Solution Manual For
Digital Control System
Analysis & Design
Fourth Edition
GloBAl Edition
Charles L. Phillips
Auburn University
H. Troy Nagle
North Carolina State University
Aranya Chakrabortty
North Carolina State University
algebra. Mathematics is crucial in many industries, including engineering, finance, data science, and technology. The primary goal of mathematics exams is to test students' understanding of
mathematical concepts, their problem-solving abilities
ISBN 10: 1-292-06122-7
, CONTENTS
algebra. Mathematics is crucial in many industries, including engineering, finance, data science, and technology. The primary goal of mathematics exams is to test students' understanding of
mathematical concepts, their problem-solving abilities
Chapter 1 INTRODUCTION 11
Overview 11
Digital Control System 12
The Control Problem 15
Satellite Model 16
Servomotor System Model 18
Antenna Pointing System 20
Robotic Control System 21
Temperature Control System 22
Single-Machine Infinite Bus Power System 24
Summary 27
References 27 • Problems 27
Chapter 2 DISCRETE-TIME SYSTEMS AND THE Z-TRANSFORM 35
Introduction 35
Discrete-Time Systems 35
Transform Methods 37
Properties of the z-Transform 40
Addition and Subtraction 40
Multiplication by a Constant 40
Real Translation 41
Complex Translation 43
Initial Value 44
Final Value 44
Finding z-Transforms 45
Solution of Difference Equations 48
The Inverse z-Transform 51
Power Series Method 51
Partial-Fraction Expansion Method 52
Inversion-Formula Method 56
Discrete Convolution 57
Simulation Diagrams and Flow Graphs 59
State Variables 63
Other State-Variable Formulations 71
Transfer Functions 80
Solutions of the State Equations 84
Recursive Solution 84
z-Transform Method 86
, Numerical Method via Digital Computer 87
Properties of the State Transition Matrix 88
Linear Time-Varying Systems 89
Summary 90
References and Further Readings 90 • Problems 90
algebra. Mathematics is crucial in many industries, including engineering, finance, data science, and technology. The primary goal of mathematics exams is to test students' understanding of
mathematical concepts, their problem-solving abilities
Chapter 3 SAMPLING AND RECONSTRUCTION 100
Introduction 100
Sampled-Data Control Systems 100
The Ideal Sampler 103
Evaluation of E*(S) 105
Results from the Fourier Transform 108
Properties of E*(S) 110
Data Reconstruction 113
Zero-Order Hold 114
First-Order Hold 118
Fractional-Order Holds 119
Summary 121
References and Further Readings 121 • Problems 122
Chapter 4 OPEN-LOOP DISCRETE-TIME SYSTEMS 126
Introduction 126
The Relationship Between E(Z) and E*(S) 126
The Pulse Transfer Function 127
Open-Loop Systems Containing Digital Filters 133
The Modified z-Transform 136
Systems with Time Delays 139
Nonsynchronous Sampling 142
State-Variable Models 145
Review of Continuous-Time State Variables 146
Discrete-Time State Equations 150
Practical Calculations 154
Summary 156
References and Further Readings 156 • Problems 156
Chapter 5 CLOSED-LOOP SYSTEMS 167
Introduction 167
Preliminary Concepts 167
, Derivation Procedure 171
State-Variable Models 178
Summary 187
References and Further Readings 187 • Problems 188
algebra. Mathematics is crucial in many industries, including engineering, finance, data science, and technology. The primary goal of mathematics exams is to test students' understanding of
mathematical concepts, their problem-solving abilities
Chapter 6 SYSTEM TIME-RESPONSE CHARACTERISTICS 198
Introduction 198
System Time Response 198
System Characteristic Equation 207
Mapping the s-Plane into the z-Plane 208
Steady-State Accuracy 215
Simulation 218
Control Software 223
Summary 223
References and Further Readings 224 • Problems 224
Chapter 7 STABILITY ANALYSIS TECHNIQUES 230
Introduction 230
Stability 230
Bilinear Transformation 234
The Routh-Hurwitz Criterion 236
Jury’s Stability Test 239
Root Locus 244
The Nyquist Criterion 248
The Bode Diagram 257
Interpretation of the Frequency Response 259
Closed-Loop Frequency Response 261
Summary 270
References and Further Readings 270 • Problems 270
Chapter 8 DIGITAL CONTROLLER DESIGN 279
Introduction 279
Control System Specifications 279
Steady-State Accuracy 280
Transient Response 280
Relative Stability 282
Sensitivity 283
Disturbance Rejection 284
Control Effort 285
Compensation 285
Phase-Lag Compensation 287
Digital Control System
Analysis & Design
Fourth Edition
GloBAl Edition
Charles L. Phillips
Auburn University
H. Troy Nagle
North Carolina State University
Aranya Chakrabortty
North Carolina State University
algebra. Mathematics is crucial in many industries, including engineering, finance, data science, and technology. The primary goal of mathematics exams is to test students' understanding of
mathematical concepts, their problem-solving abilities
ISBN 10: 1-292-06122-7
, CONTENTS
algebra. Mathematics is crucial in many industries, including engineering, finance, data science, and technology. The primary goal of mathematics exams is to test students' understanding of
mathematical concepts, their problem-solving abilities
Chapter 1 INTRODUCTION 11
Overview 11
Digital Control System 12
The Control Problem 15
Satellite Model 16
Servomotor System Model 18
Antenna Pointing System 20
Robotic Control System 21
Temperature Control System 22
Single-Machine Infinite Bus Power System 24
Summary 27
References 27 • Problems 27
Chapter 2 DISCRETE-TIME SYSTEMS AND THE Z-TRANSFORM 35
Introduction 35
Discrete-Time Systems 35
Transform Methods 37
Properties of the z-Transform 40
Addition and Subtraction 40
Multiplication by a Constant 40
Real Translation 41
Complex Translation 43
Initial Value 44
Final Value 44
Finding z-Transforms 45
Solution of Difference Equations 48
The Inverse z-Transform 51
Power Series Method 51
Partial-Fraction Expansion Method 52
Inversion-Formula Method 56
Discrete Convolution 57
Simulation Diagrams and Flow Graphs 59
State Variables 63
Other State-Variable Formulations 71
Transfer Functions 80
Solutions of the State Equations 84
Recursive Solution 84
z-Transform Method 86
, Numerical Method via Digital Computer 87
Properties of the State Transition Matrix 88
Linear Time-Varying Systems 89
Summary 90
References and Further Readings 90 • Problems 90
algebra. Mathematics is crucial in many industries, including engineering, finance, data science, and technology. The primary goal of mathematics exams is to test students' understanding of
mathematical concepts, their problem-solving abilities
Chapter 3 SAMPLING AND RECONSTRUCTION 100
Introduction 100
Sampled-Data Control Systems 100
The Ideal Sampler 103
Evaluation of E*(S) 105
Results from the Fourier Transform 108
Properties of E*(S) 110
Data Reconstruction 113
Zero-Order Hold 114
First-Order Hold 118
Fractional-Order Holds 119
Summary 121
References and Further Readings 121 • Problems 122
Chapter 4 OPEN-LOOP DISCRETE-TIME SYSTEMS 126
Introduction 126
The Relationship Between E(Z) and E*(S) 126
The Pulse Transfer Function 127
Open-Loop Systems Containing Digital Filters 133
The Modified z-Transform 136
Systems with Time Delays 139
Nonsynchronous Sampling 142
State-Variable Models 145
Review of Continuous-Time State Variables 146
Discrete-Time State Equations 150
Practical Calculations 154
Summary 156
References and Further Readings 156 • Problems 156
Chapter 5 CLOSED-LOOP SYSTEMS 167
Introduction 167
Preliminary Concepts 167
, Derivation Procedure 171
State-Variable Models 178
Summary 187
References and Further Readings 187 • Problems 188
algebra. Mathematics is crucial in many industries, including engineering, finance, data science, and technology. The primary goal of mathematics exams is to test students' understanding of
mathematical concepts, their problem-solving abilities
Chapter 6 SYSTEM TIME-RESPONSE CHARACTERISTICS 198
Introduction 198
System Time Response 198
System Characteristic Equation 207
Mapping the s-Plane into the z-Plane 208
Steady-State Accuracy 215
Simulation 218
Control Software 223
Summary 223
References and Further Readings 224 • Problems 224
Chapter 7 STABILITY ANALYSIS TECHNIQUES 230
Introduction 230
Stability 230
Bilinear Transformation 234
The Routh-Hurwitz Criterion 236
Jury’s Stability Test 239
Root Locus 244
The Nyquist Criterion 248
The Bode Diagram 257
Interpretation of the Frequency Response 259
Closed-Loop Frequency Response 261
Summary 270
References and Further Readings 270 • Problems 270
Chapter 8 DIGITAL CONTROLLER DESIGN 279
Introduction 279
Control System Specifications 279
Steady-State Accuracy 280
Transient Response 280
Relative Stability 282
Sensitivity 283
Disturbance Rejection 284
Control Effort 285
Compensation 285
Phase-Lag Compensation 287
