Fuzzy Guidance 539

8/7/2019 Fuzzy Guidance 539

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AIR-TO-GROUND INTEGRATED FUZZY GUIDANCE SYSTEM

Mohamed Rizk, SM IEEE Ahmed ElSayed

Faculty of Engineering,

Alexandria University,

Alexandria,

[email protected]

Department of Computer Science and Engineering,

University of Bridgeport,

Bridgeport, CT,

[email protected]

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 differentpositions.

Keywords: Fuzzy Control, Missile Guidance.

1 INTRODUCTIONIn 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 byconventional techniques. The missile guidance

system is one of these systems which are complex

system to analyze. There are many ways to designthe guidance system such as homing guidance,

command guidanceetc. In this paper we present

the problem of ground to air integrated missile

guidance system, which mean that the controllerworks 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 theneed of external source for tracking the target or

itself. The homing guidance systems are classified

into three general types:

a. Active homingb. Semi active homingc. Passive homing

In this paper we consider the active homing

guidance system,whichin its simplest form consists

of a transmitter and receiver of energy. The guidance

system enables the missile to detect the presence ofthe 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 completelyindependent; 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 trackingand guidance equipment when the missile hits the

target and destroys itself, which increases the costand 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 anaircraft will launch a missile on a stationary target

(such as a Tank, Artillery position). Typically the

launching occurs far from the target and theconsequence 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 thesides are more strongly protected than the top this is

a clearly disadvantage. In this paper the primaryobjective is to design guidance controller against

stationary targets with low final miss distance and

increases the final attitude of the missile to overcomethe previous disadvantage.


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2 MISSILE MODELFrom 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 themissile [2] [3] [4]

Figure 1: Forces and variables around the missile airframe

( ) ( )

( ) ( )

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

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

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

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

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

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

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

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

eWmeZ

eUmeX

WUeW

WUeU

q

yyI

Mq

gqUm

FzW

gqWm

FxTU

=

=

+=

+=

=

=

++=

+

=

&

&

&

&

&

&

( )

( )

( )

=

+=

=

=

=

=

U

W

WUV

where

1tan

22

2V

2

1q

q,,Mach,MCrefd

refSqM

,Mach,zCrefSqFz

Mach,xCrefSqFx

2rad/sinraterotationbodyinchangetheis

2m/sinaxisbodyZin theonacceleratitheis

2Kg.minaxisyaboutinertiaofmomenttheis

2m/singravityofonacceleratitheis

kg.inmassmissileis

rad/secinraterotationbudyis

radianinattitudeis

q

W

yyI

g

m

q

where

&

&

2minareareferencetheis

3Kg/mindensityairtheis

NinaxisbodyXin thethrusttheis

refS

T

m/sinairspeedtheis

Painpressuredynamictheis

axisbody

Ythealongmomentcaerodynamitheis

Ninaxis

bodyZin theforcecaerodynamitheis

Ninaxis

bodyXin theforcecaerodynamitheis

radiansinanglefintheis

minlengthreferencetheis

axisYabout the

momentcaerodynamioftcoefficientheis

axisZhet

inforcecaerodynamioftcoefficientheis

axisXhet

inforcecaerodynamioftcoefficientheis

V

q

M

ZF

XF

refd

MC

ZC

X

C

m/sinaxisearthZin thevelocitytheis

m/sinaxisearthXin thevelocitytheis

m/sinaxisbodyZin thevelocitytheis

m/sinaxisbodyXin thevelocitytheis

radiansinincidencetheis

eW

eU

W

U

minaxisearth

Xin themissiletheofpositionXtheismeX


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minaxisearth

Zin themissiletheofpositionZtheismeZ

3 FUZZY CONTROLLER DESIGNThis 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 ofthe 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 theuniverse of discourse for each input and output are

obtained from the maximum and the minimum of thecoordinate 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 RESULTSThe 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,

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

finalin 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 missileto hits the target is 100 %.

The altitude of the launching position of themissile 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 themissile in three different cases.

5 CONCLUSIONSThis paper presented the design of an air-to-

ground integrated fuzzy guidance system using fuzzycontroller. 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 startingaltitude of the missile and the X position of the

missile and directly produces the fin deflection angleas 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 themissile 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

meZ

N ZPV

S PS PM PBPV

B

NE PLPM

B

PV

B

PV

B

PV

B

PV

BZ

NM PL PS PL PLPVB

PVB

Z

FM PLPV

S

PV

BPL PL

PV

BZ

FV PLPV

S

PM

B

PV

BPL PL Z


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Missile System Suitable for Analogue Computation,

Australian Defense Scientific Service, Weapon

Research Establishment, Report SAD 20, no. 8J.S.T.U. D3, (1954).

[3] Jan Roskam: Airplane Flight Dynamics and

Automatic Flight Control, Roskam Aviation andEngineering 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

PVBPBPMPSPVSN Z

3100-20

Xe, The first input to

the controller

Xme

Zme0

FVFMNMNE

31001700

Ze0, The second input to

the controller

Zme0

Z PVS PMS PS PM PB PLPMB PVB

-8 30

, The output of the

controller

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Fuzzy Guidance 539