Engineering Design Handbook - Fire Control Series Section 3, Fire Control Computing Systems

448 Pages·1970·21.752 MB·English

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AMCP-706-329
AMC PAMPHLET AMCP 706-329
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ENGINEERING DESIGN
HANDBOOK
FIRE CONTROL SERIES
REDSTONE SCIENTIFIC INFORMATION CENTER
SECTION 3
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FIRE CONTROL
COMPUTING SYSTEMS
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HEADQUARTERS, U.S. ARMY MATERIEL COMMAND OCTOBER 1970
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tiEADQUARTERS
UNITED STATES ARMY MATERIEL COMMAND
WASHINGTON, D. C. 20315
AMC PAMPHLET 13 °ctober 1970
No. 706-329 ENGINEERING DESIGN HANDBOOK
SECTION 3, FIRE CONTROL COMPUTING SYSTEMS
Paragraph Page
UST OF ILLUSTRATIONS x
UST OF TABLES xvii
LIST OF EXAMPLES xviii
UST OF INFORMATION SUMMARIES xix
LIST OF DERIVATIONS xx
ACKNOWLEDGMENTS xxi
FOREWORD xxii
PREFACE xxiv
INTRODUCTION I- 1
PART I. MATHEMATICAL MODELS FOR FIRE CONTROL
COMPUTING SYSTEMS
CHAPTER 1. THE ROLE OF THE MATHEMATICAL MODEL IN THE DESIGN PROCESS
1-1 DEFINITION AND IILIFORTANCE OF A MATHEMATICAL MODE! 1-1
1-2 MATHEMATICAL MODELS FOR PHYSICAL SYSTEMS 1-1
1-3 CHARACTERISTICS AND LIMITATIONS OF MATHEMATICAL MODELS. 1-7
APPENDIX: PHYSICAL CONSTANTS AND CONVERSION F\CTORS ... 1-11
REFERENCES 1-15
CHAPTER 2. DETERMINATION OF THE ACCURACY AND DYNAMIC RESPONSE
OF A SYSTEM FROM STUDIES OF ITS MATHEMATICAL MODEL
2-1 INTRODUCTION 2-1
2-2 MATHEMATICAL TECHNIQUES 2-1
2-2.1 GENERAI 2-1
2-2.2 LINEAR-DIFFERENTIAL-EQiiATTON THEORY 2-2
2-2 3 FREQUENCY-IX)MAIN ANALYSIS 2-2
2-2.3.1 Laplace and Fourier Transforms , . 2-2
2-2.3.2 Useful Theorems 2-3
2-2.3.3 Solution Procedure 2-ö
2-2.4 FREQUENCY-RESPONSE. TECHNIQUES 2-10
2-2.5 BLOCK DIAGRAMS AX I) SIGNAL-FLOW GRAPHS 2-11
2-2.5.1 Block Diagrams 2-11
2-2.5.2 Signal-Flow Graphs •. 2-15
2-2.6 STATISTICAL, THEORY 2-20
2-2.7 NONLINEAR ANALYSIS 2-24
2-2.7.1 General 2-24
2-2.7.2 Nonlinearities Eound In Many Control Systems 2-27
2-2.7.2.1 Limiting 2-27
2-2.7.2 .2 Dry Friction 2-2 7
2-2.7.2.3 Hysteresis 2-27
2-2.7.2.4 Relays • 2-28
2-2.7.2.5 Diodes 2-28
2-2.7.2.6 Orifices 2-28
2-2.7.2.7 Products and Transcendental Functions 2-28
2-2.7.3 Classification of Nonlinear Systems 2-20
2-2.7.3.1 Continuous and Discontinuous Nonlinearities , 2-2!'
2-2.7.3.2 Incidental and Essential Nonlinearities 2-29
2-2.7.3.3 Zero-Memory and Nonzero-Memory Nonlinearities 2-29
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2- ■2.7.3.4 Phenomena Peculiar to Nonlinear Systems 2-30
2- -3 SIMULATION TECHNIQUES 2-30
2-- 3.1 GENERA! 2-30
2-- 3.2 ANALOG TECHNIQUES 2-30
2-- 3-3 DIGITAL TECHNIQUES 2-31
2-- 4 NUMEKICAT. TECHNIQUES 2-32
2-- 4.1 GENERAL 2-32
2-- 4.2 REPRESENTATION OE MATHEMATICAL FUNCTIONS 2-33
2-- 4.2.1 Iteration 2-33
2- -4.2.2 Series Approximation 2-34
2- -4.2.3 Interpolation 2-34
2- -4.2.4 Curve Fitting 2-37
2- -4.3 NUMERICAL DIFFERENTIATION 2-44
2- -4.4 NUMERICAL INTEGRATION 2-45
2- -4.5 METHODS FOR SOLVING DIFFERENTIAL EQUATIONS 2-46
2- -4.6 METHODS FOR SOLVING SYSTEMS OF LINEAR ALGEBRAIC
EQUATIONS 2-63
REFERENCES 2-66
GENERAL BIBLIOGRAPHY OF BOOKS AND PAPPUS RELATING
TO NONLINEAR SYSTEMS 2-68
Describing Functions 2-68
Nonlinear Differential Equations 2-68
PART II. COMPUTING DEVICES USEFUL IN FIRE CONTROL SYSTEMS
CHAPTER 3. THE CLASSIFICATIONS OF COMPUTING DEVICES
USED IN FIRE CONTROL SYSTEMS
3_1 INTRODUCTION 3-1
3-1.1 CHARACTERISTICS OF FIRE CONTROL COMPUTERS 3-1
3-1.2 CLASSIFICATION SCHEMES 3-1
3-1.3 BASIC COMPUTER CONCEPTS 3-2
3-1.4 USER CLASSIFICATIONS. 3-2
3-1.5 DESIGNER CT ASSI[ TCATIONS 3-2
3-2 MANUAL COMPUTING DEVICES 3-3
3-2.1 FIRING TABLES 3-3
3-2.2 NOMOGRAMS 3-4
3-3 MANUALLY OPERATED AUTOMATIC COMPUTERS 3-4
3-4 AUTOMATIC COMPETING DEVICES 3-4
3-5 DIGITAL, DIGITAL DIFFERENTIAL ANALYZER, AND
ANALOG COMPUTING DEVICES 3-5
3-6 TYPES OF PHYSICAL EQUIPMENT EMPLOYED IX COMPUTERS . . . 3-6
3-7 SPECIAL- PURPOSE AND MULTIPURPOSE COMPUTING DEVICES. . . 3-7
REFERENCES 3-7
CHAPTER 4. DIGITAL COMPUTERS
4-1 INTRODUCTION „ 4-1
4-1.1 DEFINITION OF A DIGITAL COMPUTER 4-1
4-1.2 NUMBER SYSTEMS 4-2
4-1.3 FUNCTIONAL FARTS OF A DIGITAL MACHINE 4-2
ii
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4-2 SYSTEM DESIGN 4-8
4-2.1 EQUATIONS TO BE SOLVED 4-8
4-2.2 USE OF NUMERICAL ANALYSIS AND OTHER
MATHEMATICAL TECHNIQUES 4-8
4-2.3 ACCURACY AN!) RESPONSE TIME 4-11
4-2.4 USE OF SAMPLED-DATA THEORY 4-12
4-3 THE GENERAL CON1 FIGURATION OF A FIRE CONTROL
DIGITAL COMPUTER 4-13
4-3.1 INPUT AND OUTPUT CONSIDERATIONS 4-14
4-3.2 COMPUTER SPEEDS 4-19
4-4 DETERMINATION OF COMPUTER STORAGE CONFIGURATION . ... 4-20
4-4.1 SIZE OF COMPUTER PROGRAM 4-20
4-4.2 CODING SYSTEM AND WORD LENGTH 4-2 5
4-4.3 SUBROUTINES. REQUIREMENTS FOR TEMPORARY STORAGE. . . 4-29
4-4.4 DATA STORAGE REQUIRE MFNTS 4-2?
4-4.5 EXAMPLE OF FA DAC MEMORY 4-29
4-5 FLEXIBILITY REQUIREMENTS 4-30
4-5.1 SPECIAL-PURPOSE VERSES GENERAL- PURPOSH COMPUTERS . . 4-30
4-5.2 CHOICII OF BUILT-IN COMPUTER OPERATIONS 4-30
4-5.3 CHOICE OF PROGRAMMING SYSTEMS 4-31
4-6 COMF1 TER T\PFS 4-32
4-6.1 S\ NCHRONOUS AND ASYNCHRONOUS 4-32
4-6.2 WIJOLE-TRANSITR AND INCREMENTAL COMPUTERS 4-37
4-6.3 OPERATIONAL COMPUTERS 4-37
4-6.3 COMPUTERS AS SERVO ELEMENTS 4-37
4-7 TYPICAL DIGITAL COMPUTER 4-38
4-8 T. OGICAI DESIGN 4-41
3-i) COMPUTER NUMBER SYSTEMS 4-46
4-!).l BINAEO SYSTEM 4-46
4-9.2 BINARY CODES 4-46
4-9.2.1 Reflected Binary (Gray) Code 4-46
4-9.2.2 Decimal Codes 4-46
4-9.2.3 Error-detecting and Correcting Codes 4-48
4-10 CLASSES OF COMPUTER LOGIC 4-49
.3-11 PRE1XYMINANT LOGICAL COMBISATIONS 4-51
4-11.1 GATES 4-5t
4-11.2 FLIP-FLOPS. 4-53
4-11.3 ADDERS AND SUBTRACTERS 4-53
4-11.3.1 Half-adder. 4-53
4-11.3.2 Full-adder 4-53
4- 11.3.3 Accumulator 4-5 3
4-11.3.4 Serial and Parallel Adders 4-57
4-11.3.5 Simultaneous Carry Techniques 4-57
4-11. i.6 Subtracters 4-57
4-11.4 MULTIPLIERS AND DIVIDERS 4-57
4-11.5 MATRLX MEMORIES 4-59
4-11.6 COUNTERS 4-5 9
4-11.7 ARITHMETIC UNITS 4-59
4-12 CIRCUIT COMPONENTS 4-59
4-12.1 VACUUM TUBES 4-59
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4-12.2 SEMICONDUCTORS . 4-60
4-12.3 MAGNETIC DEVICES 4-67
4-12.4 NEW DEVELOPMENTS 4-67
4-13 STORAGE 4-68
4-13.1 SEQUENTIAL-ACCESS STORAGE_______________ 4-68
4-13.1.1 Magnetic Sequential Storage 4-68
4-13.1.1.1 Magnetic Drums 4-68
4-13.1.1.2 Magnetic Discs . - . , 4-68
4-13.1.1.3 Magnetic Tape 4-68
4-13.1.2 Delay-line Storage 4-70
4-13.1.3 Punched Paper Tape and Cards 4-72
4- 13.1.4 Photoelectric Storage. . « > , 4-72
4-13.2 RANDOM-ACCESS STORAGE , , , , , , , , . . , 4-72
4-13.2.1 Magnetic Core and Other Coincident-current Devices»™™—————— 4-72
4-13.2.2 Diode-capacitor Storage 4-74
4-13.2.3 Cathode-ray-tube Electrostatic-mosaic Storage 4-75
4-13.2.4 Photoelectric Storage 4-75
4-13.2.5 Ferroelectric Storage - _ _ __—. — > > 4-75
4-14 CONSTRUCTION PRACTICES . . „ , _ __ __ , , , «=, 4-75
4-14.1 COMPONENT SELECTION 4-75
4-14.2 PACKAGING TECHNIQUES (MINIATURIZATION) 4-75
4-14.3 MICROMINIATURIZATION 4-76
REFERENCES 4-77
CHAPTER 5. DIGITAL DIFFERENTIAL ANALYZERS
5_1 INTRODUCTION 5-1
5_2 LOGICAL CIRCUITRY 5-3
5-3 SOLUTION OF DIFFERENTIA I EQUATIONS 5-8
5_4 SCALING 5-10
5-5 ERRORS IN THE DDA 5-12
5-6 DDA COMPONENTS, CIRCUITS, AND HARDWARE 5-15
REFERENCES 5-18
CHAPTER 6. ANALOG COMPUTERS
6-1 1\'PRODUCTION. 6"!
5-1.1 SOLUTION OF EQUATIONS PA ANA FOG MEANS . 6-2
6-1.2 Common Mechanical and Elect rical Analogs. . . 6-2
6-1.3 Block Diagrams 6-4
6-1.4 Analog Computer Diagrams 6-9
6-1.5 Analog Solution of Differential Equations 6-11
6-1.6 TYPES OF ANALOG COMPUTERS 6-13
6-1.7 Electromechanical and Electronic Analog Computers 6-13
6-1.8 A-C Type 6-14
6-1.9 D-C Type 6-15
6-1.10 Electrical Analog Computers 6-15
6-1.11 Mechanical Analog Computers 6-16
6-2 ANALOG SOLUTION OF EQUATIONS . , . . . , , 6-16
6-2.1 BASIC SOLUTION METHODS 6-16
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6-2.2 Ordinary Differential Equations 6-16
6-2.3 Simultaneous Linear Equations 6-18
6-2.4 Nonlinear Algebraic Equations 6-19
6-2.5 Partial Differential Equal ions 6-20
6-2.6 SCALE FACTORS A N I) TIME SCALES 6-21
6-2.7 LINEAR OPERATIONS 6-24
6-2.8 Scale Changing 6-24
6-2.9 Summation 6-25
6-2.10 Integration 6-25
6-2.11 Synthesis of Rational Transfer Functions 6-27
6-2.12 NONLINEAR OPERATIONS 6-32
6-2.13 Multiplication and Division 6-32
6-2.14 Vector Resolution 6-33
6-2.15 Direction Cosines 6-34
6-2.16 Euler Angles 6-35
6-2.17 Generation of Arbitrary Nonlinear Functions 6-40
6-3 ELECTRONIC DIFFER ENTIAl. ANAI.ZZER S 6-43
6-3.1 OPERATIONAL AMPLIFIERS 6-43
6-3.2 MULTIPLIERS 6-45
6-3.3 Time-division Multiplier 6-47
5-3.4 Quarter-square Multiplier 6-48
6-3.5 FUNCTION GENERATORS 6-48
6-3.6 DECISION UNITS 6-49
6-3.7 1NPUT-OUTPI T EQUIPMENT 6-52
6-3.8 Input Equipment 6-52
6-3.9 Reference Voltage Supplies 6-52
6-3.10 Noise Generators 6-52
6-3.11 Output Equipment 6-55
S-4 MECHANICAL AND ELECTROMECHANICAL DIFFERENTIAL
ANALYZERS 6-55
6-4.1 SUMMATION DE\ ICES 6-55
6-4.2 INTEGRATORS 6-55
6-4.3 MULTIPLIERS ANI) DIVIDERS 6-57
6-4.4 rileehanieal Multipliers 6-57
6-4.5 Servomultipliers 6-58
6-4.6 Mechanical Dividers 6-59
6-4.7 Electromechanical Dividers 6-60
6-4.8 COORDINATE-SYSTEM CON\ ERTERS 6-60
6-4.9 Mechanical Converters 6-61
6-4.10 Electromechanical Converters 6-61
6-4.11 Three-dimensional \ cctor Resolution by Computers 6-62
6-4.12 FUNCTION GENERATORS 6-67
6-4.13 Mechanical Trigonometric Generators 6-67
6-4.14 Electrical Trigonometric Generators 6-67
6-4.15 Arbitrary Function Generators 6-69
6-4.16 Cams and Noncircular Gears 6-70
6-4.17 Linkage Mechanisms 6-70
6-4.18 Special Potentiometers 6-71
6-4.19 Electromechanical Curve Readers 6-71
6-5 COMPLETE COMPUTERS 6-71
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6-5.1 POWER SUPPLIES 6-72
6-5.2 Filament Power Supplies 6-72
6-5.3 High-voltage D-C Supplies 6-73
6-5.4 Relay Supplies 6-78
6-5.5 A-C Supplies 6-78
6-5.6 Grounding Systems 6-80
6-5.7 PATCHING AND PROGRAMMING EQUIPMENT 6-80
6-5.8 Patching Equipment 6-81
6-5.9 Programming Equipment 6-82
6-5.10 OUTPUT AND OVERLOAD EQUIPMENT 6-85
6-5.11 Strip Recorders 6-85
6-5.12 Plotting Tables 6-87
6-5.13 Oscilloscopes 6-88
6-5.14 Servo and Digital Voltmeters 6-89
6-5.15 Overload Indication Circuits 6-90
6-5.16 CONSTRUCTION TECHNIQUES ANI) MAINTENANCE
CONSIDERATIONS 6-90
6-5.17 Maintenance and Checking 6-91
6-5.18 Maintenance 6-91
6-5.19 Checking 6-92
6-5.20 ENVIRONMENTAL EEE'ECTs 6-92
6-5.2 1 Size, Weight, and Power Considerations 6-92
6-5.22 Temperature. Humidity, Altitude. Shock, and Vibration 6-93
APPENDIX: THE BASIC OPERATIONS OF MATRIX ALGEERA .... 6-94
REFERENCES 6-98
GENERAL DTBLIOGRAPTIY FOR ANALOG COMPUTERS 6-99
CHAPTER 7. ANALOG-DIGITAL CONVERSION TECHNIQUES
7_1 PURPOSE OK CONVERSIONS 7-1
7-2 CONVERSION OF AN ANALOG VOLTAGE TO A DIGITAL OUTPUT . . 7-1
7-2.1 COMPARISON CIRCUITS 7-1
7-2.1.1 Level-at-a-time Voltage-to-digital Encoders 7-1
7-2.1.2 Digit-at-a-time Voltage-to-digital Encoders 7-5
7-2.2 THE LOGIC USE D TO OPTIMIZE THE SPEED OF CONVERSION . . 7-7
7-2.3 TJIE USE OF SERVOS WITH SHAFT ENCODERS 7-8
7-2.4 STEPPIiNG SWITCHES, RELAYS, AND TRANSISTOR SWITCFIES
FOR A D CONVERSION 7-8
7-3 CONVERSION OF MECHANICAL MOTION TO A DIGITAL OUTPUT . . 7-8
7-3.1 COMMUTATOR-TYPE ENCODING DISCS ANI) DRUMS 7-8
7-3.2 MAGNETIC ENCODERS 7-9
7_3.3 PHOTOELECTRIC ENCODERS 7-11
7-3.4 CODES ANI) ERUSTT (READING HEAD) ARRANGEMENTS
EMPLOYED 7-11
7-4 CONVERSION OF' A DIGITAL SIGNAL TO AN ANALOG VOLTAGE ... 7-11
7-5 CONVERSION OF A DIGITAL SIGNAL TO MECTTANICAL MOTION ... 7-16
REFERENCES 7-17
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CHAPTER 8. ANALOG-DIGITAL COMPARISONS
8-1 BASIS OF COMPARISON. . . '. 8-1
8-2 COMPARISONS BASED ON THE SPEED WITH WIIICTT
SOLUTIONS ARE OBTAINED 8-1
8-3 COMPARISONS BASE]; ON THE ACCURACY OF THE
SOLUTIONS OBTAINED 8-3
8-4 COMPARISONS BASED ON THE COMPLEXITY OF TITE
COMPUTING DEVICES INVOLVE11 8-4
8-5 COMPARISONS BASED ON TITE RELIABILITY OBTAINABLE 8-4
8-6 COMPARISONS BASED OK TITE NATURE OF ENVIRONMENTAL
EFFECTS 8-6
8-7 COMPARISONS BASED ON COST. SIZE. WEIGHT. AND
POWER CONSIDERATIONS 8-6
REFERENCES 8-7
CHAPTER 9. RELIABILITY AND CHECK-OUT PROCEDURES
9-1 INTRODUCTION 9-1
9-2 EFFECT OF ENVIRONMENT ON RELIABILITY 9-2
9-3 LOGICAL DESIGN OF COMPUTERS TO OBTAIN TILE DESIRED
DEGREE OF RELIABILITY 9-3
9-4 COMPUTER CHECK-OUT PROCEDURES AND EQUIPMENT 9-8
9-4.1 MAINTENANCE 9-8
9-4.2 MARGINAL CHECKING 9-8
9-5 SPECIAL-PURPOSE CHECK-OUT EQUIPMENT 9-9
9-5.1 GENERAL DESCRIPTION 9-9
9-5.2 DETAILED DATA 9-10
9-5.3 BASIC ELEMENTS 9-13
9-5.4 GENERAL. METHOD OF OPERATION 9-15
9-6 MICANS AND FACTORS TO BE CONSIDERED IN VERIFYING
THE DESIGN OF REAL-TIME FIRE CONTROL COMPUTERS 9-15
9-7 CONCLUSION 9-16
REFERENCES •. 9-17
PART III. THE REALIZATION OF A PROTOTYPE FIRE CONTROL SYSTEM
BASED UPON A MATHEMATICAL MODEL
CHAPTER 10. PROBLEMS ASSOCIATED WITH THE MECHANIZATION
OF MATHEMATICAL MODELS
10-1 KINDS OF PROBLEMS ASSOCIATED WITH MECHANIZATION 10-1
10-2 COVERAGE OF REMAINDER OF PART III 10-2
CHAPTER 11. CHARACTERISTICS PECULIAR TO COMPUTERS
USED FOR FIRE CONTROL APPLICATIONS
11-1 OVERALL DESIGN. 11-1
11-1.1 MECHANICAL ANALOG COMPUTERS H_l
11-1.2 ELECTROMECHANICAL ANAL.OG COMPUTERS ii_
2
11-1.3 OTHER COMPUTER TYPES ii_
3
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11- -2 INPUT-OUTPUT CONSIDERATIONS 11-3
11- -2.1 SOURCESOF DATA 11-3
11- -2.2 TRANSMISSION OF DATA 11-4
11 -3 TIME-RESPONSE CONSIDERATIONS 11-5
11-■ 3.1 REAL-TIME COMPUTATION 11-5
11- -3.2 CONSIDERATIONS ASSOCIATED WITH THE DESIGN O F
ANALOG COMPUTERS FOR REAL-TIME OPERATION 11-9
11-3.3 CONSIDERATIONS ASSOCIATED WITH THE DESIGN OF
DIGITAL COMPUTERS FOR REAL-TIME OPERATION 11-12
11-4 ACCURACY CONSIDERATIONS 11-13
11-4.1 GENERAL CONCEPTS 11-13
11-4.2 THE ACCURACY OF SOLUTIONS OBTAINED
FROM ANALOG COMPUTERS 11-16
11-4.3 THE ACCURACY OF SOLUTIONS OBTAINED
FROM DIGITAL COMPUTERS 11-19
11-5 OPERATIONAL CONSIDERATIONS 11-21
REFERENCES 11-22
CHAPTER 12 . EXAMPLES OF MEANS USED TO MEET PARTICULAR
TYPES OF DESIGN PROBLEMS
12-1 INTRODUCTION 12-1
12-2 GUN DATA COMPUTER T29E2 ■ 12-1
12-3 LIGHTWEIGHT FIRE CONTROL EQUIPMENT
FOR ROCKET LAUNCHERS. . 12-5
12-4 VIGILANTE COMPUTER GYRO/PLATFORM SYSTEM 12-7
12-5 MARK 20 GYRO COMPUTING SIGHT 12-12
12-5.1 COMPUTATION OF LEAD 12-17
12-5.2 TIME OF FLIGHT AND MAGNET CURRENT 12-18
12-5.3 COMPUTATION OF STJPERELEVATION 12-18
12-5.4 DISPLACEMENT OF THE LINE OF SIGHT 12-20
12-5.5 FUNCTIONS OF THE SIGMA FACTOR 12-22
12-6 CANT-CORRECTION SYSTEM OF BALLISTIC COMPUTER XM17 . . . .12-23
12-6.1 BACKGROUND OF BALLISTIC COMPUTER XM17 12-23
12-6.2 THE DESIGN USED FOR THE CANT-CORRECTION SYSTEM 12-24
12-6.3 ACCURACY ANALYSIS OF THE CANT-CORRECTION SYSTEM . . . .12-29
12-6.4 FACTORS TOBE CONSIDERED BEFORE
UNDERTAKING AN IMPROVED DESIGN 12-37
Appendix
12-1 THE MATHEMATICS OF LEAD COMPUTATION 12-38
12-2 CALIBRATION CHARACTERISTICS OF GUN SIGHT MARK 20
MOD 6 AND DATA ON LEAD ANGLE AND TIME OF FLIGHT
FOR 20 MM BALLISTICS 12-41
REFERENCES 12-49
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CHAPTER 13. EXAMPLE OF A PROBLEM INVOLVING THE
INTERCONNECTION OF A COMPLEX SYSTEM
13- 1 INTRODUCTION 13-1
13-2 TRAJECTORY COMPUTATIONS • . . . 13-2
13-3 COMPUTER DESIGN 13-4
13-4 CONCLUSIONS 13-9
INDEX IN-1