《AUTOMATIC CONTROLS:PRINCIPLES OF SYSTEMS DYNAMICS》

1Introduction3

1-1．Concept of a dynamic system4

1-2．Dynamic characteristics6

1-3．Feedback automatic control12

2System Equations of Motion15

2-1．Notation16

2-2．Static stability of a linear mass-spring-damper system16

2-3．Equations of dynamic motion of a linear mass-spring-damper system19

2-4．Application of forcing functions21

2-5．Generalized mass-spring-damper combinations24

2-6．Multidegree-of-freedom systems25

2-7．Equivalent electrical systems27

2-8．Linear accelerometer31

2-9．Combined mechanical-electrical sys-tem33

2-10．Two-phase a-c servomotor35

2-11．Hydraulic servomotor37

2-12．Summary40

3Response Solutions51

3-1．Classical solution for linear first-order systems52

3-2．Classical solution for linear second-order aperiodic systems59

3-3．Higher-order characteristic equa-tions64

3-4．Properties of complex numbers65

3-5．Classical solution of the oscillatory response68

3-6．Undamped frequency and critical damping ratio71

3-7．Generalized transient responses of second-order systems76

3-8．Analog computer81

3-9．Analog solutions of second-order system response88

3-10．Laplace transform91

3-11．Summary99

4Applying the Laplace Transform103

4-1．Properties of the Laplace transform104

4-2．Partial fraction expansion110

4-3．Second-order system aperiodic re-sponses113

4-4．Second-order system oscillatory re-sponses121

4-5．Frequency response127

4-6．Response solutions for higher-order systems134

4-7．Analog computer solutions for higher-order systems142

4-8．Summary144

5Stability Root Analysis147

5-1．Complex plane plot148

5-2．Root locus concept152

5-3．First-order root loci152

5-4．Second-order root loci154

5-5．Pole-zero concept157

5-6．Optimum response considerations159

5-7．Generalized first-order and second-order response characteristics161

5-8．Third-order response characteristics167

5-9．Comments on higher-order systems175

5-10．Summary175

6Principles of Automatic Control178

6-1．Open- and closed-loop control sys-tems179

6-2．Principles of servomechanism op-eration180

6-3．Mass-spring-damper with displace-ment feedback183

6-4．Rate and acceleration feedback188

6-5．Integral control197

6-6．General feedback control system199

6-7．Simplifying multiple-loop control systems201

6-8．Stability and response design by feedback205

6-9．Forward-loop compensation206

6-10．Electric servomotor positioner209

6-11．Hydraulic servomotor positioner214

6-12．Summary217

7Design by the Root Locus Method225

7-1．Basis of the root locus method225

7-2．Applying the method228

7-3．Root locus construction rules231

7-4．Final development of the locus238

7-5．Use of root locus method in para-metric design analysis240

7-6．Third-order systems with displace-ment feedback247

7-7．Third-order systems with displace-ment and rate feedback253

7-8．Steady-state error characteristics258

7-9．Third-order systems with displace-ment feedback and forward loop compensation264

7-10．Obtaining the closed-loop response272

7-11．Obtaining the closed-loop frequency response281

7-12．Summary286

8Analog Computation and Simulation291

8-1．Basic problem and use of the com-puter292

8-2．Transfer function elements292

8-3．Nonlinear component simulation307

8-4．Nonlinear operations317

8-5．Function generation for inputs and programming319

8-6．Human controller simulation322

8-7．Summary325

Appendix ASolution of Cubic and Quartic Algebraic Equations327

Appendix BTable of Laplace Transforms334

Appendix CHeaviside Expansion Theorems340

Appendix DBasic-Control System Element Classifications,Examples,and Dynamic Characteristics348

Appendix ETransfer Functions of Dynamic System Components355

Additional Reading364

Index365