Synthesis of Feedback Systems

PrefaceChapter 1 Introduction to Feedback Theory 1.1 Formulation of the Feedback Problem 1.2 Classification of Feedback Problems 1.3 Coverage of the Book 1.4 The Problem of Plant Identification and Representation 1.5 Canonical Representation of a Plant 1.6 Signal-Flow Graph Representation and Analysis 1.7 Terminal Representation of Systems 1.8 More Detailed System Representations 1.9 Electric Circuit Models of Mechanical Systems 1.10 Combined Translational-Rotational Systems 1.11 Conditions under Which a Passive Linear Electrical Analog Is Possible 1.12 Electrical Analogs of the Gyroscope 1.13 Electric Models of TransducersChapter 2 Foundations of Linear Feedback Theory 2.1 Introduction 2.2 The Fundamental Feedback Equation and Signal-Flow Graph 2.3 The Representation of Two-Terminal Elements by Controlled Sources 2.4 The Subjective Nature of Feedback 2.5 Return Difference: The Bilinear Theorem and Its Exceptions 2.6 Null Return Difference 2.7 Active Impedances 2.8 Invariance of the Numerator of the Return Difference for All References 2.9 The Loaded Transistor Terminal Functions 2.10 Analysis of Transistor Feedback Circuits 2.11 Use of Two Controlled Sources 2.12 The Fundamental Feedback Matrix EquationChapter 3 Introduction to the Properties of Feedback 3.1 Introduction 3.2 Reduction in the Sensitivity of a System to Parameter Variation 3.3 Design Examples 3.4 Cost of Feedback 3.5 Sensitivity as a Function of Frequency 3.6 Sensitivity Function When Leakage Transmission Is Not Zero 3.7 Magnitude and Phase Sensitivities 3.8 Systems with Multiple Inputs 3.9 Sensitivity to Parameter Variation and Noise in Feedback Return Path 3.10 The Effect of Feedback in Nonlinear Systems 3.11 Classification of Reasons for Using Feedback 3.12 Effect of Feedback on System ResponseChapter 4 The Stability Problem in Feedback Systems with Plant Parameter Variations 4.1 Introduction to Root Locus 4.2 Rules for Constructing Root Loci 4.3 Sensitivity of Roots to Variation in k 4.4 Root Sensitivity in Terms of Open-Loop Poles and Zeros 4.5 Sensitivity of Roots of 1 + kB(s) — 0 to Variations in the Zeros and Poles of B(s) 4.6 Application of Root Sensitivity to Predistortion for Incidental Dissipation in Filters 4.7 Application of Root Sensitivity to Limit the Drift in Feedback System Poles 4.8 The Stability Problem from the Root Locus Point of View 4.9 The Nyquist Stability Criterion 4.10 Application of the Nyquist Criterion to Open-Loop Stable Feedback Systems; Bode Plots 4.11 Positive Feedback 4.12 Loop Shaping for Stability, with Parameter Variations — Single-Order Systems 4.13 Extension to Higher Order SystemsChapter 5 Design of Feedback Control Systems with Single-Degree-of-Freedom Configuration 5.1 Comparison of Feedback Amplifiers with Feedback Control Systems 5.2 Distinction between the Feedback Problem, the Filter Problem, and the Control Problem 5.3 Introduction to Single-Degree-of-Freedom Feedback Control Design 5.4 Classical Control System Specifications — the Error Constants 5.5 Design for Simultaneous Achievement of Error Constant and Phase Margin by Means of Lag Compensation 5.6 Use of Lead Compensation to Achieve Specified Error Constant and Phase Margin 5.7 Loop Shaping for Simultaneous Achievement of Error Constant, Crossover Frequency, and Stability Margins 5.8 Optimization of Loop Transmission Function 5.9 Design Example 5.10 Correlation between System Frequency Response and Time Response 5.11 Relation between the Loop Transmission L and the System Transfer Function T 5.12 Synthesis from Pole-Zero Specifications of T(s) 5.13 Realization of Any Combination of Kv, Bandwidth, and Overshoot with a Pair of Poles and One Zero 5.14 Increase of Velocity Constant by Lag Compensation 5.15 Comparison of Lead and Lag Compensation Having the Same Kv, Bandwidth, and Overshoot 5.16 Determination of the Loop Transmission L(s); Validity of Canceling Plant Dynamics 5.17 Relative Merits of the Open-Loop Frequency Response Method and the T(s) Pole-Zero Method 5.18 The Price That Is Paid for a Dominant Type T(s) 5.19 T(s) Pole-Zero Method for More Complicated Dominant Pole-Zero Patterns 5.20 Root Locus Method 5.21 Design of High-Order System 5.22 Inadequacies of the Single-Degree-of-Freedom ConfigurationChapter 6 Design of Feedback Control Systems for Independent Control of Transmission and Sensitivity Functions 6.1 Configuration with Two Degrees of Freedom 6.2 Root Locus Synthesis to Control System Sensitivity to Variations in Plant Gain Factor 6.3 Root Locus s-Plane Synthesis for General Plant Parameter Variations 6.4 Location of the Far-Off Poles of L 6.5 Sensitivity of the Dominant Zeros of T(s) 6.6 Feasibility of Root Locus Sensitivity Design in High-Order Systems 6.7 Philosophy of the Frequency Response Approach to the Sensitivity Problem 6.8 Realization of Sensitivity Specifications — Frequency Response Method 6.9 Cost of Feedback, and Comparison of Two-Degree-of-Freedom Structures 6.10 The Problem of the Far-Off Poles 6.11 Design for Multiple Inputs 6.12 Design for Disturbance Attenuation Accompanied by Plant Parameter Variation 6.13 Analytical Specification of the Sensitivity Function 6.14 Achievable Benefits of Feedback in Two-Degree-of-Freedom StructureChapter 7 Fundamental Properties and Limitations of the Loop Transmission Function 7.1 Introduction 7.2 Mathematical Background 7.3 Resistance Integral Theorem and the Equality of Positive and Negative Feedback Areas 7.4 Real or Imaginary Part Sufficiency 7.5 Relation between Loop Transmission Lag Angle and Optimum Loop Transmission Function 7.6 Specification of F(s) from Its Real and Imaginary Parts in Different Frequency Ranges 7.7 The Ideal Bode Characteristic 7.8 A Different Kind of Optimum L(jω) 7.9 Minimum Phase Functions 7.10 Conditionally Stable Systems 7.11 Maximum Rate at Which