CHAPTER 1 Introduction

1-1 Introduction

1-1-1 Basic Components of a Control System

1-1-2 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

1-3 Types 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

CHAPTER 3 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 Motors

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-Matrix 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 Controllability

5-10-2 Detinition 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 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 ︳s|=∞

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 Specifiications

9-2 M?W? and Bandwidth of the Prototype Second-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

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

10-1-1 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-Order 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

CHAPTER 11 The Virtual Lab

11-1 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 Experimental 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