Dr. Boris J. Lurie


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Feedback Maximization

Boris J. Lurie, Artech House, Dedham, MA, 1986 (325 pp. with 302 figures)

The book is no longer available from the publisher. For an Artech House hardcover copy ($110), please send in an order. The price includes shipping within the US and Canada.

The book presents some theorems and design rules' justifications, and develops a theoretical basis for the practical design approach taught in Classical Feedback Control. The difference between these two books is that Feedback Maximization is more theoretical, it is of interest for a practicing engineer and also for a reasearcher. It includes some theories, proofs of concepts, and numerical examples and experiments not included in the textbook Classical Feedback Control.

From the Preface:

The book describes synthesis methods for feedback systems with nonlinear dynamic compensation, which allows for increased feeback while preserving robustness, global stability, good transient responses, and, if required, stability of the output processes.

The text is intended for the designers of single-loop and multiloop feeback systems employed in controllers, tracking systems, amplifiers, phase-locked loops, active filters, and power supplies.



Introduction - Nonlinear Dynamic Compensation

Chapter 1  Linear Single-Loop Feedback System

1.1 Transmission and Driving-Point Impedance
  1.1.1 Definitions
  1.1.2 Generic Single-Loop System
  1.1.3 Inverse Block Diagram; Two-Poles' Connection
  1.1.4 Return Ratio as a Function of the Load
  1.1.5 Balanced Bridge
  1.1.6 Examples and Exercises
1.2 Sensitivity
  1.2.1 Sensitivity of Transmission Function
  1.2.2 Sensitivity of Driving-Point Impedance
  1.2.3 Reflection Coefficients
  1.2.4 Examples and Exercises
1.3 Nonlinear Distortions
1.4 Regulation
  1.4.1 Introduction
  1.4.2 Parameter Dependence of a Circuit Function
  1.4.3 Symmetrical Regulation
1.5 Noise
  1.5.1 Noise at the System's Output
  1.5.2 Noise at the Input of the Plant
  1.5.3 Signal-to-Noise Ratio
  1.5.4 Examples and Exercises

Chapter 2  Stability and Frequency Response Constraints of Linear Systems

2.1 Nyquist Stability Criterion
  2.1.1 Nyquist Diagram
  2.1.2 Nyquist Diagram and Stability Margins for the Amplifier Return Ratio
  2.1.3 Two-Poles' Coupling
  2.1.4 Reflection Coefficients
  2.1.5 Examples and Exercises
2.2 Integral Constraints
  2.2.1 Minimum Phase Functions
  2.2.2 Integral of the Real Part
  2.2.3 Integral of the Imaginary Part
  2.2.4 Examples and Exercises
2.3 Phase-Gain Relations
  2.3.1 General Relation
  2.3.2 Phase Response Calculation
  2.3.3 Piecewise-Constant Real and Imaginary Components
  2.3.4 Examples and Exercises
2.4 Feedback Maximization
  2.4.1 Bode Optimal Cut-Off
  2.4.2 More Cut-Offs
  2.4.3 Asymptotic Losses, High-Frequency Bypass, Loop Gain Correction in Feedback Amplifiers
  2.4.4 Prediction and Feedback Maximization
  2.4.5 Negative Resistance Sensitivity
  2.4.5 Examples and Exercises
2.5 Nonminimum Phase Shift
  2.5.1 Causes for the Nonminimum Phase Shift
  2.5.2 Parallel Connection of Two Links
  2.5.3 Effect of Loading
  2.5.4 Noncascade Connection of Active Two-Ports

Chapter 3  Linear Single-Loop Feedback System

3.1 Absolute Stability Problem
3.2 Popov Criterion
  3.2.1 Nonlinear Physical Two-Poles
  3.2.2 Popov Criterion
  3.2.3 Applications
  3.2.3 Examples and Exercises
3.3 Periodical and Non-Periodical Self-Oscillation
3.4 Multifrequency Oscillation in a Bandpass System with Saturation
  3.4.1 Goals for Analysis
  3.4.2 Oscillation with Fundamental at which the Loop Gain is Large
  3.4.3 Oscillation with Fundamental at which the Loop Gain is Small
3.5 Describing Function Approach
3.6 Describing Functions for the Basic Types of Nonlinear Links
3.7 Multivalued Output-Input Relations
  3.7.1 Two-Pole with Begative dc Resistance
  3.7.2 Two-Port

Chapter 4  Forced Oscillation

4.1 Periodic Excitation
4.2 Absolute Stability of the Output Process
4.3 Jump-Resonance
  4.3.1 Conditions for the Jumps
  4.3.2 System with Dynamic Saturation
  4.3.3 System with Nondynamic Linear Link
  4.3.4 System with Nondynamic Saturation
  4.3.5 Substantiation of DF Technique for the Jump-Resonance Analysis
  4.3.6 System with Dead-Zone Element
  4.3.7 System with Nonlinear Element Having Power-Type DF
  4.3.8 Examples and Exercises
4.4 Odd Subharmonics
4.5 Second Subharmonic

Chapter 5  Nonlinear Dynamic Compensator (NDC)

5.1 Loop Regulation
  5.1.1 Variable Loop Gain
  5.1.2 Switching in the Compensator
  5.1.3 Quasilinear Variable Compensator
  5.1.4 Nonlinear Dynamic Compensator
5.2 Describing Function Approach to NDC design
  5.2.1 Generalities
  5.2.2 Stability Conditions
  5.2.3 Phase Stability Margin
  5.2.4 Design Constraints
  5.2.5 Amplitude Characteristics
  5.2.6 Effect of Loop Gain Ignorance
  5.2.7 Sufficient Stability Criterion
5.3 NDC in the Interstage Circuit of a Wideband Feedback Amplifier
5.4 Experiments
5.5 Special Applications

Chapter 6  Linear Multiloop System

6.1 Generalities
6.1 Stability Criteria
  6.2.1 Generalization of the Nyquist Criterion
  6.2.2 Examples and Exercises
6.3 Feed-Forward
6.4 System with Parallel Amplification Channels
  6.4.1 Sensitivity
  6.4.2 Stability

Chapter 7  Nonlinear Multiloop System: Describing Function Approach

7.1 Local Feedback
  7.1.1 Cascaded Links
  7.1.2 Feedback Around the Ultimate Stage
7.2 Two Parallel Channels with Saturation
  7.2.1 Frequency Responses of the Linear Part
  7.2.2 Piecewise Analysis of the AAPC
  7.2.3 Jump-Resonance
  7.2.4 Frequency Response of the Main Channel Transmission Function
  7.2.5 Modifications
  7.2.6 Numerical Examples
  7.2.7 Experiment
7.3 Two Parallel Channels with Saturation and Dead Zone
  7.3.1 Frequency Responses of the Linear Part
  7.3.2 Jump-Resonance
  7.3.3 Nonlinear Dynamic Compensator
  7.3.4 Experiment

Chapter 8  Nonlinear Multiloop System: Absolute Stability Approach

8.1 System Reducible to Single-Channel
  8.1.1 Block Diagrams
  8.1.2 Integral Constraint and Stability margin
  8.1.3 Plant with Saturation
8.2 Dead-Zone Element in the NDC Feedback Path
8.3 Positive and Negative Feedback in the NDC
8.4 Multifrequency Oscillation in a Bandpass System with Saturation
8.5 DF versus AS Techniques
8.6 Two-Channel System with a Lowpass in the Plant
  8.6.1 Block Diagram
  8.6.2 Noise
  8.6.3 Other Points of View
  8.6.3 The Allowable Discrepancy of Nonlinear Link Characteristics
  8.6.3 Experiment
8.7 NDC with Two Nonlinear Elements
8.8 Switching Regulation

List of Symbols