FEEDBACK and CONTROL SYSTEMS


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1 SCHA UM'S OUTLINE OF THEORY AND PROBLEMS OF FEEDBACK and CONTROL SYSTEMS Second Edition CONTINUOUS (ANALOG) AND DISCRETE (DIGITAL) JOSEPH J. DiSTEFANO, III, PhD. Departments of Computer Science and Mediane University of California, Los Angeles ALLEN R. STUBBERUD, PhD. Department of Electrica! and Computer Engineering University of California, Irvine IVAN J. WILLIAMS, Ph.D. Space and Technology Group, TR W, Inc. SCHAUM'S OUTLINE SERIES McGRAWHILL New York San Francisco Washington, D.C. Auckland Bogota Caracas Lisbon London Madrid Mexico City Milan Montreal New Delhi San Juan Singapore Sydney Tokyo Toronto
2 Contents Chapter / INTRODUCTION Control Systems: What They Are Examples of Control Systems OpenLoop and ClosedLoop Control Systems Feedback Characteristics of Feedback Analog and Digital Control Systems The Control Systems Engineering Problem Control System Models or Representations 6 Chapter 2 CONTROL SYSTEMS TERM1NOLOGY Block Diagrams: Fundamentals Block Diagrams of Continuous (Analog) Feedback Control Systems Terminology of the ClosedLoop Block Diagram Block Diagrams of DiscreteTime (SampledData, Digital) Components, Control Systems, and ComputerControlled Systems Supplementary Terminology Servomechanisms Regulators 23 Chapter 3 DIFFERENTIAL EQUATIONS, DIFFERENCE EQUATIONS, AND LINEAR SYSTEMS System Equations Differential Equations and Difference Equations Partial and Ordinary Differential Equations Time Variability and Time lnvarian.ee Linear and Nonlinear Differential and Difference Equations The Differential Operator D and the Characteristic Equation Linear Independence and Fundamental Sets Solution of Linear ConstantCoefficient Ordinary Differential Equations The Free Response The Forced Response The Total Response The Steady State and Transient Responses Singularity Functions: Steps, Ramps, and Impulses SecondOrder Systems State Variable Representation of Systems Described by Linear Differential Equations Solution of Linear ConstantCoefficient Difference Equations State Variable Representation of Systems Described by Linear Difference Equations Linearity and Superposition Causality and Physically Realizable Systems 57
3 Chapter 4 THE LAPLACE TRANSFORM AND THE ztransform Introduction The Laplace Transform The Inverse Laplace Transform Some Properties of the Laplace Transform and Its Inverse Short Table of Laplace Transforms Application of Laplace Transforms to the Solution of Linear ConstantCoefficient Differential Equations Partial Fraction Expansions Inverse Laplace Transforms Using Partial Fraction Expansions The ztransform Determining Roots of Polynomials Complex Plane: PoleZero Maps Graphical Evaluation of Residues SecondOrdcr Systems 98 Chapter 5 STABILITY Stability Definition« Characteristic Root Locations for Continuous Systems Routh Stability Criterion Hurwitz Stability Criterion Continued Fraction Stability Criterion Stability Criteria for DiscreteTime Systems 117 Chapter 6 TRANSFER FUNCTIONS Definition of a Continuous System Transfer Function Properties of a Continuous System Transfer Function Transfer Functions of Continuous Control System Compcnsators and Controllers Continuous System Time Response Continuous System Frequency Response DiscreteTime System Transfer Functions, Compensators and Time Responses DiscreteTime System Frequency Response Combining ContinuousTime and DiscreteTime Elements 134 Chapter 7 BLOCK DIAGRAM ALGEBRA AND TRANSFER FUNCTIONS OF SYSTEMS Introduction Review of Fundamentals Blocks in Cascade Canonical Form of a Feedback Control System Block Diagram Transformation Theorems Unity Feedback Systems Superposition of Multiple Inputs Rcduction of Complicated Block Diagrams 160 Chapter 8 SIGNAL FLOW GRAPHS Introduction Fundamentals of Signal Flow Graphs 179
4 8.3 Signal Flow Graph Algebra Definitions Construction of Signal Flow Graphs The General InputOutput Gain Formula Transfer Function Computation of Cascaded Components Block Diagram Reduction Using Signal Flow Graphs and the General InputOutput Gain Formula 187 Chapter 9 SYSTEM SENSITTVITY MEASURES AND CLASSIFICATION OF FEEDBACK SYSTEMS Introduction Sensitivity of Transfer Functions and Frequeney Response Functions to System Parameters Output Sensitivity to Parameters for Differential and Difference Equation Models Classification of Continuous Feedback Systems by Type Position Error Constants for Continuous Unity Feedback Systems Velocity Error Constants for Continuous Unity Feedback Systems Acceleration Error Constants for Continuous Unity Feedback Systems Error Constants for Discrete Unity Feedback Systems Summary Table for Continuous and DiscreteTime Unity Feedback Systems Error Constants for More General Systems 218 Chapter 10 ANALYSIS AND DESIGN OF FEEDBACK CONTROL SYSTEMS: OBJECTIVES AND METHODS Introduction Objectives of Analysis Methods of Analysis Design Objectives System Compensation Design Methods The wtransform for DiscreteTime Systems Analysis and Design Using Continuous System Methods Algebraic Design of Digital Systems, Including Deadbeat Systems 238 Chapter // NYQUIST ANALYSIS Introduction Plotting Complex Functions of a Complex Variable Definitions Properties of the Mapping P(s) or P(z) Polar Plots Properties of Polar Plots The Nyquist Path The Nyquist Stability Plot Nyquist Stability Plots of Practical Feedback Control Systems The Nyquist Stability Criterion Relative Stability M and NCircles 263
5 Chapter 12 NYQUIST DESIGN Design Philosophy Gain Factor Compensation Gain Factor Compensation Using MCircles Lead Compensation Lag Compensation LagLead Compensation Other Compensation Sehemes and Conibinations of Compensators 308 Chapter 13 ROOTLOCUS ANALYSIS Introduction Variation of ClosedLoop System Poles: The RootLocus Angle and Magnitude Criteria Number of Loci Real Axis Loci Asymptotes Breakaway Points Departure and Arrival Angles Comtruction of the RootLocus The ClosedLoop Transfer Function and the TimeDomain Response Gain and Phase Margins from the RootLocus Damping Ratio from the RootLocus for Continuous Systems 329 Chapter 14 ROOTLOCUS DESIGN The Design Problem Cancellation Compensation Phase Compensation: Lead and Lag Networks Magnitude Compensation and Combinations of Compensators Dominant PoleZero Approximations Point Design Feedback Compensation 353 Chapter 75 BODE ANALYSIS Introduction Logarithmic Scales and Bode Plots The Bode Form and the Bode Gain for ContinuousTimc Systems Bode Piots of Simple ContinuousTime Frequency Response Functions and Thcir Asymptotie Approximations Construction of Bode Plots for ContinuousTime Systems Bode Plots of DiscreteTime Frequency Response Functions Relative Stability ClosedLoop Frequency Response Bode Analysis of DiscreteTime Systems Using the wtransform 377 Chapter 16 BODE DESIGN Design Philosophy Gain Factor Compensation Lead Compensation for ContinuousTime Systems Lag Compensation for ContinuousTime Systems LagLead Compensation for ContinuousTime Systems Bode Design of DiscreteTime Systems 395
6 Chapter 17 NICHOLS CHART ANALYSIS Introduction db MagnitudePhase Angle Plots Construction of db MagnitudePhase Angle Plots Relative Stability The Nichols Chart ClosedLoop Frequency Response Functions 419 Chapter 18 NICHOLS CHART DESIGN Design Philosophy Gain Factor Compensation Gain Factor Compensation Using Constant Amplitude Curves Lead Compensation for ContimiousTime Systems Lag Compensation for ContinuousTime Systems LagLead Compensation Nichols Chart Design of DiscreteTime Systems 443 Chapter 19 INTRODUCTION TO NONLINEAR CONTROL SYSTEMS Introduction Linearized and PiecewiseLinear Approximations of Nonlinear Systems Phase Plane Methods Lyapunov's Stability Criterion Frequency Response Methods 466 Chapter 20 INTRODUCTION TO ADVANCED TOPICS IN CONTROL SYSTEMS ANALYSIS AND DESIGN Introduction Controllability and Observability TimeDomain Design of Feedback Systems (State Feedback) Control Systems with Random Inputs Optimal Control Systems Adaptive Control Systems 485 APPENDIX A 486 Some Laplace Transform Pairs Useful for Control Systems Analysis APPENDIX B 488 Some ztransform Pairs Useful for Control Systems Analysis REFERENCES AND BIBLIOGRAPHY. 489
7 APPENDIX C 491 SAMPLE Screens from thc Companton Inteructiue Outline. INDEX 507
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