The Dynamics of Automatic Control Systems

The Dynamics of Automatic Control Systems

1st Edition - January 1, 1961

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  • Author: E. P. Popov
  • eBook ISBN: 9781483184623

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Description

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.

Table of Contents


  • 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

Product details

  • No. of pages: 776
  • Language: English
  • Copyright: © Pergamon 1961
  • Published: January 1, 1961
  • Imprint: Pergamon
  • eBook ISBN: 9781483184623

About the Author

E. P. Popov

About the Editor

A. D. Booth

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