《PRINCIPLES OF AUTOMATIC CONTROL》

Preface7

Part One CLOSED LOOP CONTROL1

1．The Fundamentals and Applications of Closed Loop Contro1

1.1 A brief history of automatic control3

1.2 The principle of closed loop control4

1.3 Modes of automatic control8

1.4 Terminology10

1.5 Some examples of the application of closed loop control12

2．The Analytic Viewpoint14

2.1 The need for analysis14

2.2 Mathematical models14

2.3 The feedback amplifier16

2.4 System performance17

2.5 Methods of analysis19

Part Two ANALYSIS AND DESIGN OF LINEAR SYSTEMS23

3．Differential Equation Analysis23

3.1 Application to linear systems23

3.2 Notation used for velocity and position control systems24

3.3 First order systems24

3.4 The remote position control servomechanism29

3.5 General form and solution of the second order equation33

3.6 Errors38

3.7 The effect of additional time constants38

3.8 Summary40

4．Transfer Function Analysis42

4.1 Definition of transfer functions42

4.2 Validity of transfer functions43

4.3 Block diagrams43

4.4 Manipulation of transfer functions in closed loops44

4.5 Major and minor loops46

4.6 The open loop equivalent of a closed loop47

4.7 Direct feedback equivalent of a general system47

4.8 Application of transfer function analysis to the example of a position control servomechanism48

4.9 Systems with multiple inputs51

4.10 Systems with multiple inputs and outputs52

4.11 The general form ofa transfer function54

4.12 Signal flow diagrams or graphs57

4.13 Summary63

5．Frequency Response Analysis64

5.1 Frequency response functions64

5.2 Graphical representation of G(jω)67

5.3 Somefeatures of G(jω)69

5.4 Minimum and non-minimum phase systems72

5.5 Logarithmic plotting74

5.6 Asymptotic approximation on Bode diagrams77

5.7 Use of asymptotic approximation to construct Bode dia-grams83

5.8 Use of measured frequency response to find G(jω)85

5.9 Summary87

6.Stability Analysis88

6.1 Stable and unstable systems88

6.2 Stability analysis by pole-zero location89

6.3 The Hurwitz-Routh stability criterion92

6.4 Rootloci94

6.5 The Nyquist stability criterion102

6.6 Bode's theorems109

6.7 Methods of determining the closed loop from the open loop frequency response function111

6.8 Summary117

7.Design Procedure and Specifications118

7.1 Introduction to design118

7.2 Specifications118

7.3 Sensitivity functions127

7.4 Design procedure129

8.Compensating Techniques131

8.1 Methods of compensation131

8.2 The uncompensated proportional error system132

8.3 Proportional error system with derivative of output feedback134

8.4 Series compensation135

8.5 Parallel compensation149

8.6 Input compensation154

8.7 Compensation for two inputs155

8.8 Design techniques using the s-plane156

Part Three AN INTRODUCTION TO SOME FURTHER TECHNIQUES167

9.Nonlinear Systems167

9.1 Introduction167

9.2 The common types of nonlinearities168

9.3 Some effects of nonlinearities in closed loop control systems170

9.4 Describing functions171

9.5 Stability analysis using describing functions179

9.6 Closed loop response of a nonlinear system184

9.7 Frequency dependent describing functions186

9.8 An introduction to phase-plane analysis186

10．The Application of Statistics to Closed Loop Control Systems194

10.1 The field of statistical application194

10.2 Some important statistical terms195

10.3 The weighting function and the convolution integral200

10.4 Error criteria202

10.5 Analysis in the time domain204

10.6 Analysis in the frequency domain210

10.7 Conclusions215

11．Digital Control Systems217

11.1 Sampled data systems217

11.2 Mathematical representation of the sampled signal219

11.3 Analysis of f(t)221

11.4 The Z transform224

11.5 Manipulation of transfer functions in sampled systems225

11.6 Stability analysis of sampled systems227

11.7 Direct digital control229

12.Multivariable Systems—State Variables and Matrices231

12.1 Introduction231

12.2 Matrix algebra232

12.3 State space analysis234

12.4 Solution of the state vector differential equation238

12.5 The transition matrix239

12.6 State variable diagrams241

12.7 Representation of input functions by state variables244

12.8 Transformation of the state vector246

12.9 Observability and controllability247

12.10 Transfer function matrices249

12.11 State variable equations for digital systems249

12.12 Conclusions251

Part Four PRACTICAL ASPECTS255

13．M？thods of Mea？ring,Computing and Simulating Systems255

13.1 Measurement of transfer functions255

13.2 Computation andsimulation261

14．Syst？ Compone？ts265

14.1 General considerations265

14.2 Comparison of d．c．,a．c．and hydraulic servomechan-isms266

14.3 Servomotors and drivcs267

14.4 Referred inertia and friction268

14.5 Gearing269

14.6 Motor rating270

14.7 Structural components274

14.8 Coarse and fine systems275

14.9 Assisted braking277

14.10 Transducers278

14.11 Synchros and resolvers279

15． D．C．Servomechanisms283

15.1 Introduction283

15.2 D．C．servomotors283

15.3 Field control284

15.4 Armature control285

15.5 Power amplifiers285

15.6 Other forms of continuous control290

15.7 Relay servomechanisms293

15.8 Transfer functions of continuous d．c．motor systems295

15.9 Motor toroue-speed characteristics298

15.10 D．C．tachometers299

16．A．C．Servomechanisms300

16.1 Introduction300

16.2 Modulators and demodulators302

16.3 A．C．servomotors302

16.4 Modulator-demodulator systems304

16.5 All-a．c．systems304

16.6 A．C．tachometers306

16.7 Thyristor speed control of a．c．motors307

17．Hydraulic Servomechanisms308

17.1 Introduction308

17.2 Pumps and motors308

17.3 Methods of control309

17.4 Flow control valves312

17.5 System transfer functions317

17.6 Oil323