Stability in Nonlinear Control Systems

✍ Scribed by Aleksandr Mikhailovich Letov

• Publisher: Princeton University Press
• Year: 2015
• Tongue: English
• Leaves: 332
• Series: Princeton Legacy Library; 2020
• Category: Library

✦ Synopsis

The author, a Nobel prize-winner, has added to the American translation several chapters not in the original.

Originally published in 1961.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

✦ Table of Contents

TABLE OF CONTENTS
Author’
s Foreword to the American Edition
Author's Foreword to the Russian Edition
INTRODUCTION
1. Statement of the Stability Problem
2. Lyaptmov' s Direct Method
3· Investigation of Stability with First-Approximation Equations
4. The Hurwitz Theorem
5· Characteristic Numbers
6. Stability Under Constantly Applied Disturbing Forces
CHAPTER I: EQUATIONS OF CONTROL SYSTEMS. STATEMENT OF STABILITY PROBLEM
1. Equations of Regulated Objects
2. Equation of the Actuator
3· Collective Equations of Control Systems
4. Possible Steady State Modes of Control Systems
5· Normal Form of Collective Equations of Control Systems
6. First Fundamental Problem in the Theory of Automatic Control
CHAPTER II: FIRST CANONICAL FORM OF EQUATIONS OF CONTROL SYSTEMS
1. The Lur'e Transformation
2. Formulas for the Coefficients of the Direct and Inverse Lur'e Transformation
3· Case of Multiple Roots
4. The First Bulgakov Problem
5. Bulgakov'3 Second Problem
6. On the Theory of the Isodrome Regulator
7· Regulation of the Steady State of a System Subjected to the Action of Constant Disturbing Forces
8. The First Bulgakov Problem in the Case of Non-Ideal Sensing Devices
9. Bulgakov's Second Problem in the Case of Non-Ideal Sensing Devices
10. Indirect Control of Machines
11. Second Lur 'e Transformation
CHAPTER III: SECOND AND THIRD CANONICAL FORMS OF THE EQUATIONS OF CONTROL SYSTEMS
1. Second Form of Canonical Transformation
2. Formulas for the Transformation Coefficients
3· Bulgakov's First and Second Problems
4. On the Theory of the Isodroroe Regulator
5. Third Form of the Canonical Transformation
CHAPTER IV: STABILITY OF CONTROL SYSTEMS
1. Statement of the Problem
2. Two Quadratic Forms
3. The Lur’e Theorem
4. The First Bulgakov Problem
5. Bulgakov's Second Problem
6. Problem of the Isodrome Regulator
7. First Variant of the Lur'e Theorem
8. Second Variant of the Lur'e Theorem
9. Stability in the Case of a Multiple Root
CHAPTER V: FORMULATION OF SIMPLIFIED STABILITY CRITERIA
1. First Case of Formulation of Simplified Stability Criteria
2. Second Case of Formulation of Simplified Stability Criteria
3. Specific Problems
4. General Method for Formulating Simplified Stability Criteria
5. Certain Modifications of the Malkin Method
6. Realizability of Solutions Obtained by the Laypunov Method
7. Another Method of Formulating Simplified Stability Criteria
8. Stability in Indirect Control
CHAPTER VI: INHERENTLY UNSTABLE CONTROL SYSTEMS
1. Generalization of the Lur'e Theorem
2. Solution of the Second Bulgakov Problem for k < 0
3. Other Forms of Stability Criteria
4. Formulation of Simplified Stability Criteria
5. Stability Investigation Based on Equations (3.57) and (3.60)
6. Indirect Control in the Case of Negative Self Equalization
7. Another Method of Formulating Simplified Stability Criteria
CHAPTER VII: PROGRAMMED CONTROL
1. Statement of the Stability Problem
2. Theorem on Programmed Control
CHAPTER VIII: THE PROBLEM OF CONTROL QUALITY
1. Second Fundamental Problem of the Theory of Automatic Control
2. Solution of the Direct Problem
3. Solution of the Inverse Problem
4. First and Second Bulgakov Problems
5. Second Method of Solving the Quality Problem
CHAPTER IX: STABILITY OF CONTROL SYSTMS WITH TWO ACTUATORS
1. Statement of Problem
2. Canonical Form of Equations of Control Systems
3. Formulas for the Coefficients of the Canonical Transformation
4. Construction of the Lyapunov Function
5· Example
6. Construction of Simplified Stability Criteria
CHAPTER X: TWO SPECIAL PROBLEMS IN THE THEORY OF STABILITY OF CONTROL SYSTEMS
1. Stability in the First Approximation
2. Stability in the Case of Constant Disturbing Forces
3· Conclusion
CHAPTER XI: STABILITY OF UNSTEADY MOTION
1. Equations of Disturbed Motion
2. Statement of the Problem of Stability of Unsteady Motion
3. Stability of Unsteady Motions
4. Second BvilgaJcov Problem in the Case of Variable Coefficients
CHAPTER XII: CONTROL SYSTEMS CONTAINING TACHOMETRIC FEEDBACK
1. Case of Inherently Stable Control System
2. Case of Inherently Unstable Control System
3· Bulgakov's Second Problem
4. Stability of an Automatically Controlled Bicycle, Rolling over a Horizontal Plane
AUTHOR INDEX
SUBJECT INDEX