Automatic Control Systems
fourth edition Benjamin С. Kuo Professor of Electrical Engineering University of Illinois at Urbana-Champaign
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Introduction / 7 Complex-Variable Concept / 7 Differential Equations 20 Laplace Transform 23 Inverse Laplace Transform by Partial-Fraction Expansion 29 Application of Laplace Transform to the Solution of Linear Ordinary Differential Equations 33 Elementary Matrix Theory 36 Matrix Algebra 42 Vector-Matrix Form of State Equations 48 Difference Equations 49 The z-Transform 51 Application of the z-Transform to the Solution of Linear Difference Equations 61
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TRANSFER FUNCTION, BLOCK DIAGRAM, AND SIGNAL FLOW GRAPH 68 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12
Introduction 68 Impulse Response and Transfer Functions of Linear Systems 69 Block Diagrams 76 Signal Flow Graphs 83 Summary of Basic Properties of Signal Flow Graphs 86 Definitions for Signal Flow Graphs 86 Signal-Flow-Graph Algebra 89 Examples of the Construction of Signal Flow Graphs 91 General Gain Formula for Signal Flow Graphs 95 Application of the General Gain Formula to Block Diagrams 100 State Diagram 102 Transfer Functions of Discrete-Data Systems 113
MATHEMATICAL MODELING OF PHYSICAL SYSTEMS 135 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9
Introduction 135 Equations of Electrical Networks 136 Modeling of Mechanical System Elements 138 Equations of Mechanical Systems 153 Sensors and Encoders in Control Systems 159 DC Motors in Control Systems / 76 Two-Phase Induction Motors 186 Linearization of Nonlinear Systems 190 Systems with Transportation Lags 196
STATE-VARIABLE ANALYSIS OF LINEAR DYNAMIC SYSTEMS 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14
Introduction 211 Matrix Representation of State Equations 211 State Transition Matrix 214 State Transition Equation 218 Relationship between State Equations and High-Order Differential Equations 224 Transformation to Phase-Variable Canonical Form 227 Relationship between State Equations and Transfer Functions 233 Characteristic Equation, Eigenvalues, and Eigenvectors 236 Diagonalization of the A Matrix (Similarity Transformation) 238 Jordan Canonical Form 243 Decomposition of Transfer Functions 247 Controllability of Linear Systems 253 Observability of Linear Systems 262 Invariant Theorems on Controllability and Observability 266
Contents
5.15 Relationship among Controllability, Observability, and Transfer Functions 269 5.16 State Equations of Linear Discrete-Data Systems 272 5.17 z-Transform Solution of Discrete State Equations 276 5.18 State Diagrams for Discrete-Data Systems 279 5.19 State Diagrams for Sampled-Data Systems 284
TIME-DOMAIN ANALYSIS OF CONTROL SYSTEMS 308 6.1 Introduction 308 6.2 Typical Test Signals for the Time Response of Control Systems 309 6.3 Time-Domain Performance of Control Systems—The Steady-State Error 311 6.4 Time-Domain Performance of Control Systems— Transient Response 326 6.5 Transient Response of a Second-Order System 327 6.6 Time-Domain Analysis of a Printwheel Control System 340 6.7 Stability of Control Systems—Introduction 354 6.8 Stability, Characteristic Equation, and the State Transition Matrix 356 6.9 Methods of Determining Stability of Linear Control Systems 361 6.10 Routh-Hurwitz Criterion 362
Introduction 383 Basic Conditions of the Root Loci 384 Construction of the Complete Root Loci 389 Application of the Root Locus Technique to the Solution of Roots of a Polynomial 420 Some Important Aspects of the Construction of the Root Loci 425 Root Contour— Multiple-Parameter Variation 435 Root Loci of Systems with Pure Time Delay 444 Root Loci of Discrete-Data Control Systems 456
TIME-DOMAIN DESIGN OF CONTROL SYSTEMS 468 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9
Introduction 468 Time-Domain Design of the PID Controller 471 Time-Domain Design of the Phase-Lead and Phase-Lag Controllers 484 Pole-Zero Cancellation Control 507 Minor-Loop Feedback Control 517 State-Feedback Control 522 Pole-Placement Design through State Feedback 524 State Feedback with Integral Control 529 Digital Implementation of Controllers 536
Contents
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FREQUENCY-DOMAIN ANALYSIS OF CONTROL SYSTEMS 554 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 9.12 9.13 9.14 9.15 9.16 9.17 9.18 9.19
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Introduction 554 Nyquist Stability Criterion 558 Application of the Nyquist Criterion 572 Effects of Additional Poles and Zeros of G(s)H(s) on the Shape of the Nyquist Locus 581 Stability of Multiloop Systems 586 Stability of Linear Control Systems with Time Delays 590 Digital Computer Program for Plotting Transfer Functions 593 Frequency-Domain Characteristics 596 Mp, ыр, and the Bandwidth of a Second-Order System 597 Effects of Adding a Zero to the Open-Loop Transfer Function 601 Effects of Adding a Pole to the Open-Loop Transfer Function 606 Relative Stability—Gain Margin, Phase Margin, and M 608 Relative Stability as Related to the Slope of the Magnitude Curve of the Bode Plot 618 Constant M Loci in the G(jw)-?\ane 620 Constant Phase Loci in the G(y'u)-Plane 624 Constant M and N Loci in the Magnitude-versus-Phase Plane—The Nichols Chart 626 Closed-Loop Frequency Response Analysis of Nonunity Feedback Systems 632 Sensitivity Studies in the Frequency Domain 633 Frequency Response of Digital Control Systems 636
FREQUENCY-DOMAIN DESIGN OF CONTROL SYSTEMS 654 10.1 10.2 10.3 10.4
FREQUENCY-DOMAIN PLOTS 689 A. 1 Polar Plots of Transfer Functions 690 A.2 Bode Plot (corner plot) of a Transfer Function 697 A.3 Magnitude-versus-Phase Plot 709
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LAPLACE TRANSFORM TABLE 711
INDEX 715
Elektrische Bauelemente und Baugruppen der Automatisierungstechnik Dipl.-Ing. Werner Ausborn Dr.-Ing. Heinz Bätz Dipl.-Ing. Jürgen Heckert
