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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
lEEEEEEEEEEEEEEEEEEEEEE~lEIElEE/lEEEEEimElEE.EEEIll/IhEIEEIIIIIEEEEEE
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L10
11111 1.U
MICROCOPY RESOLUTION TEST CHART
NATIONAL BURLAO OF STANDARDS 1963 A
Z.
% 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..
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313
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_ _ _ _ _ __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
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UU
coo* ovi vi -ai o-d o-o 0-0 0
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I CcLLJZ X:6
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- . -CI
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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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