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Contents Preface Chapter 1 Introduction 1 1.1 System and System Analysis 1 1.2 Modeling the System 2 1.3 Solving the Model 4 1.4 Principle of Automatic Control Systems 5 1.4.1 Control and Control Systems 5 1.4.2 How Does an Automatic Control System Work? 6 1.5 Structure of Control Systems 8 1.5.1 Schematic Diagram for a Typical Automatic Control System 8 1.5.2 Terminologies 9 1.6 Characteristics of Control Systems 10 1.6.1 Stability 10 1.6.2 Accuracy 10 1.6.3 Dynamic Properties 11 1.6.4 Robustness 12 1.7 Classification of Control Systems (to Broadest Sense) 12 1.7.1 Open Loop Control System 12 1.7.2 Closed Loop Control System 13 1.8 Application of Control Theory in Mechanical Engineering Systems 15 1.9 Brief History of Automatic Control 15 1.10 Organization of Book 17 1.11 Drill Problems 17 Chapter 2 Laplace Transform Solution 19 2.1 Definition 19 2.2 Laplace Transforms of Common Functions 20 2.2.1 Step Function 20 2.2.2 Ramp Function 20 2.2.3 Pulse Function 21 2.2.4 Exponential Function 22 2.2.5 Trigonometric Function 22 2.2.6 Power Function 23 2.2.7 Summary 23 2.3 Laplace Transform Properties 24 2.3.1 Multiplication by a Constant 25 2.3.2 Superposition 25 2.3.3 Differential Theorem 25 2.3.4 Integral Theorem 26 2.3.5 Initial Value Theorem 27 2.3.6 Final Value Theorem 27 2.3.7 Shifting Theorem in Time Domain (Delay Theorem) 28 2.3.8 Shifting Theorem in Complex Domain 28 2.3.9 Partial Fraction Method 28 2.4 Laplace Transform Inversion 30 2.4.1 Distinct Poles 31 2.4.2 Repeated Poles 33 2.4.3 Complex Poles 34 2.5 Drill Problems 36 Chapter 3 Formulation and Dynamic Behavior of Translational Mechanical Systems 37 3.1 Introduction 37 3.1.1 Concepts of Mathematical Models 37 3.1.2 Types or Mathematical Models 37 3.2 Variables 37 3.3 Element Laws 39 3.3.1 Mass 39 3.3.2 Friction 40 3.3.3 Stiffness 42 3.4 Interconnection Laws 43 3.4.1 D'Alembert's Law 43 3.4.2 The Law of Reaction Forces 44 3.5 Obtaining the System Model 44 3.5.1 Free-Body Diagrams 45 3.5.2 Parallel Combinations 49 3.5.3 Series Combinations 50 3.6 Drill Problems 53 Chapter 4 Formulation and Dynamic Behavior of Electrical Systems 55 4.1 Element Laws 55 4.1.1 Resistor 55 4.1.2 Capacitor 56 4.1.3 Inductor 56 4.2 Interconnection Laws 57 4.2.1 Kirchhoff's Voltage Law 57 4.2.2 Kirchhoff's Current Law 58 4.2.3 The Nodal Method of Electrical Network Analysis 58 4.3 Analogue relationships among different systems 59 4.4 Examples 60 4.5 Drill Problems 62 Chapter 5 Fundamentals of Control Systems 63 5.1 Representation of Control Systems 63 5.2 The Transfer Function 63 5.2.1 Definition of the Transfer Function 64 5.2.2 Properties of the Transfer Function 65 5.2.3 The Rational Polynomial Form of a Transfer Function 66 5.2.4 Transfer Function of Elements in Series Connection 67 5.2.5 Transfer Function of Elements in Parallel Connection 68 5.2.6 Remarks 69 5.3 The Transfer Function for Typical Links 70 5.3.1 Proportion Link 70 5.3.2 Integral Link 71 5.3.3 Inertial Link 72 5.3.4 Differential Link 74 5.3.5 Oscillation Link 75 5.4 Function Block Diagrams 76 5.4.1 Introduction 76 5.4.2 Summing Point and Tie Point 76 5.4.3 Terminologies 77 5.4.4 Simplification of the Function Block Diagram 79 5.5 Plot the Function Block Diagrams 88 5.6 Signal Flow Diagrams 92 5.6.1 Introduction to Signal Flow Diagrams 92 5.6.2 Draw the Signal Flow Diagram 92 5.6.3 Mason's Gain Formula 94 5.7 Drill Problems 96 Chapter 6 Time Response Analysis of Control Systems 99 6.1 Introduction 99 6.2 Time Response from Transfer Function 100 6.2.1 Response of First-Order System 100 6.2.2 Response of Second-Order System 104 6.2.3 Approximate Analysis of High-Order System 110 6.3 Performance Specifications in Time Domain 114 6.3.1 Performance Specifications of First-Order System 114 6.3.2 Performance Specifications of Second-Order System 116¿ª 6.4 Drill Problems 121 Chapter 7 Frequency Response Analysis of Control Systems 123 7.1 Concepts 123 7.2 Graphical Descriptions: Nyquist Diagram and Bode Diagram 127 7.2.1 Simple Rules for Plotting Nyquist Diagram 127 7.2.2 The Nyquist Diagrams for Typical Links 128 7.2.3 Simple Rules for Plotting Bode Diagrams 134 7.2.4 The Bode Diagrams for Typical Links 139 7.3 The Open Loop Bode Diagram of Control System 151 7.4 Minimum Phase Systems 155 7.5 Nyquist Stability Criterion 158 7.5.1 The Explanation for Nyquist Stability Criterion 158 7.5.2 Some Tips for Nyquist Stability Criterion 16¿ª0 7.5.3 Nyquist Stability Criterion for Minimum Phase System 16¿ª1 7.5.4 Stability Margin 16¿ª1 7.6 Drill Problems 16¿ª7 Chapter 8 Stability Analysis of Control Systems 16¿ª8 8.1 Stability 16¿ª8 8.2 Conditions for