Theory of Automatic Control

Foreword

Preface to the Second Edition

Chapter I General Introduction to Automatic Controllers


1. General Considerations of Control Processes. Terminology


2. The Simplest Systems of Direct Control


3. Astatic Controllers of Indirect Action


4. Rigid (Proportional) Feedback. Static Indirect Action Controllers


5. Floating Feedback


6. Derivative Actions


7. Multiple Control


8. Two-Position (Oscillatory) Controllers


9. Controllers of Discontinuous Action


10. Extremal Controllers


11. Individual, Specialized and Universal Controllers. Aggregate Systems

Chapter II The Construction of a Linear Model Control System and the Initial Material for its Analysis


1. The Dismemberment of the System into its Elements


2. Static Characteristics of Elements and of Systems


3. The Equations of the System Elements


4. The Linear Model of an Element. The Linearization of Equations


5. The Classification of Linear Models of Elements. The Inherent Operator and the Action Operators. Typical Elements (Stages)


6. The Transfer Function of the Linear Model of a System. Its Formation from the Equations of the Linear Models of its Elements


7. The Statics of the Linear Model of an Automatic Control System. The Transfer Functions of Static and Astatic Systems


8. Frequency Characteristics of a Linear Element and of the Linear Model of a System


9. Concluding Remarks

Chapter III The Stability of the Linear Model of an Automatic Control System


1. Estimating the Stability of the Linear Model of a System, Using its Transfer Function


2. An Estimate of the Stability of a System from the Frequency Characteristics


3. General Properties of Some Classes of Systems of Automatic Control, Connected with the Conditions of their Stability


4. Estimating the Stability of the Original System from the Stability of its Linear Model


5. Concluding Remarks

Chapter IV The Construction and the Evaluation of the Processes in the Linear Model of a System of Automatic Control


1. General Considerations


2. The Construction of the Process from the Transfer Function of the System


3. A Graphical Method of Constructing the Control Process


4. The Construction of the Control Process from the Frequency Characteristics of the System


5. General Considerations of Indirect Estimates of the Control Process. The Degree of Stability


6. Integral Estimates


7. Estimates of the Process on the Basis of the Form of the Frequency Characteristic


8. The Analysis of Systems with Random Disturbances, Given Statistically


9. Concluding Remarks

Chapter V Auto- and Forced Oscillation in Non-Linear Systems


1. General Remarks Concerning Periodic States in Non-Linear Systems

A. The Approximate Determination of Periodic States which are Nearly Harmonic


2. The Conditions for which Periodic States are Nearly Harmonic


3. The Approximate Determination of Auto-Oscillations by the Harmonic Balance (Filter) Method


4. The Approximate Determination of Forced Oscillations in the Presence of an External Periodic Action


5. System Containing Several Non-Linearities


6. The Determination of the Auto-Oscillations in the Case of Auto-Resonance


7. The "Slight" Stability of Periodic Solutions Approximately Found

B. The Exact Determination of Periodic States when the Non-Linear Element has a Piecewise-Linear Characteristic


8. General Introduction to Piecewise-Linear Systems and to Exact Methods for Determining their Periodic Solutions


9. The Simplest Periodic States in a System with a Symmetric Relay


10. The Determination of the Periodic States in Systems with a Non-Relay Piecewise-Linear Characteristic


11. The Stability of Periodic States Found Exactly


12. Sliding Switchings in Systems with Piecewise-Linear Characteristics


13. Some Remarks Concerning the Phase Space of Dynamic Systems. The Value of Periodic Motions


14. Concluding Remarks

Appendix 1 Laplace and Fourier Transforms and their Application to the Integration of Systems of Linear Differential Equations with Constant Coefficients


1. A General Introduction to the Laplace Transform


2. The Integration of a Single Differential Equation


3. The Integration of a System of Linear Differential Equations


4. The Fourier Transform and Integral

Appendix 2 Table of Trigonometric Functions

Bibliography

Subject Index