Automatic Control Systems

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1 Automatic Control Systems fourth edition Benjamin С. Kuo Professor of Electrical Engineering University of Illinois at Urbana-Champaign PRENTICE-HALL, INC., Englewood Cliffs, NJ 07632

Contents PREFACE ix 1 INTRODUCTION 1 1.1 Control Systems 1 1.2 What is Feedback and What Arc Its Effects? 7 1.3 Types of Feedback Control Systems // 2 MATHEMATICAL FOUNDATION 17 2.

2 Contents PREFACE ix 1 INTRODUCTION Control Systems What is Feedback and What Arc Its Effects? Types of Feedback Control Systems // 2 MATHEMATICAL FOUNDATION Introduction / Complex-Variable Concept / Differential Equations Laplace Transform Inverse Laplace Transform by Partial-Fraction Expansion Application of Laplace Transform to the Solution of Linear Ordinary Differential Equations Elementary Matrix Theory Matrix Algebra Vector-Matrix Form of State Equations Difference Equations The z-transform Application of the z-transform to the Solution of Linear Difference Equations 61

vi TRANSFER FUNCTION, BLOCK DIAGRAM, AND SIGNAL FLOW GRAPH 68 3.1 Introduction 68 3.2 Impulse Response and Transfer Functions of Linear Systems 69 3.3 Block Diagrams 76 3.4 Signal Flow Graphs 83 3.

3 vi TRANSFER FUNCTION, BLOCK DIAGRAM, AND SIGNAL FLOW GRAPH Introduction Impulse Response and Transfer Functions of Linear Systems Block Diagrams Signal Flow Graphs Summary of Basic Properties of Signal Flow Graphs Definitions for Signal Flow Graphs Signal-Flow-Graph Algebra Examples of the Construction of Signal Flow Graphs General Gain Formula for Signal Flow Graphs Application of the General Gain Formula to Block Diagrams State Diagram Transfer Functions of Discrete-Data Systems 113 MATHEMATICAL MODELING OF PHYSICAL SYSTEMS Introduction Equations of Electrical Networks Modeling of Mechanical System Elements Equations of Mechanical Systems Sensors and Encoders in Control Systems DC Motors in Control Systems / Two-Phase Induction Motors Linearization of Nonlinear Systems Systems with Transportation Lags 196 STATE-VARIABLE ANALYSIS OF LINEAR DYNAMIC SYSTEMS 5.1 Introduction Matrix Representation of State Equations State Transition Matrix State Transition Equation Relationship between State Equations and High-Order Differential Equations Transformation to Phase-Variable Canonical Form Relationship between State Equations and Transfer Functions Characteristic Equation, Eigenvalues, and Eigenvectors Diagonalization of the A Matrix (Similarity Transformation) Jordan Canonical Form Decomposition of Transfer Functions Controllability of Linear Systems Observability of Linear Systems 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.

4 Contents 5.15 Relationship among Controllability, Observability, and Transfer Functions State Equations of Linear Discrete-Data Systems z-transform Solution of Discrete State Equations State Diagrams for Discrete-Data Systems State Diagrams for Sampled-Data Systems 284 TIME-DOMAIN ANALYSIS OF CONTROL SYSTEMS Introduction Typical Test Signals for the Time Response of Control Systems Time-Domain Performance of Control Systems The Steady-State Error Time-Domain Performance of Control Systems Transient Response Transient Response of a Second-Order System Time-Domain Analysis of a Printwheel Control System Stability of Control Systems Introduction Stability, Characteristic Equation, and the State Transition Matrix Methods of Determining Stability of Linear Control Systems Routh-Hurwitz Criterion 362 ROOT LOCUS TECHNIQUES Introduction Basic Conditions of the Root Loci Construction of the Complete Root Loci Application of the Root Locus Technique to the Solution of Roots of a Polynomial Some Important Aspects of the Construction of the Root Loci Root Contour Multiple-Parameter Variation Root Loci of Systems with Pure Time Delay Root Loci of Discrete-Data Control Systems 456 TIME-DOMAIN DESIGN OF CONTROL SYSTEMS Introduction Time-Domain Design of the PID Controller Time-Domain Design of the Phase-Lead and Phase-Lag Controllers Pole-Zero Cancellation Control Minor-Loop Feedback Control State-Feedback Control Pole-Placement Design through State Feedback State Feedback with Integral Control Digital Implementation of Controllers 536

viii Contents 9 FREQUENCY-DOMAIN ANALYSIS OF CONTROL SYSTEMS 554 9.1 Introduction 554 9.2 Nyquist Stability Criterion 558 9.3 Application of the Nyquist Criterion 572 9.

5 viii Contents 9 FREQUENCY-DOMAIN ANALYSIS OF CONTROL SYSTEMS Introduction Nyquist Stability Criterion Application of the Nyquist Criterion Effects of Additional Poles and Zeros of G(s)H(s) on the Shape of the Nyquist Locus Stability of Multiloop Systems Stability of Linear Control Systems with Time Delays Digital Computer Program for Plotting Transfer Functions Frequency-Domain Characteristics M p, ы р, and the Bandwidth of a Second-Order System Effects of Adding a Zero to the Open-Loop Transfer Function Effects of Adding a Pole to the Open-Loop Transfer Function Relative Stability Gain Margin, Phase Margin, and M Relative Stability as Related to the Slope of the Magnitude Curve of the Bode Plot Constant M Loci in the G(jw)-?\ane Constant Phase Loci in the G(y'u)-Plane Constant M and N Loci in the Magnitude-versus-Phase Plane The Nichols Chart Closed-Loop Frequency Response Analysis of Nonunity Feedback Systems Sensitivity Studies in the Frequency Domain Frequency Response of Digital Control Systems FREQUENCY-DOMAIN DESIGN OF CONTROL SYSTEMS Introduction Phase-Lead Controller Phase-Lag Controller Lag-Lead Controller 681 APPENDICES A 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 В LAPLACE TRANSFORM TABLE 711 INDEX 715

6 Elektrische Bauelemente und Baugruppen der Automatisierungstechnik Dipl.-Ing. Werner Ausborn Dr.-Ing. Heinz Bätz Dipl.-Ing. Jürgen Heckert 4., unveränderte Auflage ü VEB VERLAG TECHNIK BERLIN

Inhaltsverzeichnis 1. Bauelemente 9 1.1. Begriffsbestimmungen und Anforderungen 9 1.2. Passive Bauelemente -... 14 1.2.1. Begriffsbestimmungen und Anforderungen 14 1.2.2. Widerstände 14 1.2.3.

7 Inhaltsverzeichnis 1. Bauelemente Begriffsbestimmungen und Anforderungen Passive Bauelemente Begriffsbestimmungen und Anforderungen Widerstände Kondensatoren Spulen Kontaktbauelemente Halbleiterbauelemente Begriffsbestimmungen und Anforderungen Dioden Transistoren Thyristoren Optoelektronische Bauelemente Begriffsbestimmungen und Anforderungen Lichtsender Lichtempfänger Optoelektronische Koppler Integrierte Schaltkreise Begriffsbestimmungen und Anforderungen Digitale Schaltkreise Analoge Schaltkreise Aufgaben., Baugruppen Begriffsbestimmungen und Anforderungen Stromversorgung Begriffsbestimmungen und Anforderungen Gleichrichter Spannungsverdoppler Siebglieder Spannungsstabilisierer Analoge Schältungen Begriffsbestimmungen und Anforderungen Verstärker Sinusoszillatoren Regler Umformer und Umsetzer 162 7

2.4. Digitale Schaltungen 2.4.1. Begriffsbestimmungen und Anforderungen 2.4.2. Kombinatorische Schaltungen 2.4.3. Sequentielle Schaltungen 168 168 170 181 2.5. Aufgaben 198 3. 201 Geräte 3.1. Begriffsbestimmungen und Anforderungen 3.

8 2.4. Digitale Schaltungen Begriffsbestimmungen und Anforderungen Kombinatorische Schaltungen Sequentielle Schaltungen Aufgaben Geräte 3.1. Begriffsbestimmungen und Anforderungen 3.2. Schaltgeräte Begriffsbestimmungen und Anforderungen Schalter Relais und Auslöser Steckverbinder Anlasser Sicherungen 3.3. Wärmegeräte Begriffsbestimmungen und Anforderungen Arten der Wärmeerzeugung Widerstandswärmegeräte 3.4. Steuergeräte Begriffsbestimmungen und Anforderungen Stellantriebe Mikrorechner, Steuerungssysteme 3.5. Industrieroboter Begriffsbestimmungen und Anforderungen Prinzipieller Aufbau ' Einsatzgebiete.', Aufgaben 281 Literaturverzeichnis 283 Sachwörterverzeichnis 284

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