SERVOMECHANISMS AND REGULATING SYSTEM DESIGN VOLUME IPDF电子书下载

1 THE AUTOMATIC CONTROL PROBLEM 1

1．0 INTRODUCTION 1

1．1 DESCRIPTION OF FEEDBACK CONTROL SYSTEM 2

Requirements of Stability and Accuracy 4

Mathematical Basis for Stability 5

Features of Feedback Control System Performance 6

1．2 FEEDBACK CONTROL SYSTEM DESIGN 9

Recommended Design Procedure 10

1．3 DEVELOPMENT OF THE FIELD OF FEEDBACK CONTROL SYSTEMS 12

2 MANIPULATION OF COMPLEX NUMBERS 17

2．0 INTRODUCTION 17

2．1 THREE FORMS OF COMPLEX QUANTITLES 18

Rectangular Form 18

Polar Form 19

Exponential Form 20

2．2 FQUIVALENCE OF DIFEFENT FORMS OF COMPLEX NUMBERS 20

2．3 MANIPULATION OF COMPLEX QUANTITIES 22

Addition and Subtractio 22

Multiplication and Divsion 24

Forming the Conjugate 26

Raising to a Power;Extractin a Root 27

Logarithm of a Complex Quantity 28

2．4 EXAMPLE FROM SERVOMECHANISM APPLICATION 28

3 SOLUTION OF LINEAR DIFERENTIAL EQUATIONS 30

3．0 INTRODUCTION 31

3．1 SERIES RESISTANCE-INDUCTANCE NETWORK 31

Classical Solution 32

Transient and Steady-State Form of Solution 33

Summary of the Solution of Differential Equations 35

3．2 CHARACTERISTIC EQUATION 36

3．3 SERIES RESISTANCE-CAPACITANCE NETWORK 37

3．4 TIME CONSTANTS 39

3．5 SERIES RESISTANCE-INDUCTANCE-CAPACITANCE NETWORK 40

3．6 STEADY-STATE RESPONSE TO A SINUSOIDALLY IMPRESSED VOLTAGE 45

Replacing p by jw for Steady-State Sinusoidal Calculations 49

Summary of Method of Obtaining Steady-State Solution for Sinusoidally Impressed Voltages 50

3．7 STEADY-STATE RESPONSE TO A TIME POWER SERIES INPUT 51

3．8 SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS FOR OTHER TYPES OF SYSTEMS 53

Mechanical Spring-Mass System 54

Motor Synchronizing on a Fixed Signal 59

Modification of the Time Constant by Means of Feedback 63

4 LAPLACE TRANSFORMS FOR THE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS 66

4．0 INTRODUCTION 66

4．1 NATURE OF THE LAPLACE TRANSFORM 67

4．2 DEVELOPMENT OF A TABLE OF TRANSFORM PAIRS 68

Constant Input of Magnitude A 69

Step Function ｕ(ｔ) 69

A Damped Exponential:е-αｔ 70

A Time-Varying Sinusoid:sin βｔ 70

A Time-Varying Cosinusoid with a Phase Angle:cos(βｔ+ψ) 70

A Damped Sinusoid:е-αｔ sin βｔ 71

A Quantity That Increases Linearly with Time,ｔ 71

A Function Translated in Time,?(ｔ-α) 72

4．3 TRANSFORMATION OF DIFFERENTIATION AND INTEGRATION OPERATIONS 73

Theorem for Differentiation 74

Theorem for Integration 75

Linearity Theorem 76

Final Value and Initial Value Theorems 77

4．4 APPLICATION OF ￡ TRANSFORM TO SIMPLE CONTROL PROELEMS 78

Position Control 78

Elementary Resistance-Capacitance Network 81

4．5 PERFORMING THE INVERSE LAPLACE TRANSFORMATION 83

4．6 EXAMPLES OF THE INVERSE TRANSFORMATION 85

Factors Having Real Roots 85

One Factor Having a Root at Zero 85

Factors Having Complex Conjugate Roots 86

Factors Having Imaginary Roots 89

4．7 INVERSE TRANSFORMATION FOR REPEATED FACTORS 90

4．8 APPLICATION OF ￡-1 TRANSFORM TO PROBLEMS OF SECTION 4．4 93

Position Control Problem 93

Elementary Resistance-Capactiance Network 95

4．9 APPLICATION OF THE LAPLACE TRANSFORMATION TO SERVOMECHANISM PROBLEMS 96

5 STEADY-STATE OPERATION WITH SINUSOIDAL DRIVUNG FUNCTIONS 99

5．0 INTRODUCTION 99

5．1 IMPDNANCE CONCEPT 100

5．2 IMPEDNNCE OF INDIVIDUAL ELEMENTS 101

5．3 AIDS TO SIMPLIFYING CIRCUIT COMPUTATIONS 103

Equivalent Impedance 103

Wye-Delta Transformations 104

Superposition 105

Théveini＇s Theorem 108

5．4 PERFORMANCE AS A FUNCTION OF FREQUENCY 110

Resistance-Inductance Circuit 110

Resistance-Capacitance Circuit 112

Direct-Current Shunt Motor with Constant Field Excitation 113

Mechanical Spring-Mass System 117

5．5 ATTENUATION AND PHASE ANGLE REPRESENTATION OF SYSTEM PERFORMANCE FOR SINUSOIDAL EXCITATION 118

Definitions of Attenuation Terms 119

Illustrations of Attenuation Phase Representation as a Function of Frequency 121

6 METHODS OF DETERMINING SYSTEM STABILITY 124

6．0 INTRODUCTION 124

6．1 STABILITY 125

6．2 DETERMINING THE ROOTS OF THE CAHRACTERISTIC EQUATION 128

Formation of the Charaeteristic Equation from Its Roots 129

Quadratic 130

Cubic 130

Quartic 131

Quintic 133

6．3 ROUTH＇S CRITERION FOR STABILITY 134

Examples of the Use of Routh＇s Stability Criterion 136

Change in Scale Factor of Characteristic Equation 136

6．4 THE NYQUIST STABILTY CRITERION 138

Development of the Characteristic Equation in Terms of Transfer Functions 139

Method of Applying the Nyquist Stability Criterion 141

Limitations to the Generalized Nyquist Stability Criterion 141

Angular Change Produced by the Presence of Roots in the Positive Real Portion of the Complex Plane 142

Angular Change Produced by the Presence of Poles at the Origin 146

6．5 APPLICATION OF THE NYQUIST STABILITY CRITERION TO TYPICAL SYSTEM TRANSFER FUNCTIONS 149

7 TYPICAL CONTROL ELEMENTS AND THEIR TRANSFER FUNCTIONS 157

7．0 INTRODUCTION 157

7．1 DESCRIPTION OF THE CONTROL PROBLEM 157

7．2 DEFINITION OF CONTROL SYSTEM ELEMENT TRANSFER FUNCTION 161

7．3 COMBINATION OF CONTROL SYSTEM ELEMENTS IN SERIES 163

7．4 TRANSFER RUNCTIONS OF TYPICAL MECHANICAL CONTROL ELEMENTS 164

Mechanical Elements Having Rotary Motion 164

Mechanical Elements Having Translatory Motion 169

Spring-Dashpot Elements Used to Obtain Mechanical Displaeements 170

7．5 TRANSFER FUNCTIONS OF TYPICAL ELECTRICAL CONTROL SYSTEM ELEMENTS 172

Direct-Current Motor-Generator Control 173

Torque Motor Type Servomechanism Elements 175

ELectrical Networks Used for Stabilizing Purposes 177

7．6 TRANSFER FUNCTIONS OF TYPICAL HYORAULIC CONTROL ELEMENTS 179

Hydraulic Valve-Piston Transfer Functions for Two Common Types of Operation 179

Transfer Functions for Various Valve-Piston Linkage Combinations 181

Hydraulic Motor with Variable Displacement Hydraulic Pump 184

7．7 TRANSFER FUNCTIONS OF STEERING SYSTEMS 187

Ship-Steering Transfer Function 187

Transfer Function of Controlled Missile in Vertical Flight 190

7．8 CONCLUSIONA 192

8 TYPES OF SERVOMECHANISM AND CONTROL SYSTEMS 194

8．0 INTRODUCTION 194

8．1 DEFINITION OF FEEDBACK CONTROL SYSTEM NOMENCLATURE AND SYMBOLS 195

Block Diagram 197

8．2 EFFECT OF FEEDBACK ON CHANGES IN TRANSFER FUNCTION 199

8．3 TYPES OF FEEDBACK CONTROL SYSTEMS 202

Type 0 Servomechanism 205

Type 1 Servomechanism 208

Type 2 Servomechanism 212

8．4 SERVOMECHANISM ERROR COEFFICIENTS 215

Statie Error Coefflcients 216

Dynamic Error Coefficients 218

9 COMPLEX PLANE REPRESENTATION OF FEEDBACK CONTROL SYSTEM PERFORMANCE 221

9．0 INTRODUCTION 221

9．1 COMPLEX PLANE DIAGRAM FOR REEDBACK CONTROL SYSTEM WITH SINUSOIDAL INPUT 222

9．2 DEVELOPMENT OF LOCI OF CONSTANT M AND α 225

9．3 CLOSED-LOOP FREQUENCY RESPONSE AND ERROR RESPONSE FROM COMPLEX PLANE PLOT 229

9．4 METHOD FOR SETTING GAIN FOR SPECIFIED Mm 233

9．5 INVERSE COMPLEX PLANE PLOT 236

Inverse Plot for General Feedback Control System 236

Inverse Transfer Function Plot for Systems with Direct Feedback 238

9．6 LOCI OF CONSTANT 1/M AND-α 241

9．7 COMPARATIVE USERULNESS OF DIRECT AND INVERSE PLOTS 244

10 DESIGN USE OF COMPLEX PLANE PLOT TO IMPROVE SYSTEM PERFORMANCE 245

10．0 INTRODUCTION 245

10．1 SERIES NETWORK APPROACH TO SYSTEM DESIGN 246

Use of Phase Lag Networks 249

Use of Phase Lead Networks 255

Use of Lead-Lag Series Networks 264

10．2 FEEDBCAK METHODS FOR USE IN SYSTEM DESIGN 270

Direct Feedback 270

Feedback through Frequency-Sensitive Elements 273

Basis for Determining Characteristics for Feedback Elements 278

Regenerative Feedback 285

10．3 COMPARISON OF RELATIVE MERITS OF SERIES AND FEEDBACK METHODS OF SYSTEM STABILIZATION 288

Series Stabilization 289

Feedback Stabilization 289

11 ATTENUTION CONCEPTS FOR USE IN FEEDBACK CONTROL SYSTEM DESIGN 291

11．0 INTRODUCTION 291

11．1 CORRELATION OF THE NYQUIST STABILITY CRTETION WITH BODE＇S ATTENUATION THEOREMS 292

11．2 TWO OF BODE＇S THEOREMS 297

Theorem 1 299

Theorem 2 301

11．3 MECHANICS OF DRAWING ATTENUATION DIAGRAMS FOR TRANSFER FUNCTIONS 302

Single Time Constant 302

Complex Roots or Time Constants 310

11．4 APPLICATION OF ATTENUATION DIAGRAMS TO TYPICAL CONTROL SYSTEM TRANSFER FUNCTIONS 315

Velocity Error Coefficient Obtainable from Attenuation Diagram 316

Acceleration Error Coefficient Obtainable from Attenuation Diagram 317

11．5 CONTOURS OF CONSTANT M AND α LOCI 318

11．6 CONCLUSION 325

12 APPLICATION OF ATTENUATION-PHASE DIAGRAMS TO FEEDBACK CONTROL DESIGN PROBLEMS 327

12．0 INTRODUCTION 327

12．1 EXAMPLES OF SERIES STABILIZATION NETHODS 328

Phase Lag Networks 328

Phase Lead Networks 330

Lead-Lag Networks 334

12．2 EXAMPLES OF FEEDBACK STABILIZATION METHODS 336

Attenuation-Frequency Chatacteristic for Direct Feedback 337

Attenuation-Frequency Characteristic with Feedback through Frequency-Sensitive Element 339

12．3 ATTENUATION-FREQUENCY DIAGRAM NOMENCLATURE 345

Equalization 345

Conditional Stability 346

12．4 APPLICATION OF NICHOLS CHARTS TO OBTAIN CLOSED-LOOP PERFORMANCE 347

12．5 MORE EXACT FEEDBACK CONTROL SYSTEM REPRESENTATION OF ATTENUATION,PHASE MARGIN CHARACTERISTICS 350

System Compoesd of Series Elements 350

system with Feedback Stabilization 351

13 MULTIPLE-LOOP AND MULTIPLE-INPUT FEEDBACK CONTROL SYSTEMS 358

13．0 INTRODUCTION 358

13．1 DESIGN OF MORE COMPLEX SYSTEMS 359

Series Modification of Transfer Function 359

Inclusion of a Servomechanism in a More Comprehensive Control System 360

13．2 MULTIPLE INPUTS AND LOAD DISTURBANCES 363

General Case of Multiple Inputs 363

Multiple-Position Inputs 365

Responseto Input Signal and Load Disturbance 367

A Regulator-Type Problem 370

13．3 EQUIVALENT BLOCK DIAGRAM REPRESENTATION 373

Equivaleut Block Diagram of Stabilizing Transformer 373

Simplifying Interconnected Multiple-Loop Systems 375

13．4 POSITON CONTROL SYSTEM WITH LOAD DISTURBANCE 377

Determination of C/R 377

Determination of C/TL 383

13．5 VOLTAGE REGULATOR WITH LOAD DISTURBANCE 388

Determination of C/R=(ET/D) 390

Determination of C/Q=(ET/EL) 395

14 COMPARISON OF STEADY-STATE AND TRANSIENT PERFORMANCE OF SERVOMECHANISMS 398

14．0 INTRODUCTION 398

14．1 DESCRIPTION OF SERVOMECHANISM BEING CONSIDERED 400

Definition of Terms Used to Describe System Performance Characteristice 400

Open-Loop Attenuation-Frequency Characteristics 403

14．2 PFFECT OF ωc ON FREQUENCY RESPONSE AND TRANSIENT RESPONSE 405

14．3 COMPARISON OF STEADY-STATE AND TRANSIENT PERFORMANCE CHARTS 406

Effect of Using Parameter ω1/ωc for Abscissa 406

Comparisen of Maximum Steady-State Value[C/R｜m]and Peak Transient Value[C/R｜p]of Output-Input Ratio 407

Comparison of Frequency ωm at Which C/R｜m Occurs to ωt,the Lowest Frequency Oscillatory Term of the Transient Response 408

Time tp at Which Peak Overshoot Occurs 409

Settling Time ts to Reach 5 Per Cent of Final Value 410

Use of Figures 14．3-7 to 14．3-23 for Systems Other than Those Having a Single Integrating Element in the Controller 413

Effect of Having Non-multiple Breaks in Open-Loop Attenuation Characteristics 415

Choice of Attenuation Rates between ω1 and ω2 and ω3 and ∞ 416

14．4 EXAMPLES 435

Charts Used for System Analysis 435

Charts Used for System Synthesis 438

14．5 CONCLUSION TO VOLUME I 439

BIBLIOGRAPHY 441

PROBLEMS 447

INDEX 499