Table of Contents
 Preface v
 CHAPTER 1
 Introduction
  1-1 Introduction
   1-1-1 Basic Components of a Control System
   1-l-2 Examples of Control-System Applications
   1-1-3 Open-Loop Control Systems (Nonfeed-back Systems)
   1-1-4 Closed-loop Control Systems (Feedback Control Systems)
  1-2 What is Feedback and What are its Effects?
   1-2-1 Effect of Feedback on Overall Gain
   1-2-2 Effect of Feedback on Stability
   1-2-3 Effect of Feedback on External Disturbance or Noise
  1-3Types of Feedback Control Systems
   1-3-1 Linear versus Nonlinear Control Systems
   1-3-2 Time-Invariant versus Time-Varying Systems
  1-4 Summary
 CHAPTER 2
 Mathematical Foundation
  2-1 Introduction
  2-2 Laplace Transform
   2-2-1 Definition of the Laplace Transform
   2-2-2 Inverse Laplace Transformation
   2-2-3 Important Theorems of the Laplace Transform
  2-3 Inverse Laplace Transform by Partial-Fraction Expansion
   2-3-1 Partial-Fraction Expansion
  2-4 Application of the Laplace Transform to the Solution of Linear Ordinary Differential Equations
  2-5 Impulse Response and Transfer Functions of Linear Systems
   2-5-1 Impulse Response
   2-5-2 Transfer Function (Single-input, Single-Output Systems)
   2-5-3 Transfer Function (Multivariable Systems)
  2-6 MATLAB Tools and Case Studies
   2-6-1 Description and Use of Transfer Function Tool
  2-7 Summary
 CHAPTER3
 Block Diagrams and Signal-Flow Graphs
  3-1 Block Diagrams
   3-1-1 Block Diagrams of Control Systems
   3-1-2 Block Diagrams and Transfer Functions of Multivariable Systems
  3-2 Signal-Flow Graphs (SFGs)
   3-2-1 Basic Elements of an SFG
   3-2-2 Summary of the Basic Properties of SFG
   3-2-3 Definitions of SFG Terms
   3-2-4 SFG Algebra
   3-2-5 SFG of a Feedback Control System
   3-2-6 Gain Formula for SFG
   3-2-7 Application of the Gain Formula between Output Nodes and Noninput Nodes
   3-2-8 Application of the Gain Formula to Block Diagrams
  3-3 State Diagram
   3-3-1 From Differential Equations to State Diagram
   3-3-2 From State Diagram to Transfer Function
   3-3-3 From State Diagram to State and Output Equations
  3-4 MATLAB Tools and Case Studies
  3-5 Summary
 CHAPTER 4
 Modeling of Physical Systems
  4-1 Introduction
  4-2 Modeling of Electrical Networks
  4-3 Modeling of Mechanical Systems Elements
   4-3-1 Translational Motion
   4-3-2 Rotational Motion
   4-3-3 Conversion Between Translational and Rotational Motions
   4-3-4 Gear Trains
   4-3-5 Backlash and Dead Zone (Nonlinear Characteristics)
  4-4 Equations of Mechanical Systems
  4-5 Sensors and Encoders in Control Systems
   4-5-1 Potentiometer
   4-5-2 Tachometers
   4-5-3 Incremental Encoder
  4-6 DC Motors in Control Systems
   4-6-1 Basic Operational Principles of DC Motnrc
   4-6-2 Basic Classifications of PM DC Motors
   4-6-3 Mathematical Modeling of PM DC Motors
  4-7 Linearization of Nonlinear Systems
  4-8 Systems with Transportation Lags (Time Delays)
   4-8-1 Approximation of the Time-Delay Function by Rational Functions
  4-9 A Sun-Seeker System
   4-9-1 Coordinate System
   4-9-2 Error Discriminator
   4-9-3 Op-Amp
   4-9-4 Servoamplifier
   4-9-5 Tachometer
   4-9-6 DC Motor
  4-10 MATLAB Tools and Case Studies
  4-11 Summary
 CHAPTER 5
 State Variable Analysis
  5-1 Introduction
  5-2 Vector-Matnx Representation of State Equations
  5-3 State-Transition Matrix
   5-3-1 Significance of the State-Transition Matrix
   5-3-2 Properties of the State-Transition Matrix
  5-4 State-Transition Equation
   5-4-1 State-Transition Equation Determined from the State Diagram
  5-5 Relationship between State Equations and High-Order Differential Equations
  5-6 Relationship between State Equations and Transfer Functions
  5-7 Characteristic Equations, Eigenvalues, and Eigenvectors
   5-7-1 Eigenvalues
   5-7-2 Eigenvectors
  5-8 Similarity Transformation
   5-8-1 Invariance Properties of the Similarity Transformations
   5-8-2 Controllability Canonical Form (CCF)
   5-8-3 Observability Canonical Form (OCF)
   5-8-4 Diagonal Canonical Form（DCF）
   5-8-5 Jordan Canonical Form (JCF)
  5-9 Decompositions of Transfer Functions
   5-9-1 Direct Decomposition
   5-9-2 Cascade Decomposition
   5-9-3 Parallel Decomposition
  5-10 Controllability of Control Systems
   5-10-1 General Concept of Controllabilitv
   5-10-2 Definition of State Controllability
   5-10-3 Alternate tests on Controllability
  5-11 Observability of Linear Systems
   5-11-1 Definition of Observability
   5-11-2 Alternate Tests on Observability
  5-12 Relationship Among Controllability, Observability,and Transfer Functions
  5-13 Invariant Theorems on Controllability and Observability
  5-14 A Final Illustrative Example: Magnetic-Ball Suspension System
  5-15 MATLAB Tools and Case Studies
   5-15-1 Description and Use of the State-Space Analysis Tool
   5-15-2 Description and Use of tfsym for State-Space Applications
   5-15-3 Another Example
  5-16 Summary
 CHAPTER 6
 Stability of Linear Control Systems
  6-1 Introduction
  6-2 Bounded-Input, Bounded-Output (BIBO) Stability-Continuous-Data Systems
   6-2-1 Relationship between Characteristic Equation Roots and Stability
  6-3 Zero-Input and Asymptotic Stability of Continuous-Data Systems
  6-4 Methods of Determining Stability
  6-5 Routh-Hurwitz Criterion
   6-5-1 Routh’s Tabulation (1)
   6-5-2 Special Cases When Routh’s Tabulation Terminates Prematurely
  6-6 MATLAB Tools and Case Studies
  6-7 Summary
 CHAPTER 7
 Time-Domain Analysis of Control Systems
  7-1 Time Response of Continuous-Data Systems:Introduction
  7-2 Typical Test Signals for the Time Response of Control Systems
  7-3 The Unit-Step Response and Time-Domain Specifications
  7-4 Steady-State Error
   7-4-1 Steady-State Error of Linear Continuous-Data Control Systems
   7-4-2 Steady-State Error Caused by Nonlinear System Elements
  7-5 Time Response of a First-Order System
   7-5-1 Speed Control of a DC Motor
  7-6 Transient Response of
  7-6 Transient Response of a Prototype Second-Order System
   7-6-1 Damping Ratio and Damping Factor
   7-6-2 Natural Undamped Frequency
   7-6-3 Maximum Overshoot
   7-6-4 Delay Time and Rise Time
   7-6-5 Settling Time
  7-7 Time-Domain Analysis of a Position-Control System
   7-7-1 Unit-Step Transient Response
   7-7-2 The Steady-State Response
   7-7-3 Time Response to a Unit-Ramp Input
   7-7-4 Time Response of a Third-Order System
  7-8 Effects of Adding Poles and Zeros to Transfer Functions
   7-8-1 Addition of a Pole to the Forward-Path Transfer Function: Unity-Feedback Systems
   7-8-2 Addition of a Pole to the Closed-Loop Transfer Function
   7-8-3 Addition of a Zero to the Closed-Loop Transfer Function
   7-8-4 Addition of a Zero to the Forward-Path Transfer Function: Unity-Feedback Systems
  7-9 Dominant Poles of Transfer Functions
   7-9-1 The Relative Damping Ratio
   7-9-2 The Proper Way of Neglecting the Insignificant Poles with Consideration of the Steady-State Response
  7-10 The Approximation of High-Order Systems by Low-Order System the Formal Approach
   7-10-1 Approximation Criterion
  7-11 MATLAB Tools and Case Studies
  7-12 Summary
 CHAPTER 8
 Root-Locus Technique
  8-1 Introduction
  8-2 Basic Properties of the Root Loci (RL)
  8-3 Properties of the Root Loci
   8-3-1 K＝0 and K＝±∞Points
   8-3-2 Number of Branches on the Root Loci
   8-3-3 Symmetry of the RL
   8-3-4 Angles of Asymptotes of the RL: Behavior of the RL at|sl＝∞
   8-3-5 Intersect of the Asymptotes (Centroid)
   8-3-6 Root Loci on the Real Axis
   8-3-7 Angles of Departure and Angles of Arrival of the RL
   8-3-8 Intersection of the RL with the Imaginary Axis
   8-3-9 Breakaway Points (Saddle Points) on the RL
   8-3-10 The Root Sensitivity ［17、18、19］
  8-4 Design Aspects of the Root Loci
   8-4-1 Effects of Adding Poles and Zeros to G(s)H(s)
  8-5 Root Contours (RC): Multiple-Parameter Variation
  8-6 Root Locus with the MATLAB Toolbox
  8-7 Summary
 CHAPTER 9
 Frequency-Domain Analysis
  9-1 Introduction
   9-1-1 Frequency Response of Closed-Loop Systems
   9-1-2 Frequency-Domain Specifications
  9-2 Mn Wn and Bandwidth of the Prototype Seco-Order System
   9-2-1 Resonant Peak and Resonant Frequency
   9-2-2 Bandwidth
  9-3 Effects of Adding a Zero to the Forward-Path Transfer Function
  9-4 Effects of Adding a Pole to the Forward-Path Transfer Function
  9-5 Nyquist Stability Criterion: Fundamentals
   9-5-1 Stability Problem
   9-5-2 Definition of Encircled and Enclosed
   9-5-3 Number of Encirclements and Enclosures
   9-5-4 Principle of the Argument
   9-5-5 Nyquist Path
   9-5-6 Nyquist Criterion and the L(s) or the G(s)H(s) plot
  9-6 Nyquist Criterion for Systems with Minimum-Phase Transfer Functions
   9-6-1 Application of the Nyquist Criterion to Minimum-Phase Transfer Functions that Are Not Strictly Proper
  9-7 Relation Between the Root Loci and the Nyquist Plot
  9-8 Illustrative Examples: Nyquist Criterion for Minimum-Phase Transfer Functions
  9-9 Effects of Addition of Poles and Zeros to L(s) on the Shape of the Nyquist Plot
  9-10 Relative Stability: Gain Margin and Phase Margin
   9-10-1 Gain Margin (GM)
   9-10-2 Phase Margin (PM)
  9-11 Stability Analysis with the Bode Plot
   9-11-1 Bode Plots of Systems with Pure Time Delays
  9-12 Relative Stability Related to the Slope of the Magnitude Curve of the Bode Plot
   9-12-1 Conditionally Stable System
 xii Table of Contents
  9-13 Stability Analysis with the Magnitude-Phase Plot
  9-14 Constant-M Loci in the Magnitude-Phase Plane: The Nichols Chart
  9-15 Nichols Chart Applied to Nonunity-Feedback Systems
  9-16 Sensitivity Studies in the Frequency Domain
  9-17 MATLAB Tools and Case Studies
  9-18 Summary
 CHAPTER 10
 Design of Control Systems
  10-1 Introduction
   10-1-l Design Specifications
   10-1-2 Controller Configurations
   10-1-3 Fundamental Principles of Design
  10-2 Design with the PD Controller
   10-2-1 Time-Domain Interpretation of PD Control
   10-2-2 Frequency-Domain Interpretation of PD Control
   10-2-3 Summary of Effects of PD Control
  10-3 Design with the PI Controller
   10-3-1 Time-Domain Interpretation and Design of PI Control
   10-3-2 Frequency-Domain Interpretation and Design of PI Control
  10-4 Design with the PID Controller
  10-5 Design with Phase-Lead Controller
   10-5-1 Time-Domain Interpretation and Design of Phase-Lead Control
   10-5-2 Frequency-Domain Interpretation and Design of Phase-Lead Control
   10-5-3 Effects of Phase-Lead Compensation
   10-5-4 Limitations of Single-Stage Phase-Lead Control
   10-5-5 Multistage Phase-Lead Controller
   10-5-6 Sensitivity Considerations
  10-6 Design with Phase-Lag Controller
   10-6-1 Time-Domain Interpretation and Design of Phase-Lag Control
   10-6-2 Frequency-Domain Interpretation and Design of Phase-Lag Control
   10-6-3 Effects and Limitations of Phase-Lag Control
  10-7 Design with Lead-Lag Controller
  10-8 Pole-Zero Cancellation Design: Notch Filter
   10-8-1 Second-Ordcr Active Filter
   10-8-2 Frequency-Domain Interpretation and Design
  10-9 Forward and Feedforward Controllers
  10-10 Design of Robust Control Systems
  10-11 Minor-Loop Feedback Control
   10-11-1 Rate-Feedback or Tachometer-Feedback Control
   10-11-2 Minor-Loop Feedback Control with Active Filter
  10-12 State-Feedback Control
  10-13 Pole-Placement Design through State Feedback
  10-14 State Feedback with Integral Control
  10-15 MATLAB Tools and Case Studies
  10-16 Summary
 CHAPTER11
 The Virtual Lab
  11-l Introduction
  11-2 Important Aspects in the Response of a DC Motor
   11-2-1 Speed Response and the Effects of Inductance and Disturbance-Open Loop Response
   11-2-2 Speed Control of DC Motors: Closed-Loop Response
   11-2-3 Position Control
  11-3 Description of the Virtual Expenmental System
   11-3-1 Motor
   11-3-2 Position Sensor or Speed Sensor
   11-3-3 Power Amplifier
   11-3-4 Interface
  11-4 Description of SIMLab and Virtual Lab Software
  11-5 Simulation and Virtual Experiments
   11-5-1 Open-Loop Speed
   11-5-2 Open-Loop Sine Input
   11-5-3 Speed Control
   11-5-4 Position Control
  11-6 Design Project
  11-7 Summary
 INDEX
 APPENDIX A
 Complex Variable Theory CD-ROM
 APPENDIX B
 Differential and Difference Equations CD-ROM APPENDIX C
 Elementary Matrix Theory and Algebra CD-ROM APPENDIX D
 Laplace Transform Table CD-ROM APPENDIXE
 Operational Amplifiers CD-ROM
  APPENDIX F
 Properties and Construction of the Root Loci CD-ROM
  APPENDIX G
 Frequency-Domain Plots CD-ROM
  APPENDIX H
 General Nyquist Criterion CD-ROM
  APPENDIXI
 Discrete-Data Control Systems CD-ROM
  APPENDIX J
 z-Transform Table CD-ROM
  APPENDIX K
 ACSYS 2002: Description of the Software CD-ROM
 ANSWERS TO SELECTED PROBLEMS CD-ROM