The Dynamics of Automatic Control Systems

1st Edition - January 1, 1961
Author: E. P. Popov
Editor: A. D. Booth
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 1 - 8 4 6 2 - 3

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… Read more

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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.

English Editor's Introduction

Foreword

Part I. General Information About Automatic Control Systems

I. Forms of Automatic Control Systems

1. The Concept of Closed Automatic Systems

2. Servomechanisms and Control Systems

3. Direct and Indirect-Acting Systems

4. Continuous and Discontinuous (Relay and Pulse) Systems

II. Transients in Automatic Regulation Systems

5. Linear and Non-Linear Systems

6. Processes in Linear Systems

7. Stability and Errors of Linear Systems

8. Forced Oscillations and Frequency Characteristics of Linear Systems

9. Non-Linear Systems

10. Representation of Responses Using Phase Trajectories

III. Methods of Improving the Regulation Process

11. Static, Astatic and Oscillatory Systems. Reduction of Static and Stationary Dynamic Errors

12. Auxiliary Feedback in Linear Systems

13. Auxiliary Feedback in Non-Linear Systems

14. Regulation Function

15. Introduction of Derivatives into the Regulation Function

IV. Some Problems in the Theory of Automatic Regulation

16. The Theory of Automatic Regulation

17. On the History of the Theory of Automatic Regulation

Part II. Ordinary Linear Automatic Regulation Systems

V. Linearisation and Transformation of the Differential Equations of an Automatic Regulation System

18. Linearisation of the Equations. Liapunov's Theorem on the Stability of Linearised Systems

19. Types of Elements in Automatic Systems and their Characteristics

20. Transformation of Equations and Frequency Characteristics of Single-Tuned Systems

21. Transformation of the Equations and Frequency Characteristics of Multi-Loop Systems

VI. Setting Up the Equations of Ordinary Linear Automatic Regulation Systems

22. Equations for an Automatic Engine-Speed Regulation System

23. Equations of an Automatic Pressure Regulation System

24. Equations of an Automatic Voltage Regulation System

25. Equations of Automatic Aircraft-Course Regulator

26. Equations of a Servomechanism

VII. Stability Criteria for Ordinary Linear Systems

27. Preliminary Information

28. Mikhailov's Stability Criterion

29. Algebraic Stability Criteria

30. Frequency Stability Criterion

31. Width of Stability Region and Stability Reserve

VIII. Choice of Structure and Parameters of Ordinary Linear Automatic Regulation Systems from the Stability Condition

32. Use of the Vyshnegradskii Stability Criterion

33. Employment of the Hurwitz Stability Criterion

34. Utilisation of the Mikhailov Stability Criterion

35. Use of the Frequency Stability Criterion

IX. Approximate Criteria of the Quality of Transient Response in Linear Systems from the Roots of the Characteristic Equation

36. Vyshnegradskii Diagram. Aperiodicity and Monotonicity of the Transient Response

37. Degree of Stability and its Application

38. Choice of System Parameters from the Distribution of Several Roots of the Characteristic Equation Closest to the Imaginary Axis

39. Calculation of the Roots of Equations and Polynomials

40. Choice of System Parameters from the Locations of all Roots of the Characteristic Equation

X. Approximate Criteria of Transient Quality in Linear Systems Taking into Account the Right-Hand Side of the Equation of the Closed System

41. Integral Criteria of Transient Quality

42. Examples of the Choice of System Parameters with Respect to the Minimum Integral Criterion

43. Choice of System Parameters with Respect to the Distribution of Poles and Zeros of the Transfer Functions of the Closed System

44. Approximate Frequency Criteria of Transient Quality

Part III. Special Linear Automatic Regulation Systems

XI. Derivation of the Equations of Systems With Delay and with Distributed Parameters

45. Equations and Frequency Characteristics of Linear Systems with Delay

46. Equations of a Linear System with Distributed Parameters

XII. Investigation of Stability in Systems with Delay and with Distributed Parameters

47. The Mikhailov Stability Criterion for Linear Systems with Delay and with Distributed Parameters

48. Frequency Stability Criterion for Linear Systems with Delay and with Distributed Parameters

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

XIII. Pulse (Discontinuous) Automatic Regulation Systems

50. Equations and Frequency Characteristics of Linear Pulse Regulation Systems

51. Investigation of Stability of Pulse (Discontinuous) Linear Regulation Systems

Part IV. Non-Linear Automatic Regulation Systems

XIV. Derivation of the Equations of Non-Linear Automatic Regulation Systems

52. General Remarks

53. Equations of Systems with Relay Type Non-Linearity

54. Equations of Systems with Non-Linearity in the Form of Dry Friction and Backlash

55. Equations of Systems with Other Types of Non-Linearity

XV. Study of Stability and Self-Oscillations in Non-Linear Automatic Regulation Systems

56. Phase Trajectories and the Andronov Point Transformation Method

57. Theorems of Liapunov's Direct Method and their Applications

58. The Study of Stability in Non-Linear Systems Using Special Canonical Equations (After Lur'e)

59. Determination of Self-Oscillation in Relay Systems by the Method of Matching Solutions

XVI. The Approximate Determination of Oscillations and Stability of Non-Linear Systems

60. The Approximate Method of Krylov and Bogoliubov for Second-Order Non-Linear Systems

61. Krylov-Bogoliubov Harmonic Linearisation of Non-Linearity

62. Approximate Determination of Oscillations and their Stability Using the Mikhailov Criterion and Algebraic Criteria

63. Examples

64. Improved First Approximation in Determining Self-Oscillation

65. Approximate Frequency Method for Determining Self-Oscillation

66. Bulgakov's Approximate Methods

XVII. Self-Oscillations in the Presence of an External Force and Forced Oscillations of Non-Linear Systems

67. Approximate Determination of Self-Oscillations with Slowly Varying External Force and in the Presence of Constant Components

68. Approximate Determination of Forced Oscillations in Vibrational Linearisation of Non-Linear Systems

69. Improved Frequency Method of Determining Forced Oscillations and Self-Oscillations in Relay Systems

Part V. Methods of Plotting the Regulation-Process Curve

XVIII. Numerical-Graphical Method

70. Basis of the Bashkirov Numerical-Graphical Method. First and Second-Order Linear Equations

71. Numerical-Graphical Method for Linear Systems of Arbitrary Order

72. Numerical-Graphical Method for Systems with Time-Variable Parameters and for Non-Linear Systems

XIX. Analytic Solution and Frequency Method

73. Ordinary Analytic Solution

74. Operational Method

75. The Solodovnikov Method of Trapezoidal Frequency Characteristics

References