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 guidance…etc. 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. Active homing b. Semi active homing c. 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

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 position…). 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.

UbiCC Journal, Volume 6: Issue 2 829

Ubiquitous Computing and Communication Journal (ISSN 1992-8424)

2 MISSILE MODEL 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]

Figure 1: Forces and variables around the missile airframe

( ) ( )( ) ( )

)8.(........................................

)7(........................................

)6.....(..........cossin

)5.......(..........sincos

)4.........(........................................

)3..(........................................

)2.........(..........cos

)1...(..........sin

eWmeZeUmeX

WUeW

WUeU

q

yyI

Mq

gqUm

FzW

gqWm

FxTU

=

=

+−=

+=

=

=

++=

−−+

=

&

&

&

&

&

&

θθ

θθ

θ

θ

θ

( )( )

( )

⎟⎠⎞

⎜⎝⎛−=

+=

=

=

=

=

U

W

WUV

where

1tan

22

2ρV2

1q

qδ,α,Mach,MCrefdrefSqM

δα,Mach,zCrefSqFz

αMach,xCrefSqFx

α

2rad/sin raterotation body in change theis

2m/sin axisbody Zin theon accelerati theis

2Kg.min axisy about inertia ofmoment theis

2m/sin gravity ofon accelerati theis

kg.in mass missile is

rad/secin raterotation budy is

radianin attitude is

q

W

yyI

g

m

q

where

&

&

θ

2min area reference theis

3Kg/min density air theis

Nin axisbody X in the thrust theis

refS

T

ρ

m/sin airspeed theis

Pain pressure dynamic theis

axisbody

Y thealongmoment caerodynami theis

Nin axis

body Zin the force caerodynami theis

Nin axis

body X in the force caerodynami theis

radiansin anglefin theis

min length reference theis

axis Y about the

moment caerodynami oft coefficien theis

axis Zhe t

in force caerodynami oft coefficien theis

axis X he t

in force caerodynami oft coefficien theis

V

q

M

ZF

XF

refd

MC

ZC

XC

δ

m/sin axisearth Zin the velocity theis

m/sin axisearth X in the velocity theis

m/sin axisbody Zin the velocity theis

m/sin axisbody X in the velocity theis

radiansin incidence theis

eWeU

W

U

α

min axisearth

X in the missile theofposition X theis meX

UbiCC Journal, Volume 6: Issue 2 830

min axisearth

Zin the missile theofposition Z theis meZ

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 0meZ and the instantaneous earth X axis position of the missile meX , and will produce the elevator deviation angle (fin deflection angle) as an output.

Table 1: Fuzzy controller rules table

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.

4 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, θ0 = 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 θfinal 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-to-ground 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

meX

meoZ

N Z PVS PS PM PB PV

B

NE PL PMB

PVB

PVB

PVB

PVB Z

NM PL PS PL PL PVB

PVB Z

FM PL PVS

PVB PL PL PV

B Z

FV PL PVS

PMB

PVB PL PL Z

UbiCC Journal, Volume 6: Issue 2 831

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.

Figure 2: Inputs and output membership functions

(a)

(b)

(C)

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

(c) Zme0 = -2000, Xt = 3000

Xme

PVB PBPMPSPVSN Z

3100-20 Xe, The first input to

the controller

μXme

Zme0

FVFM NMNE

31001700 Ze0, The second input to

the controller

μZme0

δ

Z PVS PMS PS PM PB PLPMB PVB

-8 30δ, The output of the

controller

μδ

UbiCC Journal, Volume 6: Issue 2 832