Tabu Fuzzy Guidance_540

8/7/2019 Tabu Fuzzy Guidance_540

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LEARNING AIR-TO-GROUND INTEGRATED FUZZY GUIDANCESYSTEM USING TABU SEARCH

Mohamed Rizk, SM IEEE Ahmed ElSayed

Faculty of Engineering,

Alexandria University,Alexandria,Egypt.

[email protected]

Department of Computer Science and Engineering,

University of Bridgeport,Bridgeport, CT,USA.

[email protected]

ABSTRACTIn this paper we consider the problem of air to ground missile guidance systemusing fuzzy controller which uses Proportional Navigation and Pure Pursuitmethods. The fuzzy controllers rules are defined using Tabu Search (TS). Themissile model is assumed as three degree of freedom (3DOF) (assuming theanalysis in the vertical plane only). This paper presents numerical results for applying the learned fuzzy controller to the missile in different situations of control

parameters.

Keywords: Fuzzy Control, Missile Guidance, Tabu Search.

1 INTRODUCTION

In the last few In the last few years there has been an increasing interest in the applications of thefuzzy set theory in practical control problems. Fuzzycontrol is applied to processes that are too complexto be analyzed by conventional techniques. Themissile guidance system is one of these systemswhich are complex system to analyze. There aremany ways to design the guidance system such ashoming guidance, command guidance and beam-

rider guidance. In this paper we present the problemof ground to air integrated missile guidance system,which means that the controller works direct to themissile dynamics without the autopilot and theactuator, using fuzzy controller. First, the usedguidance method, homing guidance, will beexplained; then a scenario of the missile mission will

be explained.

1.1. Homing Guidance Systems:

A homing guidance system is defined as aguidance 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 classifiedinto three general types:

Active homingSemi active homingPassive homing

The active homing guidance system, in itssimplest form consists of a transmitter and receiver

of energy, which enables the missile to detect the presence of the target, and a control system, whichcomputes and analyzes the received data to get acontrol command suitable for the position of target.Missiles which use an active homing guidance iscompletely independent, the missile does not requireany signal from any external source or any guidanceintelligence [1].

The homing guidance systems have two major guidance methods:

Pure pursuit method: it's a method in which themissile velocity vector is always directed toward theinstantaneous target position.

Proportional navigation method: its a method inwhich the rate of change of missile heading isdirectly proportional to the rate of rotation of theLOS (Line of Site) from the missile to target.The active homing guidance method does not needany external guidance equipment which makes themissile works in any place without the need of

building any fixed structure, except launcher. But thedistortion of the tracking and guidance equipmentwhen the missile hits the target and destroys itself makes some problems of this method.

1.2. Missile mission description :

The missile mission presented in this paper is anair-to-ground missile mission, which means that anaircraft will launch a missile on a stationary target(such as a Tank, Artillery position). Typically thelaunching occurs far from the target and theconsequence of aligning the missile's flight path withthe target early in flight causes the missile to fly in at


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a shallow angle. The objective of this work is to hitthe targets at the top where the fronts and sides aremore strongly protected. In this paper we design aguidance controller and learn the controller ruleswith Tabu Search algorithm to get a small final missdistance and the final attitude of the missile in theorder of 900.

2 MISSILE MODEL

From the analysis of the forces of aerodynamicsaround the missile shown in Fig. 1, we can get thefollowing equations which describe the motion of themissile [2] [3] [4]

Fig. 1 : Forces and variables around the missileairframe

( ) ( )( ) ( )

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

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

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

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

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

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

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

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

eW me Z

eU me X

W U eW

W U eU

q

yy I M q

g qU m

Fz W

g qW m

FxT U

=

=

+=

+=

=

=

++=

+

=

&

&

&

&

&

&

( )( )

( )

=

+=

=

=

=

=

U

W

W U V

where

1tan

22

2V2

1q

q,,Mach,MCref dref SqM

,Mach,z

Cref

SqFz

Mach,xCref SqFx

2rad/sinraterotation bodyinchangetheis

2m/sinaxis bodyZin theonacceleratitheis

2Kg.minaxisyaboutinertiaof momenttheis

2m/singravityof onacceleratitheis

kg.inmassmissileis

rad/secinraterotation budyis

radianinattitudeis

q

W

yy I

g

m

q

where

&

&

2minarea reference theis

3Kg/mindensityair theis

Ninaxis bodyXin thethrusttheis

ref S

T

m/sinairspeedtheis

Pain pressuredynamictheis

axis body

Ythealongmomentcaerodynamitheis

Ninaxis

bodyZin the forcecaerodynamitheis

Ninaxis

bodyXin theforcecaerodynamitheis

radiansinanglefintheis

minlengthreferencetheis

axisYabout the

momentcaerodynamiof tcoefficientheis

axisZhet

inforcecaerodynamiof tcoefficientheis

axisXhet

inforcecaerodynamiof tcoefficientheis

V

q

M

Z F

X F

ref d

M C

Z C

X C

m/sinaxisearthZin thevelocitytheis

m/sinaxisearthXin thevelocitytheis m/sinaxis bodyZin thevelocitytheis

m/sinaxis bodyXin thevelocitytheis

radiansinincidencetheis

eW

eU W

U

minaxisearth

Xin themissiletheof positionXtheis me X


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minaxisearth

Zin themissiletheof positionZtheis me Z

We will define also two terms as shown in Fig. 2,which are

sec/

arg :

arg :

rad inite)(Line of S

LOS et to t missiletheof changeof rate

rad inangleite)(Line of S LOS et to t missile

&

These two terms are used in the first controller

design which is based on the proportional navigationmethod.

Fig. 2 : LOS angle from missile to target

3 FUZZY CONTROLLER DESIGN

This section presents a design of an integrated

fuzzy guidance system using two different types of homing guidance. In the two methods the fuzzy rulestable is determined by the tabu learning of the fuzzyrules.

3.1 Using proportional navigation method:

In proportional navigation method the fuzzycontroller will get the LOS angle from missile to

target ( ) and the rate of change of this angle ( &

)

as two inputs, and will produce the elevator angle (fin deflection angle) as an output.

From the missile dynamics, the fin deflection

angle will change the acceleration normal to themissile body and the moment about the missile Yaxis, which will change the position of the missile inspace [2].

First let us consider the membership function of the two inputs [5] and the output as shown in Fig. 4.Second, the fuzzy rules of the controller are learnedusing Tabu Search.

The value of the maxima and the minima of theuniverse of discourse for each input and output areobtained from the maximum and the minimum of the

coordinate of the space of the missile motion, and thevalue of maximum and minimum of the output is thesafe limit of the elevation angle which the missilecan have.

3.2 Using Pure pursuit method:

In pure pursuit method the controller will get thetwo velocity components with respect to the earthcoordinate Ue, We as its two inputs and will produce

the elevation angle (fin deflection angle) as anoutput.

The reaction of the elevation angle on the missileacceleration is the same as before. First consider themembership function of the two inputs and theoutput as shown in Fig. 5 [6] [7]. Second, the fuzzyrules of the controller are learned using Tabu Search.

The value of the maxima and the minima of theuniverse of discourse for each input and output arenormalized to the initial velocity of the missile atlaunching time, and the value of maximum and

minimum of the output is the safe limit of theelevation angle which the missile can have.

4 LEARNING FUZZY RULES USING TABUSEARCH

Tabu Search is one of the algorithms that can beused in the optimization problems Fig. 3. In thissection we will use the Tabu Search to learn thefuzzy rules of the missile guidance controller byconsider it as an optimization problem [8].

In the two methods used the relation between theinput variables and the output variable are not

obvious then the incremental learning algorithm based on Tabu Search is used. The final missdistance between the missile and the target is theenergy function for this optimization problem. Thisenergy function is a function of the controller rulesonly and all the other dynamical variables areassumed to be constant during the optimization

process. The initial position can vary only in thestarting of every learning loop but constant in theoptimization process.

By applying the algorithm for the two previouscontrollers, the fuzzy rules shown in Table (1) (2)could be found

Fig. 2: Tabu Search Algorithm

X

-Ze


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Table 1: PN method controller fuzzy rule table

&

VS S MS M MB B

VS NM PB PB PB PB PB

S NS NP NM PM NP NP

MS Z NS Z PS NP NP

M PS PS PS NM NP NP

MB NM PB NB NP Z NM

B NS NS Z PM NP NP

Table 2: Pure Pursuit method controller fuzzyrule table

Fig. 4 : PN method inputs and outputmembership functions

Fig. 5: Pure Pursuit method inputs and outputmembership functions

5 NUMERICAL RESULTS

The controller is simulated [9] with numericalexample for the missile with the previous model andthe following numerical configurations:U0 = 900 m/s (The initial velocity component inthe direction of the missile body X axis)W0 = 0 m/s (The initial velocity component inthe direction of the missile body Z axis)q0 =0 rad/s (The initial angular velocity of themissile about the missile body Y axis) 0 = 0 rad (The initial missile attitude angle)

The value of Zme0 and the target position arechosen to get the best performance of everycontroller.

In this section the numerical results of thesimulation process will be seen for the two types of the controllers.

5.1 Using proportional navigation (PN) methodand learned by Incremental Learning basedon Tabu Search:

In this method the used value of the Zme0 for learning the controller isZme0 = -2000 m (The initial missile altitude)

eU eW

NB NS Z PS PB

NB PS PB PB PM Z

NS PM PB PS NM PB

Z NS PS PB PM NS

PS PB Z PM PB PM

PB PB Z PS Z PS

VS S MS M MB B

, The first input tothe controller

&

& VS S MS M MB B

& , The second

PB NS Z NB PS

-30 0 30 0

The output of thecontroller

NM PM

NS Z NB PS PB

-1 1U e the first input of the

controller

Ue

NS Z NB PS PB

-1 1W e the second input of the

controller

We

NS Z NB PS PB

-30 0 30 0

The output of thecontroller

NM


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And the target position is:Xt0 = 2000 mZt0 = 0The resultant miss distance in order = 6.1 m = -106

This means that the effective head of missile will be approximately perpendicular to the thin area of

target, which means that probability of missile to hitthe target is 100 %.Fig. 6 shows the trajectory of the missile for this

case.

5.2 Using Pure pursuit (PP) method andlearned by Incremental Learning based onTabu Search:

In this method the used value of the Zme0 for learning the controller isZme0 = -4000 m (The initial missile altitude)And the target position is:Xt0 = 4000 mZt0 = 0The resultant miss distance in order = 0.93 m = -870

This means that the effective head of missile will be approximately perpendicular to the thin area of target, which means that probability of missile to hitthe target is 100%.

The head of the launching position of the missilecan be changed in a range of 400 m, and themaximum value of miss distance will be in order of 6m.

Fig. 7 shows the trajectory of the missile in thiscase.

6 CONCLUSIONS

This 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 fuzzycontroller can be used for any complex system withacceptable error.

Two methods of guidance were used in this paper. In these two methods the relation between theinput variables and the controlled variable were notclear then the incremental learning algorithm basedon Tabu Search was used with the final miss distance

between the missile and the target as the energyfunction. This energy function is a function of thecontroller rules only and all the other variables wereassumed to be constant during the optimization

process. The initial position can vary only in thestarting of every learning loop but constant in theoptimization process. From the simulation results wecan see that the Tabu Search algorithm produced thesame rules even though the starting rules aredifferent, which means that the algorithm alwaysconverge to the global minimum from any startingrule.

7 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

Missile System Suitable for Analogue Computation,Australian Defense Scientific Service, WeaponResearch 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] Gerard Leng : Missile guidance algorithm designusing inverse kinematics and fuzzy logic, Fuzzy Setsand Systems, Science Direct, 79, 287-295,(1996).[6]. L. A. Zadeh, Fuzzy Set, Information and Control,vol. 8, pp. 338-353, (1965).[7] J. M. Mendel: Fuzzy Logic Systems for Engineering: A Tutorial, proc. IEEE, vol. 83, no. 3,

pp. 345-377, (1995).[8] Maurizio Denna: Giancarlo Mauri, Anna MariaZanaboni. Learning Fuzzy Rules with Tabu SearchAn Application to Control, Fuzzy Systems, IEEE,

pp.1063-6706, (1999).[9] "Fuzzy Logic Toolbox," Matlab, Mathworks Inc.

Fig. 6 : PN method Missile trajectory

Fig. 7 : PP method Missile trajectory

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Tabu Fuzzy Guidance_540