AD-A140 841 COMPUTER SIMULATED DEVELOPMENT OF A COMMAND TOLINE-OF-SIGHT MISSILE USING ON-OFF CONTROL(U) NAVALPOSTGRADUATE SCHOOL MONTEREY CA J Y YEUN DEC 83

UNCLASSIFIED F/G 9/2 NI

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MICROCOPY RESOLUTION TEST CHART

NATIONAL BURLAO OF STANDARDS 1963 A

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% 4 . . . . . . . . . . . . . . .

NAVAL POSTGRADUATE SCHOOLMonterey, California

DTIC* ELECT

A SETHESISD

COMPUTER SIMULATED DEVELOPMENTOF

A COIDAnD TO LINE-OF-SIGHT MISSILEUSING ON-OFF CONTROL

* by

C) Je Young, Yeuri

December 1983

ThssAvio:H A iu

Co-advisor: Alex Gerba, Jr.

Approved for public release; distribution unlirnitted

84 04 12 067

Uncl asifitedSECURITY CLASIICATION OF THIS PAGE Slillo Does Enatered)_______________-

PAGE READ INSTRUCTIONSREPORT DOCUMENTATION PAEBEFORE COMPLETING FORM

1. REPOuRuNUME IL OYT ACCESSION NO. 3. RECIPIENT#SCATALOG NUMBER

4. TITILC (mE Su~iltw) 5. TYPE oF REPORT & PERIOD COVERED

computer Simulated Development -Master's Thesisof a Command to Line-of-Sight Missile December 1983Using ON-OFF Control 6. PERFORMING ORG. REPORT NUMGER

7. AIJTHOR(s) S. CONTRACT OR GRANT NUMBER(a)

Je Young, Yeun

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASKAREA A *ORI( UNIT NUMUERS

Naval Postgraduate SchoolMonterey, CA 93943

11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

Naval Postgraduate School December 1983Monterey, CA 93943 13. NUMIIER OF PAGES

MON DN AN AMES ODRSSSI ileumi romCaaoIagOffce ~ 8214- ONIOI"4 AENC NAE A DDRSS(f dffeentflowConrolingOffce)15.SECURITY CLASS. (@1 Chae report)

*Naval Postgraduate School UnclassifiedMonterey, CA 93943 ______________

IS&. DECLASSIFICATION/ DOWNGRADINGSCHEDULE

16. 005 RI§UION STATEMENT (Of Ala Report)

* ~. Approved for public release; distribution unlimitted

17. DISTRIBUTION STATEKMEN1T (of th 00140 aeeuai atd fa Wio 20. It4foi.,m~ fromn Report)

to. SUPPLEMENTARY NOTES

1S. KEY WORDS (Cowthine an rveril e4 ait 806an ueol d idetify k black numnber)

Line-of-Sight Guidancer. ON-OFF Control

Two-Level RelaySaturating Linear Control

20. ASSYBACI (COSEMUSe art omi adsi It oceowy and idmeitty &pblock nlimbe)

An on-off control provides a minimum time response for missile control.For application in missile control systems, it is wasteful of controleffort (due to chatter) to use a ideal relay. Hence it is necessary tomodify the ideal relay into a saturating linear control. The result wasalmost the same to that of using the ideal relay.

D i'af 73 YO FINV5 SOSL Unclassified

S/N 10- L- 0 4- 6011 SECURITY CLASSIFICATION OF THIS PAGE (When Dot& Ea101s0OO

.... A *'4 -: 4. -P 4

Approved for public release; distribution unlimited.

Computer Simulated Developmentof a Command to Line-of-S.ight Missila

Using ON-OPP Control

"- by

Je Young, YeunLieutenant Colonel, Koraan Air ForcaB.S., Korean Ai. Force Academy, 1972

Submitted.in partial fulfillment of the

requirements for the degree of

* IASTER OF SCIENCE IN ELECTRICAL ENGNEERING

from the

NAVAL POSTGRADUATE SCHOOLDecember 1983

Author:

Aprvd : Thesis Advisor

" ^F o r

, _ _ _ . Second ReaderTfran-liuncedJJstliect ion_,

Chairman# Departe t of Electrtical EngneerIng•Distribution/ -1

Availability Codes

vailia/ Special f Science and Engneerina

2

.... D....."..... .... ........-......

N 1- I

ABSTRACT

An on-off control provides a 24inimum time respcnse for

missile control. For application in missile control systems,

it is wasteful of control effort (lue to chatter) to use a

ideal relay. Hence it is necessary to mod!ify the ideal

relay into a saturating linear control. The result was

almost the same to that of using the ilea! relay.

-- I3

7t,- . -" " " . . . . . . ".- -. " " ": "-. -.-. , - -* .** * ., ,.

TABLE OF CONTENTS

I. INTRODUCTION . . . . . . . . . . . . . . . . . . . 9

II. OVERVIEW OF LINE-OF-SIGHT GUIDANCE CONTROL . . . . 11

III. TYPICAL ENGAGEMENT SEQUENCE .. . . . . ... . . 15

IV. ON-OFF (BANG-BANG) CONTROL . . . . . . . . . . . . 19

V. BASIC COMMAND TO LINE-OF-SIGHT SIMULATION . . . . 25

A. SCENARIO . . . . . . . . . . . . . . . . . . . 25

B. PROGRAMMED GUIDANCE PHASE . . . . . . . . . . 27

C. ON-OFF, THRUST VECTOR, MISSILE CONTROL .... 28

D. SIMULATION RESULTS . . . . . . . . . . . . . . 28

VI. PSEUDO-LOS COMMAND SIMULATION . . . . . . . . . . 38

VII. SIMULATIONS WITH TWO-LZVEL RELAY AND

SATURATION CONTROL. ... ......... .. 44

A. TWO-LEVEL RELAY . . . . . . . . . . . . . . . 44

B. SATURATING LINEAR CONTROL .......... 46

VIII. CONCLUSION . .... . ..... . .... . ... 59

APPENDIX A: VARIABLES LIST . . . . . . . . . . . . . . . 61

APPENDIX B: PROGRAS OF THE SWICHIN3 FUNCTION ...... 62

APPENDIX C: PROGRAM OF THE BASIC CO3MMAND TO LOS .. . . 63

APPENDIX D: PROGRAM OF THE MANEUVERING TARGET ..... 65

APPENDIX E: PROGRAM OF THE COMMAND TO PSEUDO-LOS .... 67

APPENDIX F: PROGRAM OF THE BASIC C3MMAND TO LOS WITH

TWO-LEVEL RELAY . . . . . . . . . . .. . . 69

% .

APPEN DIX G: PROGRAM OF THE MANEUVERING TARGET WITH

TWO-LEVEL RELAY . . . . . . . . . . . . . . 71

APPENDIX H: PROGRAM OF THE COMMAND TO PSEUDO-LOS

WITH TWO-LEVEL RELAY ............ 73

*APPENDIX I: PROGRAM OF THE BASIC COMMAND TO LOS i IT H

SATURATICN CONTROL . . . . . . . . . . . . . 75

APPENDIX J: PROGRAM OF THE MANEUVERING TARGET WITH

SATURATION CONTROL . . . . . . . . . . . . . 77

APPENDIX K: PROGRAM OF THE COMMAND TO PSEUDO-LOS

WITH SATURATION CONTROL . . . . . . . . . . 79

LIST OFREFERENCES .. .. .. . .. .. .. .. .... 8

INITIAL DISTRIBUTION LIST . . . . . . . . . . . . . . . . 82

-I

beL

LIST 0F TABLES

I. The Basic LOS Command Simulation Result . . ... 37

II. The Pseudo LOS Command Simulation Result . . .. 39

III. Two-Level Relay Control Result . . . . . . . . . . 45

IV. Saturating Linear Control Result (K=1) ...... 49

V. Comparison of the Basic LOS Command Results . . . 59

VI. Comparison of the Mianeuvering Target Results . . . 60

*-VII. Comparison of the Pseudo-LOS Comumand Results . . . 60

6

S..

,S.... .--.--.. .-..... ...

LIST OF FIGURES.-5

2.1 Missile rarget Encounter with LOS Guidance . . . 12

2.2 Basic Geometry ................. 13

2.3 Simplified Guidance Loop of L3S Guidance .... 13

3.1 Roland missile System Operational Schematic . . 18

4.1 Parabolic Switching Function . . . . . . . . . . 21

4.2 Blcck Diagram of ON-OFF Coatroller . . . . . . . 21

4.3 CRE versus Time . . . . . . . . . . . . . . . . 22

4.4 ChE versus Time . . . . . . . . . . . . . . . . 22

4.5 F versus Time . . . . . . . . . . . . . . . . . 23

4.6 CiE versus CRE . . . . . . . . . . . . . . . . . 234.7 U versus Time .. ..... . . .. .. . ... 24

5.1 Simplified Flow Chart of Basic LOS Command . . . 26

5.2 Geometry of Basic LOS Guidance . . . . . . . . . 27

5.3 Block Diagram of the Basic LOS Command ..... 28

5.4 The Basic LOS Command . . . . . . . . . . . . . 29

5.5 The Basic LOS Command ........ ..... 31

5.6 Tha Basic LOS Command . . . . . . . . . . . . . 32

5.7 The Basic LOS Command . . . . . . . . . . . . . 33

5.8 The Maneuvering rarqet . . . . . . . . . . . . . 34

5.9 The Maneuvering rarget . . . . . . . . . . ... 35

5.10 The Maneuveripg Target . . . . . . . . . . . . . 36

5.11 U versus Time for a Maneuvering Target ..... 37

6.1 Block Diagram of the Pseudo LOS CommandS s'tem . . . . . . . .. . .38

6.2 The Pseudo-LOS Command . . . . . . . . . . . . . 40

6.3 The Pseudo-LOS Command . . . . . . . . . . . . .

6.4 The Pseudo-LOS Command . . . . . . . . . . . . . 426.5 U versus Time for the Pseu3o-LOS Command .... 43

7

-*.S.: .

7.1 Tvo-LeVg3 Relay ....... .. .. .45

7.2 uI versus Time for the BaSiZ LOS Guidance . . . . 46

7.3 U verse Time against the MV'R target wt

Two-Level Relay . . . . . . . . . . . . . . . . 47

7.4j U verse rime of the Pseudo-LOS with

Two-Level Relay 4 . 7

7.5 Linear Switching Relay . . . . . . . . . . . . . 48

7.6 The Basic LOS Command (Sataration) . . . . . . . 50

-. 7.7 The Basic LOS Command (Satliration) . . . . . . . 51

7.8 The Basic LOS Command (Satarration) . . . . . . . 52

7.9 Maneuvering Target (Saturation) . . . .. 53

'C7.10 Maneuvering Target (Saturation) . . . . . . . . 54

7.11 Maneuvering Target (Saturation) . . . . . . . 55

7.12 Pseudo-LOS Command (Saturation) . . . . . . . 56

7.13 Pseudo-LOS Command (saturation) . . . . . . . . 57

7.141 Pseudo-LOS Command (Saturation) . . . . . . . . 58

C.8

L 0

Guided missiles are classified into four broad catego-* ries, depending on launch and target position characteris-

tics. These categories are (1) . air -to - air (2). air -to - ground (3). surface - to - air and (4). surface -to -

surface. Each category of the above will employ one or more" of the following guidance schemes; programmed command,

line-of-sight, lead-angle, proportional navigation homingand inertial. The beam rider guidance is included in theline-of-sight guidance. A number of missiles also use acombination of these methods. For example, the initial partof the missile trajectory may use programmed guidance while

the terminal phase may use beam-ril.r.This thesis discusses the surface-to-air missile

controlled by on-off, thrust vector, control. Considerationwas given to determine the effects of the two-level relayand the saturation linear ccntrol. in order to verify theresults, it was tested by using the type of control forthree different types of missile-target scenarios:

(1) . LOS command against non-maneuvering target(2). LOS command against maneuvering target

(3) . Pseudo-LOS command against non-maneuvering target.

In chapter 2, a discussion of a line-of-sight guidancewas presented and a practical example oi it was shown inchapter 3. The general concept of on-off control wasdescribed in chapter 4. The simulation results of the basiccommand to line-of-sight against both a non-maneuvering anda maneuvering target were shown in chapters 5 and that ofpseudo-LOS case was in chapter 6. Finally, a discussion oftwo-level relay and saturating linear control was presentedin chapter 7. A table of variables which were used in this

9

,,- ...'., .'.. ** ,. . *..'.,' '.. . . ... .+ * • *o ..... , . . . . . . . . . .

-7 77 -J .7 N. **A *

thesis is shown in the Appendix A. computer simulation das

accomplished using Digital Simulation Language, DSL.

-az

I. VERVIEW OP LINE-OF-SIGH UGiUDANCE CONTROL

A LOS system can be called a "3-point" guidance systemsince there is one point which defines the tracker, another

the target and a third which defines the position of -h s

missile. The object of the guidane system is to constrain

the missile to lie as nearly as possible on the line joining

the tracker and the target called the Line Of Sight (LOS).

The concept is simple and can be implemented in many ways;

perhaps it is this apparent simplicity which explains why

many of the guided weapon systems as yet designed are LOS

system.

Consider a target flying straight and at cons-.an: speed,

and a missile flying at a different angle but constant

speed, having been launched when the target occupies a posi-tion TO (see Figure 2.1).

After intervals of time of 1,2,3 -tc seconds the LOS is

shown as OT1,0T2,0T3 etc. Since the missile ideally always

lies on these lines the flight path will be a curved one,

for an approaching target, the curvature becomes increas-

ingly severe towards the end of the engagement. We note that

the tangent to the flight path at any one point defines the

instantaneous direction of the missile velocity. It is seen

that the missile velocity vector will, in general, not be

directed along the LOS; towards the end of the engagement it

may be at a considerable angle to it [Ref. 1].

In an actual situation the guidance signals transmitted

to the missile are the demanded lateral accelerations

(LkTAX) in two axes at the right angles to the beam. These

demands are resolved into missile axes within the missile.

An error compensation term endeavouring to keep the error

off the beam (6't| equal to zero.

11

'4 • •

. °" ° - . . , , . •*°- . .... *

M5T5 4, _T3 T2 _Ti TO

/5 .1 - 1-

400 .-/ 4 10- 0 .1e

I / ~ , -0/ lo -/ / ' - -,

/0 / 00

J,

// x

launcher

Figure 2. 1 Bissile Target Encounter with LOS Guida

A basic geometry and a si-mplifiad guidance loc

shown in Figure 2.2 and Figure 2.3.

Suppose that the cross range arror (GRE) of Figi

can. be measured either directly or by means of the a

difference between OT and 011, together wi.*th some knc

of missile range (Rm), then

CRE M R( dt - dM) (2.1)

if this error off the beam is used as in acceleration

U, it needs some damping so that good response chara(

tics are obtained. A dynamic equation of the form

*CRE =G1 (CRE) + G2 (CRE) (2.2)

needs to be satisfied, where G1 and G2 aze constants.necessity leads immediately to the consideration

filterei error. In the presence of noise on the sigh,

12

dt

4 Reference

Figure 2.2 Basic Geometry

F(S

A 13)-aw

% V ' -.*.. -..- ** '. .. ~ * .***-

*~CR I

Fiur 2.3 Sipife Guianc Loo of LO Guidance ..-- ~-

° * -' S - - - %

and hence on the crcss range error, CRE, such a filter

design is not simple and becomes a compromise between

requirements for smoothing the nois_ and giving an adequate

response to a demand. Modern techniques allow filters to be

designed statistically if some knowledge of the noise char-

acteristics is available or can be assumed. Figure 2.3 shows

the position of such a filter F(s) in the guidance loop. It

includes a gain G, and the acceleration demand is

U F(s) Rm ( 6t- ) (2.3)

The missile transfer function is represented by A(s) and

when the achieved acceleration is doubly integrated and

divided by Rm it represents a new measure of The missile

beam angle (6m) thus closing the loop when differenced with

the target beam angle (dt).While this concept is simply a LOS or beam ridina

guidance situation it is by no means is clear in homing howa guidance law can be devised in the absence of information

on missile and target positions (Ref. 2].

14

L94<:?

;.;'2.;"-* **~ * *

In order to provide a "vehicle" through which to better

understand the basic aspects of command to line-of-sightguidance methodology, the engagement sequence of a short-

range, air-defense, missile system is lascribed. The Roland

system was selected because the general operational aspects* of the system are available at the unclassified level

[Ref. 4].

The entry of one or more aerial targets into the range

of the search radar is indicated to the Roland vehicle

commander by an audible tone. At the same time, a syntheticdisplay of the targets appears oa a screen to give thecommmander all the information needed to select the most

threatening target. The screen images are different for

friendly and enemy targets. Also, the entry of the targetinto the missile envelope, utilizing target advanced-range

computations, is indicated by a change in the display. with

the search antenna raised and the search radar activated,target acquisition is possible even when the vehicle is in

motion.

There are three modes of identification, friend or foe(IFF) interrogation: automatic, manual, and automatic

within a given range.when the commander has recognized a target as hostile

and decided to engage it, he places a cursor over the screen

image. This automatically brings the turret to bear andtracking can commence in either the "radar" or "optical"

modes.In the "radar" mode, the tracking radar automatically

accepts target designation from the search radar, searchesfor, locks onto, and tracks the target.

15

,.

In the "optical" mode, the aimer searches for the targetin elevation with an optical sight. To aid him an electronic

instrument displays the maximum theoretical elevation forthe search. Then the aimer has acquired the target in his

S- cross-hairs, he keeps the target in his sight by manipu-

lating a control stick. This contr31 keeps the target prop-erly positioned by moving the turret in azimuth andswivelling a mirror in elevation.

As soon as the commander confirms that the target is

within missile range, he initiates the firing sequence in

the "radar" mode, or authorizes "optical" mode firing

through a command displayed in the aimer's sight. The aimer,

then, can initiate the firing sequence.

The missile is guided by a command to line-of-sight

technique. This means that the target is tracked optically- or by radar and the deviaticn of the missile from this line

of sight 4s determined and corrected by a guidance command.

The commander may switch from "radar" to "optical" and back

again, as desired, even after the missile has been launched.

Target tracking and determination of the missile's devi-

ation from the line of sight are different for each mode. Inthe "radar" mode, the guidance radar has two receiving

channels. One is used for target tracking and the other isused to locate the missile in the radar lobe through recep-

tion of the missile's radio frequency beacons. By comparingthese angles, an error between the missile and the target

line of sight can be determined. In the "optical" mode, abiaxially-stabilized mirror is maaaally controlled to keep

the target vertically in the aimer's sight and the turret is

rotated to the azimuth of the target line of sight. An

infrared goniometer is mounted to provide misile angle from

the tracker by following flares moanted on the rear of themissile. Then, a deviaticn of the missile angle from the

target line of sight can be determined.

V 16

° ._

?' "" o ° o "" " o ". ' ° °oo *" - . '. ' ' * .*°. ° . 5 . . % . - ° . % - •%

Two groups of signals are introduced into the command

computer: the velocity of the line of sight ir. azimuth and

elevation, and the deviation of the missile from the line of

sight in azimuth and elevation. Based upon data from ths

li.e-of-sight movement and the angular deviations of the

-• missile, the Mecessary guidance signals are calculated.

The guidance signals are relayed to the missile by atransmitter with highly directional characteristics. The

command-transmitting antenna. is slaved to the missile angle

in both azimuth and elevation. It, therefore, is trained on

the missile continuously.

The side forces required for missile course corrections- are produced through deflection of the exhaust jet of the

sustainer motor by spoilers at the rear of the missile

(thrust-vector control).

When the missile reaches the point of impact with the

target, the warhead is detonated by either percussion,

contact fuse or the radio-frequency, proximity fuse. The

warhead consists of'a radial-effect, multiple-fragmentation

charge.

Figure 3.1 presents an operational schematic of thebasic Roland missile system operation.

The computer simulations contaiaed herein are generic innature within the command to line-of-sight guided-missiletype and have only reasonable estimates of missile capabil-

" ities introduced. This ensures unclassified results. At the

same time, the simulations are of sufficient complexity to

properly weigh the relative merits of the guidancevariations discussed [Ref. 3].

17

"4.

* From target & miss2).e To missile,

SEARC TRACK OPTICAL CMADRADAR RADA SIGHT RASITT

OTCL MISSILE GUIDANCE

PI A TAKTARGET & CONTROLPI Sco DEVIATION COMMANDS

DEVIATION C UE

COMMANtRFIN

FIRE *Clear weather

# mode only

MISSILE LAUNCH SEQUENCER.

- .Figure 3.1 Roland flissile Systea operational Schematic

I V. ON-OF (B.ANG- iAW Q2IZL

as discussed before, LOS guidance maintains a missile3

position on the LOS. Usually missile position has a cross

range error (CRE) and we want to reduce this error to zeroV in the minimum time. This kind of problem can be solved by

using the on-off control. The basic concept of this is that;

Given a system for which the drive is limited (has a

*maximum or saturation value) , the fastest response is

obtained if maximum forward drive is applied at t =0,

and is reversed at a proper instant t =ti so that

deceleration under maximum rever-se drive reduces the

velocity to zero at precisely the command value of -the

output. The drive is then set to zero.

The ideal relay permits only two conditions; full

acceleration and full deceleration [Ref. 5].From the Bang-Bang control law, we can derive the

switching function which makes the error go to zero by using

the proper switching time. Pr.om Newton's second law;

d FCE-----(CRE) *-- U

dtm

CRE CRE dt U ttk1

But at t 0 , cre 0 and k1 0.o Therefore

dCiii a- (CRE) *Ut (4.1)

dt

CREi CiE dt U Ut' k2 ('4.2)

19

From the equation 4. 1

t CiE/ U

'S. 2 (CE/ U), (4.3)

substitute equation 4.3 into equation 4.2

CRE - (U / 2) (CAE / U)1 + k2

= (Ch?9 / (2 U) + k 2 (4.4)

where k2 is iatagration constant. But if we apply a full

deceleration at the halfway point, the equation 4.4 becomes

F a (CUE ICREI) / (2 U) + CRE (4.5)

and is called the ERROR FUNCTION. U will be

U =t

or

U = -(G) SIGN(F (4.6)

Equations 4.5 and 14.6 represent tha SWITCHING FUNCTION which

makes the error go to zero in the minimum time. The

switching function and the block diagram of the on-off

controller are depicted on the Figures 4.1 and 4.2. And we*

can obtain the cross range error, CRE, by doubly integrating

K. U with the initial condition of CRE. we have

ChE - U dt + CiE(O)

CUE - dRE dt + C E(0) (4.7)

The simulation results of these equations are given on

Figures 4.3 through 4.7 and the computer program is attached

(see Appendix B).NOV

Lm.

u -G

u +G

) ApplicationoofofPNegative Control

Boundary F 0

Figure 4.1 Parabolic Switching Func.io

J-.,CRE_ Error F U=L M C E CI

Figure 4.2 Block Diagram of ON-OFF Controller

21

I %

* .. *.-*r ... .C R CR VS TIME

TI

CECRED VS. TIMECRE SWITCHING FUNCTION

*TIM

Fiur I. i eSSTm

* I22

F vs. TIMEF SWITCHING FUNCTION

UTIM

Fiur 4.1 essTm

I U ITIME CRDVS

Figure 46 c versus Time

I 23

4 1

U VS. TIMEU SWITCHING FUNCTION

3TIM

w 1rw L. '

Fiur 4.7 a______Tim

V. BA..IC COBNAND TO LINE-OF-SIGHT SIMULATION

A. SCENARIO

The engagement was designed with the ground tracker and

missile launching unit located at tae origin.

The target was flown accross the first quadrant from a

position 4000 meters on the x-axis and 1000 meters on the

y-axis (4000,1000). The velocity vector of the target was

parallel to the x-axis and magnitude was 250 meters per

second.

Since most missiles need a few seconds of boost, the

missile is not contrclled luring this time. We assumed that

the missile was controlled after one second from the firing

time and controlled by PROGRAMMED GUIDANCE up to this time.

After the time of missile "captare", the missile was

controlled by the on-cff, TVC method with the LOS guidance

law. The simplified flow chart is shown in the Figure 5.1.-. . In order to simplify the problem, we assumed that:

1) the velocity vector of missile , Vm, was parallel to

the LOS between the target and origin and the magni-

tude of Vm was constant, 50) meters per second;

2) the LATAX was applied to the missile at right anglesto the LOS. This was a reasonable assump-on for

this kind of missile. So the angle in the• Figure 2.2 is almost same to angle 6t

"- 3) the measurement noise was zero so we omitted the

filter, F(s) ;4) the magnitude of LATAX was 150 meters/second1 which

was about 15 Gs.

' The geometry depicted in Figure 5.2 summarizes the geometric

.'. situation.

25O: ~ ** -.- *-.

. * .

.

ON OFFPROGRAMMED

CONTROL GLUIDANC

IN IsIe

Figure S. I Simplified Flow Chart of Basic LOS Coss

26

4 Y , *

Target

UIIMIisi

CRE LO

Tracker 0

Figure 5.2 Geometry of Basic LOS Guidance

For matlimatical convenience of si~ulation, we need to

define the sign of the CRE and the LATAX as follow;*jCE : Whea the missile position is upper-side of LOS

-ICREI : when the missile position is lower-side of LOS

+ JUI : when the LA1'AX is upward direction

-JUI : when the LATAX is dowaward direction

This sign was based on the positive ditwhich is defined

when 6Mis greater than

B. PUOGRANBD GUID&NCR PHISE

rsince the major emphasis of this paper was on-off

control, we assumed that the missile flew along the LOS

during the programmed guidance phasa. But, in a practical

situation, there is some cross range error which is occured

by disturbances such as wind, propulsion system and09.

27

w- %7. -k- a

autopilot time delay,etc. Hence we made initialIzation

errors, and the on-off control start-ad with these errors.

* C. ON-OFF. THRUST VECTOR, MISSILE ZONTROL

The detail of the on-off control was discussed before,

hence we applied this to the LOS guidance scheme. Tha block

diagram of this system is depicted in the Figure 5.3

(Ref. 3].

In order to determine the CRE, the tracker estimates the

missile's range (Rm) , by the elapsed time of flight and the

missile's velocity profile. The program of this simulation

is attached in kppendix C.

Position 1 tCnro

1dm RECRE

MislI CRE

TARGET TRACKER GeometryE

Figure.3 Block Diagram of the Basic LOS Command

0D. SINULATIOI RESULTS

Figure 5.14 shows the missile aad target geometry in X-Y

~ *dplane. The missile intercepted the target at the point

* A(2605#1000) with the almost zero miss distance.

7 28

bv r

Figure 5. 5(a) shows the distance between target and

missile versus time. The distance dacrgased linearly and

neared zero at the time at 5.58 seconds.

9 -CCOLNTE VS. X-COORDINATE

d Y

2K Do It.0 6 o Mc o W-

Fiur 5. hIai O omn

Fiur 5. (bghw h esu ie h nta

"missie c iure tie The Basicie LOS Commacrase

o initially. So the maximum CRE was about 58. 2 meters at the

*time 1.330 seconds. Then it decreased to almost zero meter

at 2.55 seconds. To get a faster response, we should

increase the magnitude of the LATMX We should note here

29

-° r' " " ' "~- "- " . - " - V - . "-'. -. -b r . - - - - ' -. -* - . -._ .. . . . * . . . *.. .

that the CRE does not maintain zero value because we dil not

consider the target motion terms in this phase of th- simu-

lation (Ref. 2]. So the missile hid some small cross range

error and the BANG-BANG controller had tried to reduce this

error in a chatter-mode.

Figure 5.6(a) shows the CRE versus time. Figure 5.6(b)

shows the CE versus CRE. As we expacted this curve followed

the SWITCHING FUNCTION as shown ia figure 4.4. Figures

5.7(a) and 5.7(b) show the F versus time and the U versus

time.

This program was tested using maneuvering targets and

the results were almost same except the impact position. The

results cf this simulation were shown on the Figures 5.8

through 5.11 and the program is attiched in Appendix D. The

comparison of these simulations is summarized in Table I.

a..

30a.

S..

'a :: " ,- ' -" .'' , L ' -% '- ' , ' .'' -' ''. '' .." • " ' ." ' ' -' " " . " • " " ' -.-,-

4E-4

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I2 CC )

313

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uj

_ _ _ _ _ __Km _ _ _ _4__ _

I U

ITIM

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1 'NURN ZHE AEVEIGTRE

.tm $itecet = .8sc56Ie*mYm TIME72979 1077I 29 .8).4

REU 334 5. -4a 1m g sa-msmditace _ _ __4_ 94()0489m

Fiue51 Uvru ie o raeveigTre

'I.37

* The guidance scheme cf the lead angle commard is almos-t

thea same as that of the basic LOS zommand. Instead of the

tracker-to-target line-of-sight this guildance scheme uses

the tracker-to-esti mated impact point and is called

"synthetic line-of-sight" (SLOS) , or "1pseudo line-of -sight".

The missile is controlled to fly along this 3seudo line-of-

sight. The block diagram of this system is easily modi;fisd

from that of the basic LOS and is shown in Figure 6. 1.

The estimated impact point at the instantious time is

calculated by using the "time to go" (,Tq) and the "lclos-ing

velocity" (Vc) between the target and the missile.

Compute 0&

andCeoetrolVelocty TRACKERn MISL E1RE

38

- ' T r

The "closing velocity" and "time to go" are calculated as

follow:

Vc = (Vtx-Vmx)I + (Vty-Vmy)

Tg = (distance between target and missila) / Vc

= (Xt-Xm)l + (Yt-Ym 2~ / VC

The missile goes to the impact point directly. The

simulation result is almost same as in the basic LOS case.

On other hand, this guidance scheme is poor in a ECM situ-

ation. In order to compare the results we used the same

data as that of the basic LOS command. These are shown in

Figures 6.2 through 6.5 and the summarized results are shown

in Table II. The computer program is attached it Appendix E.

I '-- : [ TABLE II1 IThe Pseudo LOS Command Simulation Result

.tima control) 1.0 secCREN(tI 49.912 (i)CREJ( 49.828 (m/sec)

.time(MAX.CRE) 1.33 sec. CRE(max) 58.184 (M)

I .time (intercept) 5.58 sac(Xm,Ym) (2604.7, 999.92)X-11, Yt) ~2605 0~ 1000.0

VE0.3517 (in)miss-distance 0.35137 (m)

39

.!%S~. ... . ** .

u -4

0 :4

V

'a

IE-4

WH

I.-Ij

U cJ

- I0

I..4

UU

coo* ovi vi -ai o-d o-o 0-0 0

.0C0

I 3

I CcLLJZ X:6

.0.0

LLI CO

CC 0.d

- . -CI

Io Goi 0U O" o-- g-aD.Q 01 0V

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=L--"

I U VS. TIMES PSUEDO -LOS COMMAND

U

TIMIo a.3

igr 6.IessTm o tePed-O omn

I I3

-7..

*VIZ. §jLA&TjQ!2 !LVI Z!21111L-j Jj~ jjL L4URTION CONTROL

The LOS guidance with an "ideal" relay has been

discussed. In this chapter, the effect of the different

types of lateral acceleration demand are discussed. In

order to compare the results with the previous simulations,

the same parameters were used.

A. TWO-LEVEL RELAY

The large magnitude of the LATAX makes a fast respcnse.

But in the case of small CRE, a smaller magnitude of LATAX

is needed. This idea was developed in a "two-level" relay as

shown on the Figures 7.1(a;b). The shaded area on Figure

7.2(b) shows the region of a lcwer level of LATAX in the

"CRE verse CRE" phase plain. It provided the minimum over-

correction. The computer programs were easily modified by

adding one statement,

IF ((ICREI+IREDI).LT. M) G = 3/(N 1/N2).We used the values 150 n/sec1 for NI and 15 m/sec1 for

N2 and 1.0 for H in the simulations of the basic LOS command

and the pseudo LOS ccmmand. The results were almost the same

as the previous, except in the figure for "U versus time".

Table III summarized these simulation results and Figures

* 7.2, 7.3 and 7.4 show the "U versus time" of each case. The

programs were attached in Appendix F, G and H.

5-.. 44

~ ~ v : **~ * V **~ *

N2

-M % _ I-N2 ICREI +ICREI -

UN N2* U. N

I (a). U versus JCREJ + c;j(b). C E versus CRE

4.Figure 7.1 Two-Level Relay

K - TABLE III

Two-Level Relay Control Result

MaTiectrl NON-IMVR 11iBzj2T ZIEUDO- 9.tiecnrl . 1.0 1.0CRE (0i) 49.910 %9.907 49.910CRED~(O) 49.832 L49.891 49.828

.time (MAX. CRE) 1.33 1.33 1.33CRE(max) 58.184 58.201 58.184.time(intercept) 5.58 5.61 5.58I. 2604.7 2597.9 2604.7

ya999.88 1057.7 999.92It 2605.0 2597.5 2605.0

*Yt 1000.0 1057.5 1000.0I CRE -2.63E-6 -3.63E-6 5.03E-8I miss-distance 0.3(489t4 3.47889 0.35137

Et45

* :4- -a

TI4igr 7. essTm o teBscLSGiac

_ _ _ SAUAIGLNA OTO

Inte peiu seto th tw -e ely w

isusd The g'a train iea.. cotrl, asa TI Ep di

teFigure 7.2 (a aersu 7.i(e for theo Bsti d LOS G sianced

area on the Figure 7.5(b) shows the region of linear control

in the "ChE versus CnE" phase plane. The computer programs

were easily modified by adding one statement,

IF (ABS (F) .LE.M) U = ~*F S .

The value of I'M" determines the linear region for F.

The Figures 7.6 through 7.8 show the simulation results of

the basic LOS command against the non-maneuvering target*case for I'M" equal 16 5 arid 10. when choosing the value I'M"

*equal to "one". the intercept time and miss distance are

almost the same as the counterpart of the ideal relay case.Hence the saturating linear control can be used in practice

4~6

ILI I

, I

I a

* I

ITIME

.j.Figure 7.3 U verse Tine against the 3IVR Target with,.;.. >Tvo-Level Relay

°***

m • Sl

4, . TIME

.0 .70 1.60 .30

Figure 7.3 9 verse Time of the Pseudo-LOS with

Two-Level Relay- 47

rr .4

I -- I. .. u.q, "£IqI , TL..L q,,aU L % L q f *.qL * , % ""*""'" -* " " """""•'" "*I " " " I

47 .. -. r

instead of the ideal relay by choosing a proper value of

"I'". The summarized results are in the Table IV.

Figures 7.9 through 7.11 show the rasults of the maneuvering

'Itarget case and Figures 7.12 through 1.14 show ths results-~of the pseudo-LOS case. These programs are given in

Appendix I, J and K.

U CRE

(a) U verse F ()CRE vreCRE Lna vthn ea

Fiur 7..LnarSithigRea

* .~.48

I TABLE IVsaturating Linear Control Result (5=1)

H"NON-MVR tIVR-TGT P ODCLS II time fccntrol) 1.0 1.0 1.0CRE(01 49.910 49.907 991I

CBED0 49.832 4I9.891 49.828I

I time(MAX. CRE) 1.33 1.33 1.33RE (max) 58. 184 58.201 58.184

I time (intercept) 5.58 5.61 5.58I Xii 2604.7 2598.0 2604.7I

Ym999.84 1057.6 999.88

Xt 2605.0 2597.5 2605.0*Yt 1000.0 1057.5 1000.0

CE -. 0349 -. 3702 -. 0349mss-distanca 0.3507 3.4841 0.3492

49

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The comparision of results for the ideal relay, two-

level relay and saturating linear control against the basic

LOS command and pseudo-LOS command igainat a nor.-maneuver ing

target and maneuvering target are provided in the Tables V,VI and VII. These simulation results clearly demonstrate

* - that "on-off" control of a missile is highly desireable and

that "saturating linear control", of a missile has littls

adverse effects compared to an "ideal relay" control.

I TABLE V(Comparison of the Basic LOS Command Results

I UNIT IDEAL rWO-LEVEL SATURATION II --- RELAY RELAY CONTROL Ii time 1control) 1.0 1.0 1.0CRE (0) 49.910 49.910 49.910CRED(O) '49.832 49.832 49.832I ime(MAX.CRE) 1.33 1.33 1.33dR (max) 58. 184 58.184 58.184.time(intercept) 5.58 5.58 5.58

VI Xm 2604.7 2604.7 2604.7YM 999.88 999.88 999.88II CRE 4.33E-5 4.33E-5 4.33E-5miss-distance 0.34894 3.34894 0.34894

59

.

. ~ ~ ~ ~ ~ ~ AL C V1~-r.- *

Icomparison of the maneuvering Target ResultsI UNIT IDEAL rW0-LVEL SATURATION

I --- RELAY RELAY CONTROL I

.time (ccntrol) 1.0 1.0 1.0S CR E (1 49.907 49.907 49.907

CRED(O) 49.891 49.891 49.891I

.time(MAX.CRE) 1.33 1.33 1.33CRE(max) 58.201 58.201 58.201

I time (interc ep t) 5.6 1 5.61 5.61X. 2597.5 2597.5 2597.5Ym 1057.5 1057.5 1057.5

I CR E -6. 4E-6 3 .63E-6 -0.0702I miss-distance 0.07889 3.47889 0.4841

Comarionof hePseudo-LOS command Results

I UNIT IDEAL rWO-LEVEL SATURATIONRELAY RELAY CONTROL

I time ccntrol) 1.0 1.0 1.0II CR EAl49.912 49.910 49.912I CRE b 49.828 149.828 49.828

.time (MAX.CRE) 1.33 1.33 1.33CRE(max) 58.184 58.184 58.184

..time (intercept) 5.58 5.58 5.58XE 2604.7 2604.7 2604.7Yu 999.92 999.92 999.92CRE 2.96E-5 5.03E-8 2.96E-5miss-distance 0.35137 0.35137 0.35137I

60

.............................

&ZLENDIX 1VARIABLES LIST

DIAGRAM COMIPUTER NOUN DESZRIPTIONVARIABLES VARIABLES

CRE CRE cross-raage-arrorCiE CRED rate of zross-range-error change

F Perror fu~nction

G G magnitxda of lateral acceleration

U U missile's lateral acceleration

dt SIGT angle between the LOS to targetand X-axis

em. SIGH angle between the beam to missile

and X-axis

dint SIGHT angle difference between m and t

*Vc VC crossing velocity

tg TG time to got(control) TC3N beginniag time of on-off control

SLOS SLOS synthetic line-of-sight

XM IH X-coordiaiate of missile positionYin YM Y-coordiaate of missile position,

It XT 1-coordiiiate of target position

Yt YT Y-coordiaate of target positionV2 TM velocity of the missileVt VT velocity of the target

Vmx TH fi -coinpoaant Of missile's velocityTiny THY Y-component of missile's velocity

Vtx VTX 1-componant of target's velocity

Tty VTY Y-componant of target's velocity

61dp-

PROGRAM OF TiDL HE SUICHING FUNCTION

TITLE BANG-BANG CONTROLTITLE SWITCHING FUNCTIONTITLE * YEUN, J.Y*INTGER NPLOrCONST NPLO?1lINITIAL

CRE = 1.0CRED = 0.&CRED = 0.

DERIVATIVE

NO SORT

G = 1.0F = C"R +CRED*ACRED)/(2*G)U= -E SIG I

CRED = INTGR100CRE = INTGEL (CR ~CRED)ACRED = ABS ICRED)

SAMPLE IF(CRE.LE. 0.0) CALL ENDJOBCALL DRWG11: lTIME CR!)CAL DRUG (21 .CRE RDCALL DRUG 3~,1 TI~ECRDCALL DRWG 4, 1: TIME gUR)

CALL ENDRW (NPLOT)CONTRL FINTI 2. 1 DELT=O.01,DELSO0.31PRINT 0. 1 .G, F:U:CRECREDENDSTOP

62

* . .. ~ - . - . . *

PROGRAM OF THE BASIC COMMAND TO LOS

TITLE BASI- COMMAND TO L.O.STITLE WITH IDEAL RELAYTITLE ***** YEUN, J.Y. **INTEG RKSFXINTGER NPLO,KILLCONST NPILOT=1,TCON-1.0CONST VM=500. ,VT= 250, P1=3.1 11593, KILL=OINITIAL

ITO = '4000.YTO = 1000.GANT =PI

P 0.

DERIVATIVE

NOSORT

**TARGET PARAMETERS**

VTX = VT*COS (GA?!?)VTY = VT*SIN (GAMT)XT = VTI*TIME + IToYT = VTY*TIME + YrOSIGT =ATAN2 (YT XT)IF (TIME.GE. TCON) GO TO 50

MISSLE PARAMETERS *

*PROGRAMMED GUIDANCE********************

SIGN =SIGT+0.1VIM =VM * COS (11VYM Vl * SIN (SI_ M)X11 INI!GRL0. VXM)YM INTGRL (0.,VMRM SQRT( (I**V+ yM**2)SIGN? = SIGN M-SIGJTCRE =RN * SIN(SIGMT)CRED =DERIV(0.,CRE)GO TO 200

*ON-.OFF GUIDANCE (BANG-BANG CONTROL) **********

50 CONTINUE

G = 15-0.ACRED - ABS (CRED)F = CRE + (CRED*KC RED)/(2*G;)U = -G * SIG N (1 F)6CRED INTGRL(. ,CRE sINTGRL(C E.oR~D

RN z VM*TIMEA3 = CRE lENSIGMT AR SIN(A3LSIGN z SIGT + SIGNMT

A 63

01

XII = H11 * COS (SIGN)YM=RM * SIN ISIG [)

200 CONTINUE

M* ISSION RESULT **KILL = 0 ;TGT MISSED* **************** KILL = 1 ;TGT DESTROYED

XDisr = KT-XM* * YDIST = IT-!?!

DIST = SQRT(XDISI!**2 + YDIST**2)IF (DIST .LE 5t KILL = 1IF (DIST .GT:5) KILL = 0IF (N .GT. (XT*30))CALL ENDJOB

SORT

*******OUTPUT AND PLOT -ONTP.OL CARD **********

SAM5PLECALL DRWG 1, Xm,YMlCALL DRWG 1,2:XTYT)CALL DRWG 2,1eTIIIEDIST)CALL DRWG 3 ,1, TIME CRE)CALL DRWG 4 1,TIME CRED)CALL DRWG15,,1 CRE 6cRED)CALL DRWG 6 1 1TIM , EF)

TERMNALCALL DRWG 7 9 1,TIMEU)

CALL ENDRW (NPLOT)* * CONTRL FINTIM=6 0D DLT0.rJ0l DELS=O 003

PRINT .005,Xi .,IXT,YTCRE,CRE-D,5ISTKILLENDSTO P

6L4

PROGRAM OF THE MANEUVERING TARGET

TITLE BASI: COMMAND TO LOSTI T LE WITH MANEUVERING TGTTITLE *** YEUN, 3.Y. *INTEG RKSFXINTGER NPLOT,KILLCONST NPLOT1, TCON=1.0CONST VM=50 .,VT=250,PI=3.141593,KILL=OINITIAL

XTO = 4000.YTO = 1000.GAMT = PI

* F =0.

NOSORT

**TARGET PARAMETERS**

VTX = VT*COS (GAMfl)VTY VT*SIN (GAMT)XT = VTI*TM + XTYT = 100*SIN (0.5*P'I*TI'IE) +fTOSIGT =ATAN2 YT XTIF (T!IME.GE. TCO~ GO TO 50

MISSLE PARAMETERS *

*PROGRAMMED 3UIDANCE *******************

SIGM SIGT+0.1VIM =Vl * COS (SIGHVIM =V11 * SIN (SIGM)xII INTGRL (0.,VXm)YM =INTGRL(0VM

RM= S QRT (XI + tM**2)

CRE = M * SIN(SIGMT)CRED *DERIV(0..CRE)GO TO 200

ONOFGIAC*BANG-BANG CONTRE)L) **********

*50 CONTINUEG = 150.ACRED mABS CRED)CRD/ 23* ~~F = CRE + MRD*ARD/2)CRED xINTG RL~..CRE= INTGRL (CRE.CRED)ACRE =ABS (C RE)

RH * VtI*TIMEA3 =CRE,/RM

* SIGHT k RSIN(A3)SIGM SIGT + SIGHT

65

SM -M * COS (SIGN)YM f RN * SIN (SISN)-ii *************************** *************

200 CONTINUE

*** MISSION RESULT *** KILL = 0 ; TGT MISSEDS********************* KILL = 1 ; TGT DESTROYED

XDIST = XT-XMYDIST = YT-YMDIST =SQRT(XDITS?**2 + YDIST**2)IF (DIST .LE.5) KILL = 1IF (DIST .GI.5) KILL = 0IF (XH .GT. (ZT+30))CALL ENDJOB

SORT

S******* OUTPUT AND PLOT CONTROL CARD *********** ****

SAMPLECALL DRWG 1,1,XM,YM)CALL DRWG 1, XTYT)

' " CALL DRWG 2,TIME,DIST)CALL DRWa 3,1 TIMECRECALL DRWG 4,1TIM E,CRED)CALL DR WG 15 ,1,CRE, CRED)CALL DRWG 6,1 TIME F)

TER II NA LCALL DRWG 7,1.TIMEU

CONTRL CALL ENDRW(NPLOT) 0 1DCONTRL FINTIM5. 9. D ELT=. DELS=0.003PRINT 0.005,Xf M,XT, YT,CR ,CRED,DISr,KILLEND

-ST3P

66

.. ?..:-

* **.*. ... .. * . - * . . . .g

PROGRAM OF THE COMMAND TO PSEUDO-LOS

TITLE PSEUDO -LOS COMMANDTITLE WITH IDEAL RELAYTITLE *** YEUNE J.Y. *INTEG RKSFXINTGER NPLOT,KILLCONST NPLOT=1,]TCON=1.0CON1ST VM=500. .VT=250,PI=3. 141593, KILL=0INITIAL

XTO = 4000.YTO = 1000.TG =0.f =0.GAMT =PI

DERIVATIVE

NOSORT

* . *** TARGEOT PARAMETERS**

VTX = VT*COS (GANT)oVTY = VT*SIN (GAMT)XT = VTX*TI +E XTYT = VTY*TIME + YTOSIGT = ATAN2 2T XT)XLOS = XT + lTX*TGYLOS = YT + VTY*T3SLOS = ATAN2 (YLOS.XLOS)IF (TIME.GE. TCON) GO TO 50

HISSLE PARAMETERS

*PROGRAMMED GUIDANCE ************~******

SIGH =SLOS + 0.1VfHX= VM * COS (SIGH)VHY =VH * SIN (SIG)XM INTGRL (0. VHX)

=M INTGRL (0. 7MYRM SQRT (XH**; +. YM**2)

4SIGHS = SIGH - SLOSCRE = RH * SIN(SIgHS)CRED = DERIV(0.,CRE)GO TO 200

ONOF GUIDNCE-BANG CONTROL)*J

AN

* *50 CONTINUEG = 150.ACRED = ABSfCRED)CED,F = CED*AC(ERED* (2*G)

CR DI~rGRL REHD)

RH VM*TIME

A3 =CRE/RMSIGNS =ARSIN(A3)SIGNl SLOS + SIGNS

* VIX = Vil * COS(LOSVMY = VM * SIN(SL3S~

* -- XM = RM * COS(SIGMYM = RM * SIN(SIGM)

*200 CONTINUE

***MISSION RESULT ** KILL = 0 T TGT M13SE D***************** KILL = 1 ;TGT DESTROYED

XDIST = XT-XIYDIST = YT-YMDIST = S QRT(XDIST**2 + YDIST**2)VC = SUPT (VTX-VMX)**2+(VTY-VIY)**2)TG = DIST /VCIF (DIST .LE.5) KILL =1IF (DIST .GI.5) KILL =0IF IN~ .GT. (XT+30))h..ALL ENDJOB

SO RT

*******OUTPUT AND PLOT CONTROL CARD **~*****

* SAMPLECALL DRG 1,1,IM, YM)

*CALL DRUG 1, XT,YT)CALL DRUG 2,1.,TIMEDIST)CALL DRUG 3 ,1, TIME CRE)CALL DRUG 4J,1 TIL\1E CR ED)CALL DRUG 5,1,CR,-' 6RED)CALL DRWG 6 1 TIMh,F)CALL DRWG 7 :1: TIME ,U)

TERBMI NA&LCALL =ENDRU (NPLOT)

*CONTRL FINTIM 5.9 DE LT=0.00 1 DELS=0.003PRINT 0. 1,Ts.XMUYN,XT1 YT9 CRh,CRED,DIST,KILLENDSTOP

68

PROGEAN OF THE BASIC COMMAND TO L3S WITH TWO-LEVEL RELAY

TITLE BASIC COMMAND TO L.O.STITLE WITH TWO LEVEL RELAYTITLE ***YEUN, J.Y. **

- .INTEG RKSFXINTGER NPLOTIPKILLCONST NPLOT=l rCON=1.0CONST VM=500 . VT=250,?I= 3.141593, KILL=0INITIAL

XTO = 4000.YTO = 1000.GAMT =PIF =0.

DERIVATIVE

NOSORT

TARGET PARAMETERS**VTX = VT*COS (GAMT)VTY =VT*SIN (GAMT)XT = VTX*TIIE + XTOYT =VTY*TILME + YTOSIGT = ATAN2 (YT, XT)IF (TIME.G E.4CON) GO TO 50

** !ISSLE PARAMETERS**

*PROGRAMMED 3UIDANCE *******************

SIGN SIGT+0.1VXM =VN * COS (SIGN)VYN = VM * SI (IGN)XM INTGRL (.VI)YM INIGEL (0.:VYN)

* *RN =SQRT (X*2 + YM**2)SIGMT = SIG - SI GTCRE =RM * SIN (S13 MT)CRED =DERIV(O.,CRE)GO TO 200

ONOF GUDN*B ANG- BANG CONTROL)

50 CONTINUE

G =150.* ACRE = ABS(CRE)

ACRED = ABS (CRED)IF((ACRE+ACRED) .LT 1. - = 15F =CRE + (CRED*kCRE)/(2*31)U = -G * SIGN(110F)CRED =INTGRL (0.6,CRE =INTGRL(CRE, CRD

* RN VM*TIMEA3 =CRE/RM

69

- . . . . . . . . . . . .-- °..'.--. . --- -. J .. - - ° ° . - ° . . . .

SIGMT = ARSIN(A3)SIGH = SIGT + SIGMTXM = RM * COS (SINm)YM = RM * SIN(SIGH)

200 CONTINUE

"- *** MISSION RESULT *** KILL = 0 ; TG! MISSEDS********************* KILL = ; TGT DESTROYED

XDIST = XT-XMYDIST = YT-YMDIST = SQRT(XDIST**2 + YDIST**2)IF DIST .LE.5) KILL = 1IF (DIST .GT.5) KILL = 0IF (IM .GT. (XT+30))CALL ENDJOB

SORT•*************************** ********************** *****************OUTPUT AND PLOT CONTROL CARD***********

SAMPLECALL DRG11,X',HCALL DRWG 1,2,XT,YT)CALL DRUG 2,1,TIME,DIST)CALL DRWG 3,1,TIME,CRE)CALL DRWG 4, 1TIME CRED)CALL DRWG 5,1,CRE RED)CALL DRWG 6,1TIM ,F)CALL DRUG 7,1TIME,U)

TERM INALCALL vNDRW NPLOT)

CONTRL FINTIM=5. 9, D LT=O.001,DELS=. 003PRINT 0.005, XH, M,XT,YT, CRE,CRED, DIST, KILLENDSTOP

70

-. -. '

12YEN2II j

PROGRAM OF THE MANEUVERING TARGET WITH TWO-LEVEL RELAY

TITLE BASIC CONIAND TO LOSTITLE WITH MANEUVERING TGTTITLE *** YEUN. 3.1. *INTEG RKSFXINTGER NPLOT,KILLCONST NPLOT1,1rCON=1.0CONST VM=500.,VT=250,PI=3.141593,KI-.L=0INITIAL

XTO = 4000.ITO = 1000.GAMT = PIF =0.

DERIVATIVE

* NOSORT

**TARGET PARAMETERS**

VTX = VT*COS (GANT)VTY = VT*SIN (GANT)XT = VTX*TIME + XTO

* YT = 100*SIN (0.5*PI*T"IME).ITOSIGT = &TAN2 CYT XT)IF (TIME.GE. TCO&) GO TO 50

**MISSLE PARAMETERS***PROGRAMMED GUIDANCE *******************

SIGH = SIGT+0.1VXM = VH * Cos( (IG )VYK = VM * SIN (SIGH)

XX=INTGRL 0O*.,VIH)YM = INTGRL(O0 W1HRM z SQRT (XH** + YM*2)SIGHT = SIGH - SIGTCRE =RH * SIN(SI MT)CRED DERIV(0.,CHE)GO TO 200

ONOF GUDNC BANG-BANG CONTROL) **********

50 CONTINUE

G =150.ACRE m ABS (CRE)

* ~~~ACRED *AS(RDIF ((ACRE.ACRED) .LT. 1.) G =15.F = CR+ (CED*ACRED)/(2*G)U= -G *SIG 1. FD

CRED - INTGELO 06,CRE = INrGRL(CRE, CR6ACRE = ABS (CRE)

d*RM = MIE13 c CRE/RM

71

SIGH ARSIN(A3)SIGN SIGT + SIGNTXM = RH * COS (SIGN)Ym = RM * SIN (SIGH)

200 CONTI NUE2

* ~-. **MISSION RESULr * KILL = 0 ;TGT MISSED* ****************KILL = 1 ;TGT DESTROYED

XDIST z XT-XH*YDISr z TY

DIST,,; SQRT(XDIST**2 + YDIST**2)-IF I? (IT .LE.St KILL = 1

IF DI1ST .GT.5) KILL = 0IF (Xl .33T. (XT.30))CALL ENDJOB

SORT

*******OUTPUJT AND PLOT CONTROL CARD***********

SAMPLECALL DWG (1,1XMe7M)CALL DRUG 1, ~X TT)CALL D RUG (2., T MEDIST)CALL DRUG (3,1 TIME cRE)CALL DRUG (4,1,TIME CREDCALL DRUG {5,1 CRE iRED)CALL DRWG 6,1eTIM F)CALL DRUG 7,1.TIME:Ui

TERM INALCALL ENDRW (NPLOT)

CONTRL FINTI=5. 9,DE LT0. 001 DHLS=0 003PRINT 0. 005, XMYMXTYT, CR!heCREDIST, KILLEND

* STOP

7 72

PROGRAN OP THE CORNAND TO PSEUDO-L3S WITH TWO-LEVEL RELAY

TITLE PSEUDO - LOS COMMANDTITLE WITH TWO-LEVEL RELAYTITLE ***** YEUN, 3.1'. *$

II4TEG RKSFXINTGER NPLO?,vK ILLCONST NPLOT=1,TCON=1.OCONST VH=500.,VT=250,,P133.1L41593,KILL0OINITIAL

-~ XT0 = 4000O.YTO = 1000.TG = 0.GANT =PI

DERIVATIVE

NOSORT

**TARGET PARAMETERS *

VTX - VT*COS GA MT)VTY = VT*SIN (GANT)XT = VTX*TIME * + ToYT = VTY*TIME + YTOSIGT = AT!AN2 2YT,XT)XLOS = XT +VgX*TGYLOS = Y'! + VTY*TGSLOS = kTAN2 (YLOS,,XLOS)IF (?IME.GE. TCON) GO TO 53

MISSLE PARAMETERS**

*PROGRAMMED GUIDANCE *******************

SIGN SLOS + 0.1TM! 7 M * COS (IG

*VMY = M * SIN (SIGHXM INTGRL 0. 7 IYlM = INTGRL 0. VHYSIGNS -SIGNf - SLOSCRE *RH * SIN(SIGHS)

* CRED aDERIV(0.,CRE)GO TO 200

*ON-OFF GUIDANCE JBANG-BANG CONTRO)L)***********

*50 CONTINUE

G - 150.ACRB =ABS (CBEI)ACRED &BS (CREDIP((ACRE+ACREDI LT 1.) G a15.F a CRE +ICRED *CRiD)/(2*:;)U = -G *SIGN 1 F)CRED *INTGRL ~0 6U1.DCRE *INTGRL(CRE#CED

73

RM = VM*TIMEA3 = CRE/RMSIGNS = ARSIN(A3)SIGH - SLOS + SIGNSVMX c VM * COS(SLOS)VMY- VM * SIN (SLOS)XM = RM * COS (SIGN)YM = Rm * SIN (SIGH)

200 CONTINUE

* * MISSION RESULT *** KILL = 0 : TGT MISSED-***** ** ****** * KILL = 1 TGT DESTROYED

XDIST = XT-XHYDIST = YT-YHDIST = SQRT(XDIST**2 + YDrST**2)VC = S QRZ ((VTX-VHX)**2+(VTY-VMY)**2)TG = DIST/VCIF (DIST oLE.5) KILL = 1IF (DIST .GT.5) KILL = 0

$ SOT IF (KM .GT. (XT+30))CALL ENDJOB,"'- SORT

S***** OUTPUT AND PLOT CONTROL CARD ********************

SAMPLECALL DRWG 1,1,XMYH)CALL DRWG 1,2XTYTCALL DRWG 2,1,TIME, IST)CALL DRWG 3,1,TIMECRE)CALL DRWG 4,1TIME CREDf)CALL DRWG 5 1 CRE MD)CALL DRWG 6,1,TIME, F)CALL DRWG 7, , TIMIE :)TER HI NALCALL ENDRW(NPLOT)

CONTRL FINTI-5.7 DELT-O.bo1 DELS=0.003PRINT 0.1TGXHIY ,XTYTeCRE,CREDDIST,KILLENDSTOP

74

&?.PENDIX IPROGRAN OF THE BASIC COMMAND TO LOS WITH SATURArIoN CONTROL

*TITLE BASIZ COMMAND TO L.O.STITLE MISSLE CONTROLTITLE WITH SATURATION CONTROLINTEG RKSFXINTGER NPLOrKILL CUR

CONST NPL'OT!1l,TC6Nul.OC~CONST VM=500.,VT=250.PI=3.141593,KILL=0PARAM M = 10.INITIAL

XTO = 4000.ITO = 1000.

-- GANT =PIF =0.

DERIVATIVE

NOS OR T

**TARGET PARAMETERS**

VTX a VT*COS GANT)iVTY z VT*SIN (GAMT)XT = VTX*TIMN + XTYT = VTY*TIME + ITOSIGT = ATAN2 (YT XT)IF (rINE.GE. ICC I) GO TO 50

HISSLE PARAMETERS *

*PROGRAMMED GUIDANCE *******************

SIGH SIGT+0.1VXM VN * COS (SIGN)VIM =VN * SIN (SIGN)XM =INTGRL (0. VXN)IN INrGRL 0. VYH)RN SQRT(X*;+[*2SIGN]= SIA N - SIG?

*-CEE = RN * SIN(SIG N'T)CRED =DERIV(0.,CRE)

- GO TO 200

*ON-OFF GUIDANCE (BANG-BANG CONTROL) **********

50 CONTINUE

G = 150.* ACRED =ABSCRED)

U = -G* SIGN (1.,F)* IF (ABS(FJ .LT. M) U= -G*P/N

CR ED N INGERL(00CRE z INTGRL(CERED

RN = VN*TINEA3 z CRE/RNSIGHT = RSIN(A)

'.5-,75

SIGH SIGT + SIGHTXH = RM * COS SIGH)Yd = RH * SIN(SIGH)

200 CONTINUE

.-. ** MISSION RESULT * KILL = 0 ; TGT HISSED.'*."************** KILL = 1 ; TGT DESTROYED

XDIST = XT-XM"'- YDIST = YT-YMDIST = SQRT(XDIST**2 + YDIST**2)IF (DIST .LE.5) KILL = 1IF (DIST .GT.5) KILL = 0

SORT

-******* OUTPUT AND PLOT CONTROL CARD ********************

SAMPLECALL DRWG (1,C RXN Yb)CALL DRWG (2 ,CURTIAE, ST)CALL DRWG (3 ,CUR,TIME,CRE)CALL DRWG (,CURCRE CEED)CALL DRWG (5,CURTIMf, FCALL DRWG (6,CURTIlEU)

TERMINALIF (CUR .EQ. 3) CALL ENDRW(NPLOT)CUR = CUR + 1

CONTRL FINTIH=5.65,DELT=0.001.DELS=3.003PRINT 0. 005, XMYM, XTYT, CRE,CRED, DIST, KILLENDPARAM M = 5.ENDPARAM M = 1.ENDSTOP

76

- ~~~.. .. ... ...• . .. . .. . . . •o. .. .. "... % . . .. "•.-.. -.-- ,- %'--,, -. ,, . .",S * .= .' -. ' =" "" - ' '" a. i * ,"."- -*-' " " "."-" ", -*-". *. -" * "S -' ' '''. <: , ;" . . . ... .:''

PROGRAM OF THE MANEUVERING TARGET KITH SATURATION CONTROL

TI T LE BASIC COMMAND TO LOSTITLE (MANEUVEEING rGT)TITLE WIT HSATURATION CONTROL

-: INTEG RKSFX U

- -CONST NPL.OT1TC6N=1 0 CUR~1*CONST VH=z500.,VT=250;Pfa3.l&1593,KILL=3

PARAM M = 10.INITIAL T=40.

ITO = 1000.GAMT =PI

* P =0.

DERIVATIVE

NO SORT

**TARGET PARAMETERS**

VTX = VT*COS GAMT)VTY = VT*SIN(G AM?)XT = VTX*TIZIE + 1i 0YT = 100*SIN (0.5*ITIME) +ITOSIGT = ATAN21YT.IT)IF (riME.GE. .CON) GO ro 50

**MISSLE PARAMETERS**

*PROGRAMMED GUIDANCE *******************

SIGN SIGT+0.1

VYM =VM * SINI (SMHIXVM *CO SNGE ( XM)

* Y~M x INTGRL~O~Y1SIGH 1 IE 11IG

CREM = R1H -SISGTCRED =DERIV(0..CRE)GO TO 200

*ON-OFF GUIDANCE (BANG-BANG CONTR3L) **********

50 CONTINUE

G = 150.0 ACRED = ABS (CREDICR +CRED*CRED)/(2*G)

IF ABSF .LTH) U s-G*F/MCREDx INrGRL( RE, R~DACRE aABS (CRE)

RH = YM*TIMEA3 = CRE/RM

77

6~ 'e

SIGHT = ARSIN(A3)SIGH = SIGT + SIGHTXM = RH * COS (SIGH)YN = RM * SIN(SIGM)

200 CONTINUE

***MISSION RESULT ** KILL = 0 ; TG! MISSEDKILL = 1 ; TGT DESTROYED

XDIST = XT- XBYDIST = YT-YMDIST = SQRT(XDIST**2 + YDIST**2)IF (DIST .LE.5) KILL = 1IF (DIST .GT.5) KILL = 0

SORT

******** OUTPUT AND PLOT CONTROL CARD *******************

SAMPLECALL DRG (1CURXH,,YB)CALL DRWG 2,CURTIME,DIST)CALL DRWG 3,CURIME CRE)CALL DRWG 4,CURCRE,6RED)CALL DRUG 5,CURTImE, )

TCALL DRWG (6,CUR,TIHE: U)TERMINALIF (ZUR EQ.3) CALL ENDRW(NPLOT)CUR = CUR + 1

CONTRL FINTIM=5. 65 DELT=O.O01,DELS=0.003'"* PRINT 0.005,XHY&,KTYT,CRE,CRED,DIST,KILL

ENDPARAM M = 5.ENDPARAM M = 1.*ENDSTOP

10

'U,78

S .

- . . ' - U U . U - - 'U* . . .

PROGRAM OF THE COIM&D TO PSEUDO-LOS WITS SkTURArioN CONTROL

A TITLE PSEUDO - LOS COMMHANDTITLE WITH SATURATION CONTROLTITLE *** YEUN, J.Y. **INTEG RKSFI

INIGER NPLOT CILL C1

CON ST VM50O.,VT=2 0lP 3.141593,KILL=OPARAM IN = 10 .INITIAL

ITO =4000.YTO =1000.TG = 0.GAMT = PI

F=0.

NOSO0R T

**TARGET PARAMETERS *

VTX =VT*COS (GANT)VTY VT*SIN (GAMT)IT = VTX*TIHE + ITOY= VTY*TIME + YTO

SIGT = ATP.N2!(YTXr)XLOS = IT + VTX*TGYLOS = YT + VTY*TGSLOS = ATAN2 (YLOS,.XLOS)IF (TIME.G E.TCON) GO TO 53

M* ISSLE PARAMETERS *

P ROGRAMMNED GUIDANCE

SIGM SLOS + 0.1V V M * COSESIH

THSY TH * SIN; SIM~IM, INTGRLIO (0.TX)YM = INTG 1,L (0. TY)RM SQRT (I** + MH 2)SIGHS =SIGM - SLOSCRE aRM * SIN(SIGMS)CRED =DERIV(O.,CRE)GO To 200

ON-OFF GUIDANCE JBANG-BANG CONTROL) ****p*****

*50 CONTINUEG = 150.F CRE =+B(K..~ = ACE Z ASICED DCRED)/ (2*3)U =-G *1GN (1.FIF (ABS(FV .LT.f$U = -G *F /3CREDIN GL(0.tUCRE =INTGRL(CRECRD)

79

RN f VM*TI MEA3 = CRE RMSIGNS = ASIN(A3)SIGM = SLOS + SIGNSVMX = VM * COS(SLOS)VNY = VM * SIN(SLOS)XM = RM * COS (SIG)YM = RN * SIN (SIG

200 CONTINUE

* €MISSION RESULT * KILL = 0 ; TGT MISSED******* KILL = 1 ; TGT DESTROYED

XDISr = XT-XMYDIST = YT-YMDIST = S QRT(XDIS?**2 + YDIST**2)VC = SQRT(( 4TX-VMX) **2+(VTY-VMY)**2)TG = DIST / CIF (DIST LE.5) KILL = 1IF (DIST .GT.5) KILL = 0

SORT

*******OUTPUT AND PLOT CONTROL CARD***********

SAMPLECALL DRWG (1,CURXM,YN)CALL DRWG (2,CURTIME,DIST)CALL DRWG 3,CURIME, CRE)CALL DRWG 4,CUR, CR CRED)CALL DRWG 5,CURTIMI, FCALL DRWG 6CUR,TI ME, O}

TERMINALIF (CUR .EQ.3) CALL ENDRW(NPLOT)CUR = CUR 4 1

CONTRL FINTIM=5.65,DELT=O.001 ,DELS=0.003PRINT 0.0OC5,TG,XM, YM,XT,YTCRECRED, DIST,KILLENDPARAM M = 5.ENDPARAM M = 1.ENDSTOP

80

! I I I i i~iliIli fl Il m il i li.a,..,.. i , . . . .. , . ..80. "

LIST OF REFRENMCES

1. Garnell, P. and East, D.J. Guded 5W.,Aror Co-trolSystems, p. 134 - 153, Pergamnn Press, 1977I.

2. Heap* E., "Methodology of Research into*Command-to-L ine- of-Sight and Homing Guidance"f,

G uid anca aad Cont' ol of ractical Missile, AGARDLecture series No. 52, 1972.

*3. Hewitt, Frank F., LCDR, C uer Simu1ated eve' o ment

California, march 1979.

4. U.S. Army Foreign Science and Technology Center Re pcr-:FSTC- 120 2- 75, The Roland-i Prmi.-ed Seif-Pr~ellq1 AA

i leSvstm, by-Johannes add Weyand, p. 9 - 20U,I(.

5. Thaler, George J. and Pastel, Marvin P., Analysis and- - D g 2f Noaj1;;ag Feedback Zon-;rol systesP. 53

29Mcuraw-tHill,1 9b 2

INITIAL DtSTRIBUTIDN LIST

No. C

1. Defense t~echnical Information Ceater 2Cameron StationAlexandria, Virginia 22314

2. Library, Code 0142 2Naval ostgraduate S chool.

* -, Monterey, C alifcrnia 93943

3. Department Ch ai man, ,Code 62* 1Department of Elect rical EnginaeringNaval Postgraduate SchoolMonterey, Cal ifirnia 939L43

4. Division of Foreign Education 3Department of Personnal~ AdmnastrationHeadguaters of Korean Air ForczeDaebang-dong, Ycungdungpo-g uSeoul, Korea

5. Professor H. A. Titus, Code 62rs 5Department of Electrical Enginserin-igNaval Post graduate School

* - Monterey, California 93943

*6. Professor Alex Gerba, J;., CQde 6?GS 2Department of Electrical EngineeringNaval Postgqraduate SchoolMonterey, California 93943

7. Aipademi~c Dean 1Ai: Force AcademyDaebang-dong, Youngdun gpo-guSeoul, Korea

8. LTC. Je Young, Yeun8Jamsil 221-4, Gangdong-guSeoul, Korea

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