 0 rad/s, Î¸0 = 0 rad, Xme0 = 0 m, Zme0 = range between -1800 to -3000 m And the target position is: Xt0 = range between 2000 to 4000 m Zt0 = 0 The resultants miss distance in the range between 2 to 9.5 m Î¸final in range between -870 to -1100 Which means that the effective head of missile will be approximately perpendicular to the thin area of target, which means that the probability of missile to hits the target is 100 %. The altitude of the launching position of the missile can be changed with in a range of 1200 m, and the maximum value of miss distance will not be greater than 10 m. Fig. 3 shows the trajectory of the missile in three different cases.

5

CONCLUSIONS

This paper presented the design of an air-toground integrated fuzzy guidance system using fuzzy controller. The missile model used was the nonlinear exact 3DOF model which shows the fact that fuzzy controller can be used for any complex system with acceptable error. The controller got the starting altitude of the missile and the X position of the missile and directly produces the fin deflection angle as an output. So the missiles not need the autopilot and the actuator any more, which reduce the cost of the missiles. The resultants miss distance of the missile not excess 10 m; if these miss distances compared with the dimensions of targets we can see that the missile will hit the targets. The last point is that the final attitude of the missile around -900, which increases the probability of distortion of target. In the other researching results either the missile guided by the using of autopilot and actuator or it must be launched closed to the target to increase the probability of target distortion.

6

REFERENCES

[1] M. Abdel Rahim: Design of a Robust Controller for a Command Guidance System, PhD. Thesis, Faculty of Engineering, Alexandria University, (1994). [2] A.G. Biggs, B.E.: A Mathematical Model of the

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Missile System Suitable for Analogue Computation, Australian Defense Scientific Service, Weapon Research Establishment, Report SAD 20, no. 8 J.S.T.U. D3, (1954). [3] Jan Roskam: Airplane Flight Dynamics and Automatic Flight Control, Roskam Aviation and Engineering Co., (1979). [4] Aerospace Toolbox, Matlab, Mathworks Inc [5]. L. A. Zadeh: Fuzzy Set, Information and Control, vol. 8, pp. 338-353, (1965). [6] J. M. Mendel: Fuzzy Logic Systems for Engineering: A Tutorial, proc. IEEE, vol. 83, no. 3, pp. 345-377, (1995). [7] Fuzzy Logic Toolbox, Matlab, Mathworks Inc. (a)

μXme N Z PVS PS

PM

PB

PVB

-20

3100 Xme Xe, The first input to the controller

μδ Z

PVS PMS PS

PM PB PMB PVB PL

-8

30

(b)

δ

δ, The output of the controller

μZme0

NE

NM

FM

1700

FV

3100

Zme0

Ze0, The second input to the controller

Figure 2: Inputs and output membership functions

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(C) Figure 3: Missile trajectory in three different cases (a) Zme0 = -2800, Xt = 2000 (b) Zme0 = -2000, Xt = 2000 (c) Zme0 = -2000, Xt = 3000

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