Calhoun: The NPS Institutional Archive
Theses and Dissertations Thesis Collection
1983 Computer simulated development of a command to line-of-sight missile using on-off control.
Yeun, Je Young. http://hdl.handle.net/10945/19694
NAVAL POSTGRADUATE SCHOOL
Monterey, California
THESIS
COMPUTER SIMULATED DEVELOPMENT Ur A COMMAND TO LINE-OF-SIGHT MISSILE USING ON-OFF CONTROL by Je Young, Yeun December 1983
Th asis Adv:Lsor: H. A. Titus
Co--adv Lsor : Alex Gerba, Jr.
Approved for public release; distribution un limit ted
T2 15720
unclassified SECURITY CLASSIFICATION OF THIS PACE (*hen Data Snfrtd) READ INSTRUCTIONS REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM I. REPORT NUMBER 2. GOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER
4. TITLE (and Subtitle) 5. TYPE OF REPORT a PERIOD COVERED Computer Simulated Development Master's Thesis of a Command to Line-of-Sight Missile December 1983
Using ON-OFF Control 6. PERFORMING ORG. REPORT NUMBER
7. AUTHOR<«> 8. CONTRACT OR GRANT NUMBER^*,) Je Young, Yeun
9. PERFORMING ORGANIZATION NAME ANO AOORESS 10. PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERS Naval Postgraduate School Monterey, CA 93943
II. CONTROLLING OFFICE NAME ANO AOORESS 12. REPORT DATE Naval Postgraduate School December 1983 Monterey, CA 93943 13. NUMBER OF PAGES
14. MONITORING AGENCY NAME 4 AOORESSfJ/ different Irom Controlling Office) IS. SECURITY CLASS, (ol thte report) Naval Postgraduate School Unclassified Monterey, CA 93943 15a. DECLASSIFICATION/ DOWNGRADING SCHEDULE
14. DISTRIBUTION STATEMENT (of ihle Report) Approved for public release; distribution unlimitted
17. DISTRIBUTION STATEMENT (of the aoetrect entered In Block 20, It different Iron Report)
IS. SUPPLEMENTARY NOTES
19. KEY WORDS (Continue on rovorao old* II nocoooery Identity by block number) Line-of-Sight Guidance ON-OFF Control Two-Level Relay Saturating Linear Control
20. ABSTRACT (Continue on reveree tide It necoeemry end Identity by block number) An on-off control provides a minimum time response for missile control. For application in missile control systems, it is wasteful of control effort (due to chatter) to use a ideal relay. Hence it is necessary to modify the ideal relay into a saturating linear control. The result was almost the same to that of using the ideal relay.
DO MTn 1473 EDITION OF I NOV 89 IS OBSOLETE Unclassified S/N 0102- LF- 0M- 6601 1 SECURITY CLASSIFICATION OF THIS PAGE (When Date Kntered
Approved for public release; distribution unlimited
Computer Simulated Development of a Command to Line-of-Sight aissil; Using ON-OPF Control
by
Je Young, ^eun Lieutenant Colonel, Koraan Air Force B.S., -Korean Air Force Academy, 1972
Submitted in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE IN ELECTRICAL ENGNEERING
from the
NAVAL POSTGRADUATE SCHOOL December 1933
i 939 ABSTRACT
an on-off control provides a minimum time response for missile control. For application in missile control systems, it is wasteful of control effort (due to chatter) to use a ideal relay. Hence it is necessary to modify the ideal relay into a saturating linear control. The result was almost the same to that of using the ideal relay.
TABLE OP 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 LIN E-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-LEVEL RELAY AND SATURATION CONTROL 4U A. TWO-LEVEL RELAY 4U B. SATURATING LINEAR CONTROL 46
VIII. CONCLUSION 59
APPENDIX A: VARIABLES LIST 61
APPENDIX B: PROGRAM OF THE SWICHIN3 FUNCTION 62
APPENDIX C: PROGRAM OF THE BASIC COMMAND TO LOS .... 63
APPENDIX D: PROGRAM OF THE MANEUVEBING TARGET 65
APPENDIX E: PROGRAM OF THE COMMAND TO PSEUDO-LOS .... 67
APPENDIX F: PROGRAM OF THE BASIC COMMAND TO LOS WITH TWO-LEVEL RELAY 69
APPENDIX 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 WITH SATURATION 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 OF REFERENCES 81
INITIAL DISTRIBUTION LIST 82
LIST OP TABLES
I. The Basic LOS Command Simulation Result 37 II. The Psaudo LOS Command Simulation Result 39 III. Two-Level Relay Control Result 45
IV. Saturating Linear Control Rasult (M = 1) 49 V. Comparison of the 3asic LOS Command Results ... 59 VI. Comparison of the Maneuvering Target Results ... 60 VII. Comparison of the Pseudo-LQS Command Results ... 60
LIST OF FIGURES
2. 1 Missile Target Encounter with LOS Guidance ... 12
2. 2 Basic Geometry 13
2. 3 Simplified Guidance Loop Df LOS Guidance .... 13
3. 1 Roland Missile System Operational Schematic . . 18
4. 1 Parabolic Switching Function 21 a. 2 Block Diagram of ON-OFF Controller 21
4. 3 CRE versus Time 22 a. 4 CRE versus Time 22 a. 5 F versus Time 23
4. 6 CRE versus CRE 23
4. 7 versus Time 24
5. 1 Simplified Flow Chart of Basic LOS Command ... 26
5. 2 Geometry of Easic 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 The Basic LOS Command 32
5. 7 The Basic LOS Command 33
5. 8 The Maneuvering Target 34
5. 9 The Maneuvering Target 35
5. 10 The Maneuvering Target 36
5. 1 1 U versus Time for a Maneuvering Target 37
6. 1 Block Diagram of the Pseudo LOS Command System 38
6. 2 The Pseudo-LOS Command 40
6. 3 The Pseudo-LOS Command 41
6. 4 The Pseudo-LOS Command 42 6. 5 versus Time for the Pseudo-LOS Command .... 43
7.1 Two-Leval Relay 45
7.2 U versus Time for the Basic: LOS Guidance .... 46 7.3 U verse Time against the MVR Target with Two-Level Relay 47 7.4 U verse Time of the Pseudo-LOS with Two-Level Relay 47 7.5 Linear Switching Relay 48 7.6 The Basic LOS Command (Saturation) 50 7.7 The Basic LOS Command (Saturation) 51 7.8 The Basic LOS Command (Saturation) 52 7.9 Maneuvering Target (Saturation) 53 7.10 Maneuvering Target (Saturation) 54 7.11 Maneuvering Target (Saturation) 55 7.12 Pseudo-LOS Command (Saturation) 56 7.13 Pseudo-LOS Command (Saturation) 57 7.14 Pseudo-LOS Command (Saturation) 58
I. INTRODUCTION
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 abov= will employ one or more of the following guidance schemes; programmed command, liae-of-sight, lead-angla, proportional navigation homing and inertial. The beam rider guidance is included in the line-of-sight guidance. A number of missiles also use a combination of these methods. For axample, the initial part of the missila trajectory may use programmed guidance while the terminal phase may use beam-ridsr. This thesis discusses the surf ace-tc-air missile controlled by on-off, thrust vector, control. Consideration was given to determine the effects of the two-level relay and the saturation linear control. In order to verify the results, it was tested by using the type of control for three 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 guidance was presented and a practical example of it was shown in chapter 3. The general concept of on-off control was described in chapter 4. The simulation results of the basic command to line-of-sight against both a non-maneuvering and a maneuvering target were shown in chapters 5 and that of pseudo-LOS case was in chapter 6. Finally, a discussion of two-level relay and saturating linear control was presented in chapter 7. A table of variables which were used in this thesis is shown in the Appendix A. Computer simulation was accomplished using Digital Simulation Language, DSL.
10
II. QVEBVIEW OF LINE-OF-SIGBT GUIDANCE CONTROL
A LOS system can be called a "3-point" guidance system since there is one point which defines the tracker, another the target and a third which defines the position of the missile. The object of the guidance 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 constant 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 etc seconds the LOS is shown as OT1,OT2,OT3 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 [Bef. 1], In an actual situation the guidance signals transmitted to the missile are the demanded lateral accelerations (LATAX) 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 ( &mj.) equal to zero.
1 1
A Y T5 T4 T3 T2 Tl TO m= « t J t t _r
/ 1 ' s ' f A ' y s ' / '4 * s ' '
X MO *-
laur cher
Figure 2.1 Hissile Target Encounter with LOS Guidance
A basic geometry and a simplified guidance loop are shown in Figure 2.2 and Figure 2.3. Suppose that the cross range error (CRE) of Figure 2.2 can be measured either directly or by means of the angular difference between OT and ON, together with some knowledge of missile range (Rm) , then
CRE = RMtft -tfm ) (2.1)
If this error off the beam is used is an acceleration demand
U, it needs some damping so that good response characteris- tics are obtained. A dynamic equation of the form
CRE G1 (CRE) G2 (CRE) (2.2) needs to be satisfied, where G1 and G2 are constants. This necessity leads immediately to the consideration of a filtered error. In the presence of noise on the sight-line.
12
T ^
LOS yr
\ CRE ^ V \ Jf m fa "^M ^ y/W ^^ 0^^W^T Reference
Figure 2.2 Basic Seometry
* Ucom Ufld C!-k»* Missile T. F. ^ y F(S) ACS)
CRE 1 * -\XJ*-
Figure 2.3 Simplified Guidance Loop of LOS Guidance
13 and hence on the cress range error, CRE, such a filtar design is not simple and becomes a compromise between requirements for smoothing the noise 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
F(s) Rm " 2 - 3 = ( <5t 6m ) < >
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
, the when with beam angle (tfm ) thus closing loop differenced the target beam angle (dt) . While this concept is simply a LOS or beam riding guidance situation it is by no means as clear in homing how a guidance law can be devised in the absence of information on missile and target positions [Ref. 2].
14
Ill- TYPICAL ENGAGEMENT SEQUENCE
In order to provide a "vehicle" through which to better understand the basic aspects of command to line-of-sight guidance methodology, the engagemaat seguence of a short- range, air-defense, missile system is iescribed. The Roland system was selected because the general operational aspects of the system are available at the unclassified level [Ref. *]. 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 synthetic display of the targets appears on a screen to give the commmander 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 target into 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 and tracking can commence in either the "radar" or "optical" modes. In the "radar" mode, the tracking radar automatically accepts target designation from the search radar, searches for, locks onto, and tracks the target.
15
In the "optical" mode, the aimer searches for the target in elevation with an optical sight. To aid him an electronic instrument displays the maximum theoretical elevation for the search. ahen the aimer has acquired the target in his cross-hairs, he keeps the target in his sight by manipu- lating a control stick. This control keeps the target prop- erly positioned by moving the turret in azimuth and swivelling a mirror in elevation. As soon as the commander confirms that the target is within missile range, he initiates the firing seguence 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 deviation of the missile from this line of sight is 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. In the "radar" mode, the guidance radar has two receiving channels. One is used for target tracking and the other is used to locate the missile in the radar lobe through recep- tion of the missile's radio frequency beacons. By comparing these angles, an error between the missile and the target line of sight can be determined. In the "optical" mode, a biaxially-stabilized mirror is manually 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 mounted on the rear of the missile. Then, a deviation of the missile angle from the target line of sight can be determined.
16
Two groups of signals are introduced into the command computer: the velocity of the line of sight in azimuth and elevation, and the deviation of the missile from xhe line of sight in azimuth and elevation. Based upon data from the line-of- sight movement and the angular deviations of the missile, the necessary guidance signals are calculated.
The guidance signals are relayed to the missile by a transmitter 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 the basic Roland missile system operation. The computer simulations contained herein are generic in nature within the command to line-of-sight guided-raissile type 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 guidance variations discussed [Ref. 3].
17
From target & missive To mxssile,
/ s
OPTICAL COMMAND SIGHT TRANSMITTiJr I I MISSILE OPTICAL GUIDANCE TARGET TRACK & CONTROL DEVIATION COMMANDS L_J MISSILE/ TARGET COMMAND DEVIATION i COMPUTER
COMMANDER.MANDE] FIRING AIMEI AUTHORIZATION
FIRE FIRE* *Clear weather X mode only MISSILE LAUNCH SEQUENCER
Figure 3, 1 Roland Hissile System Operational Schematic
18
17. ON-OFF (BANG^BANG) CONTROL
As discussed before, LOS guidance maintains a missile position on the LOS. Usually missile position has a cross range error (CRE) and we want to reduce this error to zero 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 = t1 so that deceleration under maximum reverse drive reduces the velocity to zero at precisely tha command value of the output. The drive is then set to zero.
Tha ideal relay permits only two conditions; full acceleration and full deceleration [Bef. 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. From Newton's second law;
F = m CRE
.. d . F CRE (CRE) = = dt m
CRE = CRE dt - II t U1
But at t , ere and k1 = 0. Therefore
d CRE = (CRE) = t (4. 1) at
2 CRE = CRE dt = II t + k2 (4.2)
19
From the equation 4.1
t = CRE /
2 2 t = (CRE / U) (4. 3)
Substitute equation 4.3 into equation 4.2
2 CRE = (0 / 2) (CRE / U) + k2
2 = (CRE) / (2 0) k2 (4.4) where lc2 is integration constant. But if we apply a full deceleration at the halfway point, the equation 4.4 becomes
F = (CRE |CRE|) /(2 0) CRE (4.5) and is called the ERROR FUNCTION. U will be = ±G or = -(G) SIGN(F) (4.6)
Equations 4.5 and 4.6 represent the 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 U with the initial condition of CRE. We have
CRE = dt CRE(O)
CRE = CRE dt + CRE(O) (4.7)
The simulation results of these equations are giver, on Figures 4.3 through 4.7 and the computer program is attached
(see Appendix B) .
20
Application of Negative Control
Figure 4,1 Parabolic Switching Function
r i
G
CRE Error F C-) U I CRE I CJ2E FuNction s S -& ' i CRE
i
Figure 4.2 Block Diagram of ON-OFF Controller
21
CRE CRE VS. TIME SWITCHING FUNCTION
TIME
0.00 9.10 0.80 1.20 1.80 2.00 J. 10 2.00 3.20 3.80
Figure 4.3 CRE versus Time
CRED VS. TIME CRE SWITCHING FUNCTION
TIME
oo o.«o o.ao 1.20 i.ao 2.00 2.10 2.ao 9.20
Figure 4.4 CBE versus Time
22
... . o - F VS. TIME F SWITCHING FUNCTION 3
B o" -
B o" o9 a a ni o s o TIME 'o oo 0.40 o'.eo i'.2a t'.ao e'.oo z'.u 2. BO 3.20 3. 80 Figure 4.5 P versus Time CRE CRED VS. CRE SWITCHING FUNCTION CRE -_ t~z. ~y. -b.20 o.ao o.20 o.w o.aa o.ao i.oo 1.20 i.u Figure 4.6 CRE versus CRE 23 U VS. TIME SWITCHING FUNCTION TIME o.oo o.io o.w :.20 l.ao 2.00 2.10 2.90 3.20 ?.ao Figure 4.7 versus Time 24 V- BASIC COM MAND TO LJNE^OF; SIGHT SIMULATION A. SCENABIO The engagement was designed with the ground tracker and missile launching unit located at tie 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 controlled during this time. We assumed that the missile was controlled after one second from the firing time and controlled by PROS RAMMED GUIDANCE up to this time. After the time of missile "capture", the missile was controlled by the on-cff r 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, 503 meters per second; 2) the LATAX was applied to the missile at right angles to the LOS. This was a reasonable assumption for this kind of missile. So the angle Figure 2.2 is almost same to angle <& ; 3) the measurement noise was zero so we omitted the filter , F(s) ; 2 4) the magnitude of LATAX was 150 meters /second which was about 15 Gs. ' The geometry depicted in Figure 5.2 summarizes the geometric situation. 25 c START 3 NO YES ON - OFF PROGRAMMED CONTROL GUIDANCE NO YES C END 3 Figure 5.1 Simplified Plow Chart of Basic LOS Command 26 Target Tracker Figure 5.2 Geoaetry of Basic LOS Guidance For mathmatical convenience of simulation, we need to define the sign of the CRE and the LATAX as follow; 1CRE| : When the missile position is upper-side of LOS -|CRE| : when the missile position is lower-side of LOS I U\ : when the LATAX is upward direction - | Q | : when the LATAX is dowaward direction This sign was based on the positive 6^ which is defined when 6^ is greater than dl . B. PBOGBAMHED GUIDANCE PHASE Since the major emphasis of this paper was on-off control, we assumed that the missile flew along the LOS during the programmed guidance phass. But, in a practical situation, there is some cross range error which is occured by disturbances such as wind, propulsion system and 27 autopilot time delay,etc. Hence we made initialization errors, and the on-off control started with these errors. C. ON-OFF, THRUST VECTOR, MISSILE CONTROL The detail of the on-off control was discussed before, hence we applied this to the LOS guidance scheme. The 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 elapsad time of flight and the missile's velocity profile. The program of this simulation is attached in Appendix C. LOS 1 Target T.V.C. <*tl 4 Position +G /VVA^mt Control F, (-) 1 1 C —— - ( + Function F K+y -G S S i 1 R <*m m CRE CRE Missile CRE Position Geometry TARGET TRACKER MISSILE Figure 5.3 Block Diagram of the Basic LOS Coamand D. SIMULATION RESULTS Figure 5.4 shows the missile and target geometry in X-Y plane. The missile intercepted the target at the point A(2605,10Q0) with the almost zero miss distance. 28 Figure 5.5(a) shows the distance between target and missile versus time. The distance decreased linearly and neared zero at the time at 5.58 seconds. ' " r MSL - TGT TRAJECTORY ao T-CQQRDINRTE VS. X-COQRDINRTE a go. a Y a oa a o d a a D W - oS- » z tkA a a s- o a S o o 5- a a a. o a X oo sb.oo 120.00 iso.oo auo. oo Jbfl.oo sso.oo j^c .ao abo.oo 5uo. 1 __J Pigure 5.4 The Basic LOS Command Figure 5.5(b) shows the CRE varsus time. The initial cross range arror at the missile capture time one second after firing was about 50 meters. Since tha CRE at the "missile capture time" was positive, the CRE increased 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 gat a fastar response, we should increase the magnitude of the LAT&X. We should note here 29 . that the CRE does not maintain zero value because we did not consider the target motion terms in this phase of the simu- lation [Bef- 2]. So the missile had 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 CRE versus CRE. As we expected this curve followed the SWITCHING FUNCTION as shown in figure 4.4. Figures 5.7(a) and 5.7(b) show the F versus time and the versus time This program was tested using maneuvering targets and the results ware 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 attached in Appendix D. The comparison cf these simulations is summarized in Table I. 30 1 < 2:2 — IX a at a U m o u o -3 u •H 00 -a 00 'o 00 - a- W (0 CO -C in a u r" fO M 4J 3 en •w a CO e 4J H a> c-1 cr en - > (0 W H 3 UJZ 1 i/i c_)cr cy M zx »H CU err • ^ > 1—0 in tnc_) in •— acj W •— u >— - oo oeri aa'odn •oris oo-ods 00 "OS? 00*002 ,0t" 31 1 UJQ T3 O C_)d a in M a cn UJQ a 3TZ W — en M > .S3 en OCX UJCQ cc .S3u 00-08 00 -on M*£ L 32 2: ex p 1—3: (0 o a o >o">c_>— u en S in M a LU 2:0 (no >C_) .(_) Cm OO'K boTS OO'dK 00 i WW OO'il 33 4J 0> or> W H(0 en ~ •H M > Q) O 23 0) J3 £1 >1 u o P u 0) •n OS H H +J CD •H CP W i 0) r-4 •H cn 1/1 •H S oo-o7i oo-ooi oo 'do 35 oVtP ,0l» 3U o M (0 t^ a •H M a> oo do go -da oo-d* oo-oa oo-'o oo-o^- oo'oti- oo-aa- oo - oi- oo-ooi'-° > a in - o cc •H a Bu UJO U c oo'te aa'di do s ao-o no's- 35 2 H E-t oUJ (X —.O crz cduj a SC i 1 0) U a en LJO en UJ • > .22 a a -so oo'da oo'dit ooTa «ro oo-o^- oo-oti- oo'0»- oo-oo- oo'ooi- 36 TIME a. qo 0.70 Figure 5*11 versus Time for a Maneuvering Target TABLE I The Basic LOS Command Simulation Result NO N- MANEUVERING TARGET MANEUVERING TARGET . time (control) = 1.0 sec 1.0 sec CRE(O) = 49.910(m) 49. 907 (m) CRED(O) = 49.832(m/sec) 49.891 (i/sec) .time (max. CRE) 1.33 sec 1.33 (sec) CRE (max) = 53. 1 84(m) 58.201 (m) . time (intercept) - 5, 58 sec 5.61 s ec (Xm,Ym) = (2504.7,999.88) (2597.9, 1057.7) CRE = 4.3344 E-5 -6.5448 S-6 distance= 0.34894(m) 0.47889(m) 37 71. PSE UDO- LOS COMMAND SIMULATION The guidance scheme cf the lead angle command is almost tha same as that of the basic LOS command. Instead of the tracker-to-target line-of- sight this guidance scheme uses the tracker-to-estimated impact point and is called "synthetic line-of- sight" (SLOS) , or "pseudo line-of-sight". The missile is controlled to fly along this pseudo line-of- sight. The block diagram of this system is easily modified 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" (Tg) and the "closing velocity" (Vc> between the target and the missile. I Compute SLOS CRE Missile Position A Geometry CRE TARGET TRACKER | MISSILE Figure 6.1 Block Diagra* of the Pseudo LOS Command System 38 The "closing velocity" and "time to go" are calculated as fellow: 2 Vc = ((Vtx-Vmx) (Vty-Vmy)*).xJfc Tg = (distance between target and missile) / Vc 2 2 f(Xt-Xm) + (Yt-Ym) )^ / 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 schema 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 in Appendix E. 1 TABLE II The Pseudo LOS Co mmand Simulation Result .time (control) 1.0 sec CRE(O) 49.912 (m) CRED (0) 49.828 (m/sec) .time (MAX.CRE) 1.33 sec CRE (max) 58. 184 (m) .time (intercept) 5.58 sec (Xm,Ym) (2604.7, 999.92) (2605.0, 1000.0) 2.9572 E-5(m) miss-distance 0.35137 (m) _ i 39 1 en CD u H o *3 •H > (3 en (0 en a •H a g o u oen oi oo-odn tn - 6-t O 4J U CD •n •H CD o> M oj £- I CD H<-\ Cfl en oo 091 oo'os'i oo'orii MTOCI oo'odi oo-do oo 'dn oo-'P ,01" 40 73 (TJ a a o u oV) oI 73 0) 01 Q4 0» 43 m d) 9 41 J w Ms CD S a LUCE C_) en en a (0 a a o o era u OLU CCZD ocen w UJQ_ o -: O1 oo as JO'.TC QQ-8 0CT0 OO'S- =3 0) w a* (V a. o2: LlJO o ejeno en> 00 tUQ CCUJ or> en Q_ u 00 -c6 eo-da 00-02 42 U VS. TIME PSUEDO - LOS C3MMPND TIME 0. 00 0.70 l-<0 ?-lO 8.80 j'.SO It'. 20 u'.90 5.80 Figure 6.5 versus lime for the Pseudo-LOS Command 43 VII. SIMULATIONS WITH TWO^LEVEL RELAY AND SATURATION CONTROL The LOS guidance with an "ideal" relay has beer. discussed. In this chapter, the affect 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 response. But in "che case of small CRE f a smaller magnitude of LATAX is needed. This idea was developed in a "two-level 1 * 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 ((|CRE| + |3RSD|) .LT. M) G = 3/(N1/N2). 2, 2 We used the values 150 m/sec for N1 and 15 m/sec for N2 and 1.0 for M in the simulations of the basic LOS command and the pseudo LOS command. 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 "0 versus time" of each case. The programs were attached in Appendix F, G and H. 44 4 F = i * CRE u -N2 N2 1 CRE 1 M ^ / njd P^fc* 1 ^ -M i |CRE|T|CREJ U = Nl -N2 ^g = -Nl U N2^ U = -Nl (a). U vers us |CFLE| + |CREJ (b) . CRE ver:3us CRE • - J Figure 7.1 Two-Level Helay TABLE III Two-Level Relay Control Result NON-MVR MVR^TGT PSEUDO-LOS .time (control) 1.0 1.0 1.0 CRE (0) 49. 910 49.907 49.910 CRED(O) 49. 832 49.891 49.828 .time (MAX. CRE) 1.33 1.33 1.33 CRE (max) 58. 184 58.201 58. 184 . time (intercept)) 5.58 5.61 5.58 Xm 2604.7 2597.9 2604.7 Ym 999.88 1057.7 999.92 Xt 2605.0 2597.5 2605.0 Yt 1000.0 1057.5 1000.0 CRE -2. 63E-6 -3.63E-6 5.03E-8 miss-distance 0.34894 0.47889 0.35137 45 a u O a o O S o o M i o aZ3 p a a o TIME Figure 7.2 0* versus lime for the Basic LOS Guidance B. SATURATING LINEAR CONTROL In the previous section tha two-level relay was discussed. The "sautrating linear control" as depicted in the Figure 7.5(a) and 7.5(b) was also studied. The shaded area on the Figure 7.5(b) shows the region of linear control in the "CRE versus CRE" phase plans. The computer programs were easily modified by adding one statement, IF (ABS (F) .LE. M) U = -3 * F / M. The value of "H" 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 "M" equal 1, 5 and 10. When choosing the value "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 46 Figure 7.3 U verse Tiae against the J1VR Target with Two-Level Relay TIME i i 0. 00 3.70 L.U 2.10 {.SO ).50 11.20 U.30 s.oo a. so L Figure 7.4 a verse Time of the Pseudo-LOS with Two-Level Relay U7 instead of the ideal relay by choosing a proper value of "M". The summarized results are in the Table IV. Figures 7.9 through 7.11 show the results of the maneuvering target case and Figures 7.12 through 7.14 show the results of the pseudo-LOS case. These programs are given in Appendix I, J and K. i k u G 1 \ CRE + M 1 \ - M \ i \ -G j F=0 (a) U verse F ( b) CRE verse CRE Figure 7.5 Linear Switching Relay 48 TABLE IV Saturating Linear Control Rasult (H=1) UNIT NON3MVR MVR^TGT PSEUDO-LOS • time (control) 1.0 1.0 1.0 CRE (0) 49. 910 ^9.907 49. 912 CRED(O) 49. 832 49.891 49. 828 .time (MAX. CRE) 1.33 1.33 1.33 CRE (max) 58. 184 58.201 58. 184 . time (intercept) 5.58 5.61 5.58 Xm 2604.7 2598.0 2604.7 Ym 999.84 1057.6 999.88 Xt 26 5.0 2597.5 2605.0 Yt 1000.0 1057.5 1000.0 CRE -.0349 -.0702 -.0349 miss-distance 0.3 507 0.4841 0.3492 49 o i w 0) M H E*_ 8 Eh cn 3 8 cn V u 0) > UJ R 8 tn co cc "« •H Q I O LUO CJCJ O I CO _i en a I s 0»T>«TI 00-OWl Ot'OU 00 'Ode 00'OC? 00-002 DO "Oil 00-001 W(P I o U Oto -J o •H W (d 03 0) 6-t o 4-1 o M •H UJ ft-. E-» I CO 50 o •H -P u =J 4-» CO c (d a a o u oen O •H V) nJ 03 <1> 1-1 D> •H 51 o CD. a> E-i ao CD M a 3 •H a) > M'W M> "35 mtX »-ck STS mm 52 >X 3 en •JJ > t-O U cc C •ex 03 cnt— +J > Ui a UJZ cj— zcr +J CXLU (1) a tr< I— u o cnzD •H to •—iljLl oz Eh 4-> I ex M I—o h-X +J _!-< 8 woct ot'odn n*os oo-obc 00', 00'f ,0l« i-l M 0) > d a) a Brd u o t— +J ex u z OJ •n t a (0 r* >-ar OO(TO Eh f-CJ -P M CO O I LUX CT« ") Vj •H cr . 03 cccn Eh t— I 'D rH CJUJ — t— I Z _ia cntr I "MI M*«3l •odi to 'da ao da oo'ds oo 'dz ocPcP ,0t« 53 C o •H -M (d u -P (0 CO -p 0) O* M en (3 •H M <0 > 0) a rii 50 a> M 9 •H a. 5a o •H M o fd en a •H M (1) a 3B LU CD tr CE a> (U M He E-« •H ui 3 cn>> Ul 0) uuz > u.cr fa 3: -s iol» n*S to*ds niz wiii oo's oo-^- oo*ot-° 55 1 3 H "0 2 HH Eh 8 'Jl 03 !h a) " > UJ 2: 8 a 1— 'm -0 t—o +J z CO • en. H cox B Q >2T "r» O -U o UJC_> a X Q / cd s a wo«n ofl-odti oa'au oo-oas 00 "042 00*002 oo'oei oo-odi 00 as 00 0° a ,01- o U oi O -J oI x r3 >i d) >h ff) O u O CD •r-i (0 CM M Eh t a +J r- >-cc oca ga 1) 00 Cn a> f-CJ u rO 9 u 1 Eh UJX I -) CD •H cr . H aztn H U) CO 1 z tnac 3:0a u 1 a* -Mi M-odi oo-orli L 56 U d X 3 a X W o CD -H UJ(_> i az > I .p (_>(/"> o I (d ._) ! 3 «n u > i o I to i_JLU -a CO 0- a (0 a a - - - woo oo-dn oo o? oo 'o oo ai- oo ot>- 00-08- 00 -oo- 00 001- o u o I O 2 d) on *• t P* d) u a x •H X zu t— > I O ijJO (_)UJ Q_ ici L 57 S •H Eh W 3 UJ C S > -P id t3 C (d a 00*0»- WMI- 00091-° a uo o -J oI a in a. M •H M'kl oo'B 00'2- oo-oi- 58 fill. CONCLUSION The co m par i s io n of results for the ideal relay, two- level relay and saturating linear control against the basic LOS command and pseudo-LOS command against a non-maneuvering target and maneuvering target are provided in the Tables V, VI and VII. These simulation results clearly demonstrate that "on-off" control of a missila is highly desireable and that "saturating linear control" of a missils has little adverse effects compared to an "idaal relay" control. TABLE 7 Comparison of the Basic LOS Command Results UNIT IDEAL TWO-LEVEL SATURATION RELAY RELAY CONTROL .timejccntrol) 1.0 1.0 1.0 CRE(O) 49.910 49.910 49.910 CRED(0) 49.832 49.832 49.832 .time (MAX. CRE) 1.33 1.33 1.33 CRE(max) 58.184 58.184 58.184 .time (intercept) 5.58 5.58 5.58 Xm 2604.7 2604.7 2604.7 Ym 999.88 999.88 999.88 CRE 4.33E-5 4.33E-5 4.33E-5 miss-distancs 0.34894 3.34894 0.34894 59 TABLE VI Comparison of the Maneuvering Target Results UNIT IDEAL TWO- LEVEL SATURATION RELAY RELAY CONTROL .time (control) 1.0 1.0 1.0 CRE(O) 49. 907 49.907 49.907 CRED(O) 49. 891 49.891 49. 891 -time (MAX. CRE) 1.33 1.33 1.33 CRE (max) 58. 201 58.201 58. 201 .time (intercept) 5.6 1 5.61 5.61 Xm 2597.5 2597.5 2597.5 Ym 1057.5 1057.5 1057.5 CRE -6. 54E-6 3.63E-6 -0.0702 miss-distance 0.47889 3.47889 0.4841 TABLE 711 Comparison of the Pseudo-•LOS Command Results UNIT IDEAL TWO- LEVEL SATURATION RELAY RELAY CONTROL . time (control) 1.0 1.0 1.0 CRE (0) 49. 912 49.910 49.912 CRED(0) 49. 828 49.828 49.828 .time (MAX. CRE) 1.33 1.33 1.33 CRE (max) 58. 184 58.184 58. 184 .time (intercept) 5.58 5.58 5.58 Xm 2604.7 2604.7 2604.7 Ym 999.92 999.92 999.92 CRE 2.96E-5 5.03E-8 2.96E-5 miss-distanca 0.35137 0.35137 0.35137 60 APPENDIX A VARIABLES LIST DIAGRAM COMPUTER NOON DESCRIPTION VARIABLES VARIABLES CRE CRE cross -range- error CRE CRED rate of :ross-range-error change F F error function G G magnitude of lateral acceleration a missile's lateral acceleration 6t SIGT angle between the LOS to target and X-axis 6m SIGM angle between the beam to missile and X-axis dmt SIGMT angle difference between m and t vc VC crossing velocity tg TG time to go t (control) TCON beginning time of on-off control SLOS SLOS synthetic line-of-sight Xm XM X-coordinate of missile position Ym YM Y-coordiaate of missile position Xt XT X-coordinate of target position Yt YT Y-coordinate of target position Vm VM velocity of the missile Vt VT velocity of the target Vmx VMX X-componsnt of missile's velocity Vray VMY Y-componsnt of missile's velocity Vtx VTX X-component of target's velocity Vty VTY Y-componsnt of target's velocity 61 APPENDIX B PROGRAM OF THE SWICHING FONCTION TITLE BANG-BANG CONTROL TITLE SWITCHING FONCTION TITLE * YEUN, J.Y. * INTGER NPLd CONST NPLOT=1 INITIAL CRE = 1.0 CRED = 0. ACRED = 0. ********** DERIVATIVE ********** NOSORT * G = 1 .0 F = C RE + (CRED*ACRED) /(2*G) = - G * SI GN(1.,F) CRED = INTG BL(0.,U) CRE = INTG BL(CRE, CRED) ACRED = ABS (CRED) IF (CR E. LE. 0.0) CALL ENDJ3B SAMPLE CALL DRWG (1 , 1, TIME, CRE) CALL DRWG 2 , 1, CRE, CRED CALL DRWG 3 ,1,TIME,F) CALL DRWG 4 ,1, TIME, CRED) CALL DRWG 5;i,time;u) TERMINAL CALL ENDRW(NPLOT) CONT RL FINTIM=2. 1,DELT=0.01 ,DELS = 0.31 PRIN T 0. 1 ,G,F,U, CRE, CRED END STOP 62 APPENDIX C PROGRAM OP THE BASIC COMMAND TO LOS TITLE BASI3 COMMAND TO L.O.S TITLE WITH IDEAL RELAY TITLE ***** YEUN, J.Y. ***** INTEG RKSFX INTGER NPLOT,KILL CONST NPLOT=1 ,TCON=1.0 CONST VM=50 0. ,VT= 250, PI= 3. 141593, KILL=0 INITIAL XTO = U000. YTO = 1 000. GAMT = PI F =0. * *************************** ********************************* DERIVATIVE *************************** ********************************* NOSORT ************************* *** TARGET EARAMETERS *** ************************* VTX = VT*COS (GAMT) VTY ' VT*SINJGAMTf XT = VTX*TIME XTO YT = VTY*TIME + YTO SIGT = ATAN2(YT,XT) IF (IIME.GE.TCON) GO TO 50 ************************* *** MISSLE PARAMETERS *** ************************* * PROGRAMMED GUIDANCE ************************************** * SIGM = SIGT+0. 1 VXM = VM * COS (SIGM) VYM = VM * SIN(SI3M) XM = INTGRL(0. ,VXM) YM = INTGRL(O..VYM) RM = SQRT(XM**2 YM**2) SIGMT = SIGM - SI3T CRE = RM * SIN (SIGMT) CRED = DERIV(0. ,CRE) GO TO 200 *************************** ** * ON-OFF GUIDANCE (BANG-BANG CONTROL) ********************* ***************************** * 50 CONTINUE * G = 150. ACRED = ABS(CRED) F = CRE (CRED*ACRED)/(2*3)fCRED*AC = -G * SIGN(1. t Fi CRED = INTGRLfO.O.U) CRE = INTGRL(CRE,CRED) RM = VM*TIME A3 = CRE/RM SIGMT = ARSIN(A3) SIGM = SIGT + SI3MT 63 XM = RM * COS (SIGM) YM - RM * SIN (SIGM *************** ******************************************** 200 CONTINUE * *************************** ******************************** *** MISSION RESULT *** KILL = ; TGT HISSED ********************** KILL = 1 ; TGT DESTROYED XDIST = XT-XM YDIST = YT-YM DIST = SQRT(XDIST**2 YDIST**2) IF (DIST .LE.5) KILL = 1 IF (DIST .GT.5) KILL = IF (XM .GT. (XT+30) ) CALL ENDJOB * SORT *************************** ******************************** ******** OUTPUT AND PLOT CONTROL CARD ********************* *************************** ******************************** SAMPL E CALL DRWG (1 ,1,XM,YM) CALL DRWG (1,2,XT,YT) CALL DRWG (2, 1 f TIME, DIST) CALL DRWG (3,1, TIME, CRE) CALL DRWG (4,1, TIME, CRED) CALL DRWG (5 ,1,CRE,CRED) CALL DRWG (6, 1,TIME,F) CALL DRWG (7,1, TIME , U) TERMINAL CALL ENDRW(NPLOT) CONTRL FINTIM=6. 0,DELT=0.0 1, DEL 5=0. 03 PRINT 0. 005, XM, YM, XT, YT, CRE, CRED, DIST, KILL END STOP 64 AP PENDIX 2 PROGRAM OF THE MANEUVERING TARGET TITL E BASIC COMMAND TO LOS TITL E WITH MANEUVERING TGT TITL E *** YEUN, J.Y. *** INTE G RKSFX INTG ER NPLOr,KILL CONS T NPLOT=1 ,TCON=1.0 CONS T VM=50 0. ,VT=250,PI=3. 1415 93, KILL=0 INIT IAL XTO 4000. YTO = 1000. GAMT = PI F = 0. * **** *********************** ********************************* DERI VATIVE **** ******************************************************** NOSO RT **** ********************* *** TARGET PARAMETERS *** **** ********************* VTX = VT*COS (GAMT) VTY = VT*SINJGAMT) XT = VTX*TIME XTO YT = 100*SIN(0.5*PI*TIME) + !fT0 SIGT = ATAN2(YT,XT) IF (riME.GE.TCON) GO TO 50 **** ********************* *** MISSLE PARAMETERS *** **** ********************* * PR OGRAMMED GUIDANCE ************************************** * SIGM = SIGT+0.1 VXM = 7M * COS (SIGM) VYM = VM * SIN(SIGM XM = INTGRL(0. ,7XM YM = INTGRL(0. .VYMi RM = SQRT(XM**2 YM**2) SIGMT = SIGM - SIGT CRE = RM * SIN (SIGMT) CRED = DERIV(0. ,CRE) GO TO 200 **** *********************** ** * ON -OFF GUIDANCE (BANG- BANG CONTROL) ********************* *************************** ** * 5 CONTINUE * G = 150 ACRED = ABS (CRED) F = CRE (CRED*ACRED)/(2*G) U = -G * SIGNM..F) CRED = INTGRLfO.O, U) CRE = INTGRL(CRE,CRED) ACRE = ABS (CRE) RM = VM*TIME A3 = CRE/RM SIGMT = ARSIN(A3) SIGM = SIGT SIGMT 65 XM = RM * COS (SIGM) YM RM * SIN (SIGM) ****::******* **************** ******************************** 20iiO CONTINUE *************************** ******************************** *** MISSION RESULT *** KILL = ; TGT MISSED **********************:****************** KILL -= 1 ; TGI DESTROYED XDIST = XT-XM YDIST = YT-YM DIST = SQRT(XDIST**2 YDIST**2) IF (DIST .LE.5) KILL 1 IF (DIST .GI.5) KILL = IF (XM (XT + 30) ) CALL ENDJOB * SORT **** **** ******************* ******************************** **** **** OUTPUT AND PLOT CONTROL CARD ********************* **** **** ******************* ******************************** SAMP LE CALL DRWG 1 ,1, XM, YM) CALL DRWG 1 ,2,XT,YT) CALL DRWG 2,1, TIME, DIST) CALL DRWG 3 r 1,TIME,CRE) CALL DRWG 4,1, TIME, CRED) CALL DRWG 5,1,CRE,CRED) CALL DRWG (6, 1,TIME,F) CALL DRWG (7,1, TIME ,U TERMINAL CALL ENDRW(NPLOT) CONT RL FINTIM=5. 9, DELT=0.00 1,DELS=0. 03 PRIN T 0.0 05, XM, Y M, XT, YT,C RE, CRED, DIST, KILL END STOP 66 * APPENDIX 5 PROGRAM OP THE COMMAND TO PSEUDO-LOS TITLE PSEUDO - LOS COMMAND TITLE WITH IDEAL RELAY TITLE *** YEUN, J.Y. ** INTEG RKSFX INTGER NPLOT,KILL CONST NPLOT=1 ,TCON=1.0 CONST VM=50 0. , VT= 250, PI= 3. 1415 93, KILL=0 INITIAL XTO = 4000. YTO = 1000. TG = 0. f = 0. GAMT = PI * *************************** ********************************* DERIVATIVE ************************************************************ NOSORT ************************* *** TARGET PARAMETERS *** *********** *** *********** VTX = VT*COS(GAMr) VTY = VT*SINJGAMT) XT = VTX*TIME « XTO YT = VTY*TIME + YTO SIGT = ATAN2(YT.XT) XLOS = XT * VTX*rG YLOS = YT VTY*TG SLOS = ATAN2 (YLOS, XLOS) IF (TIME. GE. ICON) GO TO 50 ************************* *** MISSLE PARAMETERS *** ************************* * PROGRAMMED GUIDANCE ************************************** * SIGM = SLOS + 0.1 VMX = VM * COS(SIGM) VMY = VM * SINJSIGM XM = INTGRL(0. ,VMX) YM = INrGRL(0. .VMY) RM = SQRT(XM**2 * YM**2) SIGMS = SIGM - SLOS CRE = RM * SIN(SIGMS) CRED = DERIV (0. f CRE) GO TD 2 00 ***************************** * ON-OFF GUIDANCE (BANG-BANG CONTROL) ********************* *************************** ** * 50 CONTINUE * G = 150. ACRED = ABS (CRED) F = CRE + (CRED*ACRED)/(2*G) U = -G * SIGNM..F) CRED = INTGRLfO.O, U) CRE = INrGRL(CRE,CRED) * RM VM*TIME 67 A3 = CRE/RM SIGMS = ARSIN(A3) SIGM = SLOS + SIGMS VMX = VM * COS (SLOS' VMY = VM * SIN(SL3S XM = RM * COS(SIGM YM = RM * SIN(SIGM' **** ***********»*******?************************* *** ******* 20 CONTINUE * **** *********************** ******************************** *** MISSION RESULT *** KILL = ; TGT MISSED **** ****************** KILL = 1 ; TGT DESTROYED XDIST = XT-XM YDIST = YT-YM DIST = SQRT(XDIST**2 + YDIST**2) VC = SQRT ( (VTX-VMX) **2+ ( VTY- VMY) **2) TG = DIST/VC IF (DIST .LE.5) KILL = 1 IF (DIST .GT.5) KILL = IF (XM -GT. (XT+30) ) CALL ENDJOB * SORT **** *************** **************************************** **** **** OUTPUT AND PLOT CONTROL CARD ********************* **** *********************** ******************************** SAMP LE CALL DRWG M*KM) CALL DRWG 1 ,2,XT,YT CALL DRWG 2/1, TIME, DIST) CALL DRWG 3,1, TIME, CRE) CALL DRWG 4, 1,TIME,CRED) CALL DRWG 5 ,1,CRE,CRED) CALL DRWG 6,1,TIME,F) CALL DRWG 7,1, TIME ,U) TERMINAL CALL ENDRWfNPLOT) CONT RL FINTIM=5. 9, DELT=0.00 1 ,DELS=0.003 PRIN T 0. 1,TG,XM,YM , XT, YT , CRE ,CRED, DIST , KILL END STOP 68 APPENDIX F PROGRAH OF THE BASIC COMMAND TO LDS WITH TWO-LEVEL EELAI TITL E BASIC COMMAND TO L.O.S TITL E WITH TWO LEVEL RELAY TITL E YEUN, J.Y. ***** INTE G RKSFX INTG ER NPLOT ,KILL CONS T NPLOT = 1 ,rcoN=i.o CONS T VM=50 0. ,VT=250,PI=3.1415 93,KILL=0 INIT IAL XTO - au oooooo. YTO = 1000. GAMT = pi F = o. * **** **** ******************* ********************************* DERI VATI VE **** **** **************************************************** NOSO RT **** **** ***************** *** TARG ET PARAMETERS *** **** **** ***************** VTX = VT*COS(GAMT) VTY = VT*SIN?GAMT) XT = VTX*TIME + XTO YT = VTY*TIME YTO SIGT = ATAN2(YT / XD IF (TIME. GE. ICON) GO TO 50 **** **** ******** ********* *** MISS LE PARAMETERS *** **** **** ***************** * PR OGRA MMED GUIDANCE ***** ********************** *********** SIGM = SIG T + 0.1 VXM = VM * COS(SIGM) VYM = VM * SIN(SIGM XM = INTG RL(0.,VXM YM = INTG RL (0. -VYM RM = SQRT (XM**2 YM**2) SIGMT = SI GM - SIGT CRE = RM * SIN (SIGMT) CRED = DER IV (0. ,CRE) GO TO 2 00 **** ********** ***** ******** ** * ON -OFF GOIDA HCE BANG-BANG CONTROL) ********************* **** ***********************£ ** * 5 CONTINUE * G = 150. ACRE = ABS(CRE) ACRED = ABS (CRED) IF ((ACRE+ACRED) .LT. 1.) G = 15 F ' CRE (CRED*ACRED)/(2*G) = -G * SIGNM..F) CRED = INTGRL(0.0,O) CRE = INTGRL(CRE,CRED) RM = VM*TIME A3 = CRE/RM 69 SIGMT = ARSIN(A3) SIGH = SIGT SIGMT XM = RM * COS (SISM) YM = RM * SIN(SIGM) *********** ******* ********* **************** ****** ********** 200 CONTINUE * *************************** ******************************** *** MISSION RESULT *** KILL = ; TGT MISSED ********************** KILL = 1 * TGT DESTROYED XDIST = XT-XM YDISr = YT-YM DIST = SQRT(XDIST**2 + YDIST**2) IF (DIST .LE.5) KILL = 1 IF (DIST .GT.5J KILL = IF (XM .ST. (XT+30))CALL ENDJOB * SORT *********************************************************** ******** OUTPUT AND £LOT CONTROL CARD ********************* *************************** ******************************** SAMPLE CALL DRWG (1 ,1,XM,YM) CALL DRWG (1 ,2,XT,YT) CALL DRWG(2, 1,TIME ,DIST) CALL DRWG 3, 1,TIME,CRS) CALL DRWG (4,1, TIME ,CRED) CALL DRWG (5,1, CHE, CRED) CALL DRWG/6 ,1,TIME ,F) CALL DRWG (7, 1, TIME, U) TERMINAL CALL ENDRWjNPLOT) CONTRL FINTIM=5. 9,DELT=0.00 1,DELS=0. 003 PRINT 0.0 05,XM,YM,XT,YT,CRE,CRED,DIST, KILL END STOP 70 APPENDIX 6 PROGRAM OF THE MANEUVERING TARGET WITH TWO-LEVEL RELAY TITL E BASIC COMMAND TO LOS TITL E WITH MANEUVERING T GT TITL E *** YEUN, J.Y. *** INTE G RKSFX INTG ER NPLOT,KILL CONS T NPLOT=1,TCON=1.0 CONS T VM=50 0. ,VT=250,PI=3.1415 93, KILL=0 INIT IAL XTO = 4000. YTO = 1000. GAMT = PI F = 0. * **** ***************** ************************ *************** DERI VATIVE **** ******************************************************** NOSO RT **** ********************* *** TARGET PARAMETERS *** **** ********************* VTX = VT*COS(GAMT) VTY = VT*SINJGAMT) XT = VTX*TIME + XTO YT = 100*SIN(0.5*PI*TIM2) +YT0 SIGT = ArAN2(YT.XT) IF (TIME.GE.TCON) GO TO 50 **** ************ ********* *** MISSLE PARAMETERS *** **** ********************* * PR OGRAMMED GUIDANCE ************************************** * SIGM = SIGT+0.1 VXM = VM * COS (SIGM) VYM = VM * SIN (SIGM ] XM - INTGRL(0. f VXM YM = INTSRL JO. .VIM'i RM = SQRT(XM**2 «• YM**2) SIGHT = SIGM - SIGT CRE = RM * SIN(SIGMT) CRED = DERIV(0. ,CRE) GO TO 2 00 **** *********************** ** * ON -OFF GUIDANCE (BANG-BANG CONTROL) ********************* *************************** ** * 50 CONTINUE * G 150. ACRE = ABS(CRE) ACRED = ABS (CRED) IF((ACRE*ACRED) .LT. 1.) G = 15 F = CRE (CRED*ACRED)/ (2*3) U -G * SIGN(1..F). CRED = INTGRL(0.0, U) CRE = INrGRL(CRE r CRED) ACRE = ABS (CRE) * RM = VM*TIME A3 = CRE/RM 71 SIGHT = ARSIN(A3) SIGH = SIGT + SIGMT XM = RH * COS(SIGM) YM = RM * SIN (SISM) *************** ******************************************** 200 CONTINUE * *************************** ******************************** *** MISSION RESULT *** KILL = ; TGT MISSED ********************** KILL = 1 ; TGT DESTROYED XDIST = XT-XM YDIST = YT-YM DIST = SQRT(XDIST**2 YDIST**2) IF (DIST . LE.5) KILL = 1 IF (DIST .GT.5J KILL = IF (XM .ST. (XT+30) ) CALL ENDJOB . SORT *********************************************************** ******** OUTPUT AND PLOT CONTROL CARD ********************* *********************************************************** SAMP LE CALL DRWG (1 ,1,XM,YM) CALL DRWG (1 ,2,XT,YT) CALL DRWG (2,1, TIME , DIST) CALL DRWG (3,1, TIME, CRE) CALL DRWG(4, 1, TIME , CRED) CALL DRWG (5, 1, CRE, CRED) CALL DRWG(6,1,TIME ,F) CALL DRWG (7, 1, TIME, U) TERMINAL CALL ENDRW (NPLOT) CONTRL FINTIM=5. 9,DELT=0.00 1,DELS=0. 003 PRINT 0.005, XM,YM, XT, YT, CRE, CRED, DIST, KILL END STOP 72 APPENDIX H PROGRAM OF THE COMMAND TO PSEUDO-LOS WITH TWO-LEVEL RELAY TITLE PSEUDO - LCS COMMAND TITLE WITH TWO-LEVEL RELAY TITLE ***** YEUN, J.Y. ***** INTEG RKSFX INTGER NPLOr,KILL CONST NPLOT=1 ,TCON=1.0 CONST VM=50 0. ,7T = 250, PI = 3. 1 41 5 93, KILL=0 INITIAL XTO = 4 000. YTO = 1000. TG = 0. GAMT = PI F = 0. * *************************** ********************** *********** DERIVATIVE *************************** ********************************* NOSORT ************************* *** TARGET PARAMETERS *** ************************* VTX = VT*COS(GAMT) VTY = VT*SINJGAMIJ XT = VTX*TIME + XTO IT = VTY*TIME YTO SIGT = ArAN2(YT.XT) XLOS = XT VTX*TG YLOS = YT VTY*TG SLOS = ATAN2(YLOS, XLOS) IF (HME.GE.TCON) GO TO 50 ************************* *** MISSLE FARAMEIERS *** ************************* * PROGRAMMED GUIDANCE ************************************** * SIGM = SLOS 0.1 VMX = VM * COS (SIGM) VMY = VM * SIN (SIGM XM = INTGRL(0. ,VMX YM = INTGRLJO..VMY RM = SQRT(XM**2 YM**2) SIGMS = SIGM - SLOS CRE = RM * SIN(SIGMS) CRED = DERIV(0. ,CRE) GO TO 200 *************************** ** * ON-OFF GUIDANCE (BANG-BANG CONTROL) ********************* *************************** ** * 50 CONTINUE * G = 150. ACRE = ABS(CRE) ACRED = ABS(CRED) IF ((ACRE* ACRED) .LT. 1.) G 15. F = CRE (CRED*ACRED)/ (2*3) U = -G * SIGN(1..F) CRED = INTGRLIO.O, U) CRE INTGRL(CRE,CRED ) 73 RM = VM*TIME A3 = CRE/RM SIGMS = ARSIN(A3) SIGH = SLOS SIGMS VMX = VM * COS(SLOS] VMY = VM * SINfSLOS XM = RH * COS (SIGM YM = RM * SIN(SIGM) *************************** ******************************** 200 CONTINUE * *********************************************************** *** MISSION RESULT *** KILL = ; TGT MISSED ********************** KILL = 1 ; TGT DESTROYED XDIST = XT-XM YDISI = YT-YM DIST = SQRT(XDIST**2 + YDIST**2) VC = SQRT ( (VTX-VMX) ** 2+ ( VTY- VMY) **2) TG = DIST/VC IF (DIST .LE.5) KILL = 1 IF (DIST .GT.5) KILL = IF (XM .GT. (XT + 30))CALL ENDJOB * SORT *************************** ******************************** ******** OUTPUT AND PLOT CONTROL CARD ********************* *********************************************************** SAMPLE CALL DRWG (1 , 1,XM,YM) CALL DRWG(1 ,2,XT,YT) CALL DRWG (2, 1,TIME, DIST) CALL DRWG (3,1, TIME, CRE) CALL DRWG(4, 1,TIME,CRED) CALL DRWG(5 ,1,CRE,CRED) CALL DRWG (6,1,TIME,F) CALL DRWG (7,1, TIME , U) TERMINAL CALL ENDRW(NPLOT) CONTRL FINTIM=5. 7,DELT=0.00 1 ,DELS=0.003 PRINT 0. 1,TG, XM, YM , XT, YT, CRE ,C RED, DIST , KILL END STOP m . 1 APPENDIX I PROGRAM OF THE BASIC COMMAND TO LOS WITH SATURATION CONTROL TITLE BASI3 COMMAND TO L.O.S TITLE MISSLE CONTROL TITLE WITH SATORATION CONTROL INTEG RKSFX INTGER NPLOI r KILL- CUR CONST NPLOT=1 ,TCO N-1 0,C UR= CONST VM=5Q0. ,VT= 250, PI= 3. 1 41 5 93, KILL=0 PARAM M = 10. INITIAL XTO = 4000. YTO = 1000. GAMT = PI F = 0. * *************************** ********************************* DERIVATIVE *************************** ********************************* NOSORT ************************* *** TARGET PARAMETERS *** ************************* VTX = VT*COS(GAMT) VTY = VT*SINJGAMT| XT = VTX*TIME + XTO YT = VTY*TIME + YTO SIGT = ATAN2(YT,XI) IF (TIME. GE. ICON) GO TO 50 **************** ********* *** MISSLE PARAMETERS *** ************************* * PROGRAMMED 3UIDANCE ************************************** * SIGM = SIGT+0.1 VXM = VM * COSfSIGM] VYM = VM * SIN (SIGM XM = INTGRLfO. ,VXM YM = INrGRL(0. .VYM} RM = SQRT(XM**2 YM**2) SIGMr SIGM - SIGT CRE = RM * SIN (SI3MT) CRED DERIV(0. ,CRE) GO TO 2 00 *** * ************** ********* ** * ON-OFF GUIDANCE (BANG-BANG CONTROL) ********************* **** **************** ******* ** * 50 CONTINUE * G = 150. ACRED = ABS (CRED) F = CRE (CRED*ACRED)/(2*G) U = -G * SIGN(1.,F) IF (ABS(F) .LT. M) 0= -G*F/M CRED = INTGRL(0.0,U) CRE = INTGRL(CRE,CRED) RM = VM*TIME A3 = CRE/RM SIGMT ARSIN(A3) 75 SIGM = SIGT + SIGMT XM = RM * COS (SIGM) YM = RM * SINfSIGMJ *************#-****##******* ******************************** 200 CONTINUE *************************** ******************************** *** MISSION RESULT *** KILL = ; TGT MISSED ********************** KILL = 1 ; TGT DESTROYED XDIST = XT-XM YDISr = YT-YM DIST = SQRT(XDIST**2 YDIST**2) IF (DIST .LE.5) KILL = 1 IF (DIST .GT.5) KILL = SORT *************************** ******************************** ******** OUTPUT AND PLOT CONTROL CARD ********************* *************************** ******************************** SAMPLE CALL DRWG (1 , CUR, XM.YM) CALL DRWG(2 , CUR, TIME, DIST) CALL DRWG (3 , CUR, TIME, CRE) CALL DRWG (4 ,CUR,CRE,CRED) CALL DRWG (5 , CUR, TIME, F) CALL DRWG (6 , CUR, TIME, U TERMINAL IF (3UR .EQ. 3) CALL ENDRW(NPLOT) CUR = CUR 1 CONTRL FINTIM=5. 65 ,DELT=0. 1 , DELS=3 . 00 3 PRINT 0.005,XM,YM, XT, YT, CRE, CRED, DIST, KILL END PARAM M = 5. END PARAM M = 1. END STOP 76 1 APPENDIX J PROGRAfl OF THE MANEUVERING TARGET IITH SATURATION CONTROL TITLE BASIC COMMAND TO LOS TITLE (MANEUVERING TGT) TITLE WITH SATURATION CONTROL INTEG RKSFX INTGER NPLOr, KILL-CUR CONST NPLOT=1 ,1 CO N=1 . 0, CUR= CONST VM=50 0. ,VT=250, PI a 3 . 1 41 5 93 , KILL=0 PARAM M = 10. INITIAL XTO = 4000. YT0 = 1000. GAMT = PI F = 0. * *********** A************************************* *********** DERIVATIVE *************************** ********************************* NOSORT ************************* *** TARGET PARAMETERS *** ************************* VTX = VT*COS (GAMT) VTY = VT*SINjGAMTJ XT = VTX*TIME XTO YT = 100*SIN(0.5*PI*TIME) +?T0 SIGT = ATAN2JYT,XT) IF (TIME. GE. ICON) GO TO 50 ************************* *** MISSLE PARAMETERS *** ************** *********** * PROGRAMMED GUIDANCE ************************************** * SIGM = SIGT+0.1 VXM = VM * COS (SIGM] VYM = VM * SIN (SIGM XM = INrGRL(0.,VXM YM = INTGRL(0. .VYM) RM = SQRT(XM**2 YM**2) SIGMT = SIGM - SIGT CRE = RM * SIN (SIGMT) CRED = DERIV(0. ,CRE) GO TO 2 00 *************************** ** * ON-OFF GUIDANCE (BANG-BANG CONTR3L) ********************* *************************** ** * 50 CONTINUE G = 150 ACRED = ABSAB (CRED) RE (CRED*ACRED)/(2*G) U = G * SIGN(1.,F) IF (ABS (F) . LT.M) U=-G*F/M CRED = INTGRLfO.OINTGRLfO.O, U) CRE = INTGRL(CR~INTGRL(CRE,CRED) ACRE = ABS (CRE) RM = VM*TIME A3 = CRE/RM 77 SIGHT = ARSIN(A3) SIGM = SIGT « SIGMT XM RM * COS (SIGM) YM = RM * SIN(SIGM) *******#*#*******#**#*##****£#*******#*#****#*$** ********** 200 CONTINUE * *************************** ******************************** *** MISSION RESULT *** KILL = ; TGT MISSED ********************** KILL = 1 ; TGT DESTROYED XDIST = XT-XM YDIST YT-YM DIST = SQRT(XDIST**2 YDISI**2) IF (DIST . LE.5) KILL = 1 IF (DIST .GT.5) KILL = * SORT *************************** ******************************** ******** OUTPUT AND PLOT CONTROL CARD ********************* *********************************************************** SAMP LE CALL DRWG (1 ,CUR,XM,YM) CALL DRWG (2 ,CUR,TI ME, DIST) CALL DRWG (3, CUR, TIME, CRE) CALL DRWG (4 ,CUR,CRE,CRED) CALL DRWG (5, CUR, TIME, F) CALL DRWG (6, CUR, TIME, U) TERMINAL IF (CUR .EQ.3) CALL ENDRW(NPLOT) CUR = CUR + 1 CONTRL FINTIM=5. 65 , DELT=0. 01 , DELS=0 . 00 3 PRINT 0.005, XM,YM, XT, YT, CRE, CRED, DIST, KILL END PARAM M = 5. END PARAM M = 1. END STOP 78 PROGRAM OF THE COMMAND TO PSEUDO-LOS WITH SATURATION CONTROL TITLE PSEODO - LOS COMMAND TITLE WITH SATURATION CONTROL TITLE ***** YEUN, J.Y. ***** INTEG RKSFX INTGE R NPLOT, KILL, CUR CONST NPLOT=1 ,TCON=1.0,CUR=1 CONST VM=50 0. ,VT=250,PI=3.1415 93,KILL=0 PARAM M = 10. INITI AL XTO = 4000. YTO = 1000. TG = 0. GAMT = PI F = 0. * ***** ******************************************************* DERIV ATIVE ***** ********************** ********************************* NOSOR T ***** ******************** *** T ARGET PARAMETERS *** ***** ******************** VTX = VT*COS(GAMT) VTY = VT*SINJGAMT) XT = VTX*TIME + XTO YT = VTY*TIME YTO SIGT = AIAN2(YT,XT) XLOS = XT VTX*T3 YLOS = YT VTY*TG SLOS = ATA N2j YLOS, XLOS) IF (TIME. GE.TCON) GO TO 50 ***** ******************** *** m ISSLE PARAMETERS *** ***** ******************** * PRO GRAMMED GUIDANCE ************************************** * SIGM = SLOS 0.1 VMX = VM * COS (SIGM) VMY = VM *[ SIN(SI3SIN (513 MM) XM = INTGRL;rl(0. ,vmx YM = INTGIRL(0. .VM Y' RM = SQRT'(XM**2 Y M**2) SIGMS = SIGM - SLOS CRE = RM * SIN (SIGMS) CRED = DERIV(0. ,CR E) GO TO 2 00 ***** ********************** ** * ON- OFF GUIDANCE (BANG-BANG CONTR3L ********************* ***************************** * 50 CONTINUE * G = 150. ACRED = ABS(CRED) F = CRE (CRED*ACRED)/(2*3) U = -G * SIGN(1.,F) IF (ABS(F) -LT.M) U = -G * F /M CRED = INTGRLfO.O, U) CRE = INTGRL(CRE,CRED) 79 * RM = VM*TIME A3 = CRE/RM SIGHS = ARSIN(A3) SIGM = SLOS + SI3MS VMX = VM * COS (SLOS] VMY = VM * SIN(SLOS XM = RM * COS (SIGM YM = RM * SIN (SIGM **** * ************* ********* ********************** ********** 200 CONTINUE * *********************************************************** *** MISSION RESULT *** KILL = ; TGT MISSED ********************** KILL = 1 ; TGT DESTROYED XDIST XT-XM YDIST = YT-YM DIST = SQRT(XDIST**2 YDIST**2) VC = SQRTMVTX-VMX) **2+ (VTY-VMY) **2) TG = DIST/VC IF (DIST .LE.5) KILL = 1 IF (DIST .GT.5) KILL = * SORT **************** *** ******** ********************** ********** ******** OUTPUT AND PLOT CONTROL CARD ********************* *************************** ******************************** SAMPL E CALL DRWG (1 ,CUR,XM,YM) CALL DRWG(2 , CUR ,TI ME r DIST) CALL DRWG (3 , CUR, TIME, CRE) CALL DRWG (4 ,CUR ,CR E ,CRSD) CALL DRWG(5, CUR, TIME, F) CALL DRWG (6, CUR, TIME, U) TERMINAL IF (CUR .EQ.3) CALL ENDRW(NPLOT) CUR = CUR 1 CONTRL FINTIM=5. 65 ,DELT=0. 01 ,DELS=0.003 PRINT 0.005,TG,XM, YM, XT, YT, CRE, CRED, DIST, KILL END PARAM M ~ 5. END PARAM H 1. END STOP 80 LIST OF REFERENCES 1. Garnell, P. and East, D.J., Guided weapon Control Systems , p. 134 - 153, Pergamon Press , 1977. 2. Heap, E. , "Methodology of Research into Command-to-L ine-# of-Sight and Homing Guidance", Guidance and Control of Tactical Missile. AGARD Lecture Series No. b2 , T3TZZ 3. Hewitt, Frank F., LCDR, Computer Simulated Development of Improved Command to Line-of-SighT Missile Guidance Techniques . hseE tussis, Naval Postgraduate scnooi, California, March 1979. 4- U.S. Army Foreign Science and Technology Center Report FSTC- 120 2- 75, The Roland-1 ftrmired Self-ProEelled AA Missive System , py Johannes aad Weyand. pi 9 - ZQ, To June 19 76. 5. Thaler, George J., and Pastel, Marvin P., Analysis and - Design of Nonlinear Feedback Control Systems . p. 2b3 28?7 fic5raw-HiIl, 1%2 81 u INITIAL DISTRIB0TI3N LIST No. Copies 1. Defense Technical Information Center 2 Cameron Station Alexandria, Virginia 22314 2. Library, Code 1U2 2 Naval Postgraduate School Monterey, California 93943 3. Department Chairman, Code 62 1 Department of Electrical Engineering Naval Postgraduate School Monterey, Califirnia 93943 4. Division of Foreign Education 3 Department of Personnal Adminstration Headquaters of Korean Air Force Daebang-dong, Ycungdungpo-g Seoul, Korea 5. Professor H. A. Titus, Code 62Ts 5 Department of Electrical Engineering Naval Postgraduate School Monterey, California 9 3943 6. Professor Alex Gerba, Jr., Cods 62Gs 2 Department of Electrical Engineering Naval Postgraduate School Monterey, California 9 3943 7. Academic Dean 1 Air Force Academy Daebang-dong, Youngdun gpo-gu Seoul, Korea 8. LTC. Je Young, Yeun 8 Jamsil 221-4, Gangdong-gu Seoul, Korea 82 . 2 Thesis Yl+5 Yeun c.l Computer simulated development of a com- mand to line-of- sight missile using on-off control. 1 i 25 FEB 86 3 3111 Thesis Y^5 Yeun c.l Computer simulated development of a com- mand to line-of-sight missile using on-off control