Popov / Booth The Dynamics of Automatic Control Systems

1. Auflage 2014
ISBN: 978-1-4831-8462-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 776 Seiten, Web PDF

The Dynamics of Automatic Control Systems focuses on the dynamics of automatic control systems and the fundamental results of the theory of automatic control. The discussion covers theoretical methods of analysis and synthesis of automatic control systems common to systems of various physical natures and designs. Concrete examples of the simplest functional circuits are presented to illustrate the principal ideas in the construction of automatic control systems and the application of the theoretical methods. Comprised of 19 chapters, this book begins by describing different forms of automatic control systems, with emphasis on open and closed loop automatic systems. The reader is then introduced to transients in automatic regulation systems; methods for improving the regulation process; and some problems in the theory of automatic regulation. Subsequent chapters deal with linearization and transformation of the differential equations of an automatic regulation system; stability criteria for ordinary linear systems; equations of systems with delay and with distributed parameters; and equations of nonlinear automatic regulation systems. The oscillations and stability of nonlinear systems are also considered. This monograph will be of interest to engineers and students.

Autoren/Hrsg.

Popov, E. P.

Booth, A. D.

Inhaltsverzeichnis

1;Front Cover;1
2;The Dynamics of Automatic Control Systems;4
3;Copyright Page;5
4;Table of Contents;10
5;ENGLISH EDITORS INTRODUCTION;6
6;FOREWORD;8
7;PART I: GENERAL INFORMATION ABOUT AUTOMATIC CONTROL SYSTEMS;16
7.1;CHAPTER I. FORMS OF AUTOMATIC CONTROL SYSTEMS;18
7.1.1;1. The concept of closed automatic systems;18
7.1.2;2. Servomechanisms and control systems;21
7.1.3;3. Direct and indirect-acting systems;32
7.1.4;4. Continuous and discontinuous (relay and pulse) systems;37
7.2;CHAPTER II. TRANSIENTS IN AUTOMATIC REGULATION SYSTEMS;45
7.2.1;5. Linear and non-linear systems;45
7.2.2;6. Processes in linear systems;51
7.2.3;7. Stability and errors of linear systems;69
7.2.4;8. Forced oscillations and frequency characteristics of linear systems;79
7.2.5;9. Non-linear systems;87
7.2.6;10. Representation of responses using phase trajectories;99
7.3;CHAPTER III. METHODS OF IMPROVING THE REGULATION PROCESS;116
7.3.1;11. Static, astatic and oscillatory systems. Reduction of static and stationary dynamic errors;116
7.3.2;12. Auxiliary feedback in linear systems;127
7.3.3;13. Auxiliary feedback in non-linear systems;135
7.3.4;14. Regulation function;141
7.3.5;15. Introduction of derivatives into the regulation function;146
7.4;CHAPTER IV. SOME PROBLEMS IN THE THEORY OF AUTOMATIC REGULATION;150
7.4.1;16. The theory of automatic regulation;150
7.4.2;17. On the history of the theory of automatic regulation;154
8;PAET II: ORDINARY LINEAR AUTOMATIC REGULATION SYSTEMS;162
8.1;CHAPTER V. LINEARISATION AND TRANSFORMATION OF THE DIFFERENTIAL EQUATIONS OF AN AUTOMATIC REGULATION SYSTEM;164
8.1.1;18. Linearisation of the equations. Liapunov's theorem on the stability of linearised systems;164
8.1.2;19. Types of elements in automatic systems and their characteristics;173
8.1.3;20. Transformation of equations and frequency characteristics of single-tuned systems;194
8.1.4;21. Transformation of the equations and frequency characteristics of multi-loop systems;205
8.2;CHAPTER VI. SETTING UP THE EQUATIONS OF ORDINARY LINEAR AUTOMATIC REGULATION SYSTEMS;215
8.2.1;22. Equations for an automatic engine-speed regulation system;215
8.2.2;23. Equations of an automatic pressure regulation system;227
8.2.3;24. Equations of an automatic voltage regulation system;233
8.2.4;25. Equations of automatic aircraft-course regulator;241
8.2.5;26. Equations of a servomechanism;249
8.3;CHAPTER VII. STABILITY CRITERIA FOR ORDINARY LINEAR SYSTEMS;256
8.3.1;27. Preliminary information;256
8.3.2;28. Mikhailov's stability criterion;265
8.3.3;29. Algebraic stability criteria;271
8.3.4;30. Frequency stability criterion;283
8.3.5;31. Width of stability region and stability reserve;294
8.4;CHAPTER VIII. CHOICE OF STRUCTURE AND PARAMETERS OF ORDINARY LINEAR AUTOMATIC REGULATION SYSTEMS FROM THE STABILITY CONDITION;298
8.4.1;32. Use of the Vyshnegradskii stability criterion;298
8.4.2;33. Employment of the Hurwitz stability criterion;304
8.4.3;34. Utilisation of the Mikhailov stability criterion;310
8.4.4;35. Use of the frequency stability criterion;323
8.5;CHAPTER IX. APPROXIMATE CRITERIA OF THE QUALITY OF TRANSIENT RESPONSE IN LINEAR SYSTEMS FROM THE ROOTS OF THE CHARACTERISTIC EQUATION;329
8.5.1;36, Vyshnegradskii diagram. Aperiodicity and monotonicity of the transient response;329
8.5.2;37. Degree of stability and its application;337
8.5.3;38. Choice of system parameters from the distribution of several roots of the characteristic equation closest to the imaginary axis;349
8.5.4;39. Calculation of the roots of equations and polynomials;358
8.5.5;40. Choice of system parameters from the locations of all roots of the characteristic equation;368
8.6;CHAPTER X. APPROXIMATE CRITERIA OF TRANSIENT QUALITY IN LINEAR SYSTEMS TAKING INTO ACCOUNT THE RIGHT-HAND SIDE OF THE EQUATION OF THE CLOSED SYSTEM;377
8.6.1;41. Integral criteria of transient quality;377
8.6.2;42. Examples of the choice of system parameters with respect to the minimum integral criterion;388
8.6.3;43. Choice of system parameters with respect to the distribution of poles and zeros of the transfer function of the closed system;397
8.6.4;44. Approximate frequency criteria of transient quality;403
9;PART III: SPECIAL LINEAR AUTOMATIC REGULATION SYSTEMS;416
9.1;CHAPTER XI. DERIVATION OF THE EQUATIONS OF SYSTEMS WITH DELAY AND WITH DISTRIBUTED PARAMETERS;418
9.1.1;45. Equations and frequency characteristics of linear systems with delay;418
9.1.2;46. Equations of a linear system with distributed parameters;424
9.2;CHAPTER XII. INVESTIGATION OF STABILITY IN SYSTEMS WITH DELAY AND WITH DISTRIBUTED PARAMETERS;434
9.2.1;47. The Mikhailov stability criterion for linear systems with delay and with distributed parameters;434
9.2.2;48. Frequency stability criterion for linear systems with delay and with distributed parameters;443
9.2.3;49. Choice of structure and parameters of linear systems with delay and with distributed parameters from the condition of stability and the quality of the transient process;449
9.3;CHAPTER XIII. PULSE (DISCONTINUOUS) AUTOMATIC REGULATION SYSTEMS;460
9.3.1;50. Equations and frequency characteristics of linear pulse regulation systems;460
9.3.2;51. Investigation of stability of pulse (discontinuous) linear regulation systems;469
10;PART IV. NON-LINEAR AUTOMATIC REGULATION SYSTEMS;478
10.1;CHAPTER XIV. DERIVATION OF THE EQUATIONS OF NON-LINEAR AUTOMATIC REGULATION SYSTEMS;480
10.1.1;52. General remarks;480
10.1.2;53. Equations of systems with relay type non-linearity;483
10.1.3;54. Equations of systems with non-linearity in the form of dry friction and backlash;491
10.1.4;55. Equations of systems with other types of non-linearity;496
10.2;CHAPTER XV. STUDY OF STABILITY AND SELF-OSCILLATIONS IN NON-LINEAR AUTOMATIC REGULATION SYSTEMS;502
10.2.1;56. Phase trajectories and the Andronov point transformation method;502
10.2.2;57. Theorems of Liapunov's direct method and their applications;526
10.2.3;58. The study of stability in non-linear systems using special canonic equations (after Lur'e);541
10.2.4;59. Determination of self-oscillation in relay systems by the method of matching solutions;556
10.3;CHAPTER XVI. THE APPROXIMATE DETERMINATION OF OSCILLATIONS AND STABILITY OF NON-LINEAR SYSTEMS;565
10.3.1;60. The approximate method of Krylov and Bogoliubov for second-order non-linear systems;565
10.3.2;61. Krylov-Bogoliubov harmonic linearisation of non-linearity;577
10.3.3;62. Approximate determination of oscillations and their stability using the Mikhailov criterion and algebraic criteria;590
10.3.4;63. Examples;603
10.3.5;64. Improved first approximation in determining self-oscillation;635
10.3.6;65. Approximate frequency method for determining self-oscillation;644
10.3.7;66. Bulgakov's approximate methods;660
10.4;CHAPTER XVII. SELF-OSCILLATIONS IN THE PRESENCE OF AN EXTERNAL FORCE AND FORCED OSCILLATIONS OF NON-LINEAR SYSTEMS;683
10.4.1;67. Approximate determination of self-oscillations with slowly varying external force and in the presence of constant components;683
10.4.2;68. Approximate determination of forced oscillations in vibrational linearisation of non-linear systems;689
10.4.3;69. Improved frequency method of determining forced oscillations and self-oscillations in relay systems;701
11;PART V: METHODS OF PLOTTING THE REGULATION-PROCESS CURVE;712
11.1;CHAPTER XVIII. NUMERICAL-GRAPHICAL METHOD;714
11.1.1;70. Basis of the Bashkirov numerical-graphical method. First and second-order linear equations;714
11.1.2;71. Numerical-graphical method for linear systems of arbitrary order;727
11.1.3;72. Numerical-graphical method for systems with time-variable parameters and for non-linear systems;736
11.2;CHAPTER XIX. ANALYTIC SOLUTION AND FREQUENCY METHOD;747
11.2.1;73. Ordinary analytic solution;747
11.2.2;74. Operational method;752
11.2.3;75. The Solodovnikov method of trapezoidal frequency characteristics;762
12;REFERENCES;774