CONTENTS

Preface

1    General Concept of Control-System Design

1.1.    Introduction

1.2.    Open-Loop Control Systems

1.3.    Closed-Loop Control Systems

1.4.    Human Control Systems

1.5.    Modern Control-System Applications with a Preview of the Future

1.6.    Illustrative Problems and Solutions

Problems

References

2    Mathematical Techniques for Control-System Analysis

2.1.    Introduction

2.2.    Review of Complex Variables, Complex Functions, and the s Plane

2.3.    Review of Fourier Series and Fourier Transform

2.4.    Review of the Laplace Transform

2.5.    Useful Laplace Transforms

2.6.    Important Properties of the Laplace Transform

2.7.    Inversion by Partial Fraction Expansion

2.8.    Application of MATLAB to Control Systems

2.9.    Inversion with Partial Fraction Expansion Using MATLAB

2.10.  Laplace-Transform Solution of Differential Equations

2.11.  Transfer-Function Concept

2.12.  Transfer Functions of Common Networks

2.13.  Transfer Functions of Systems

2.14.  Signal-Flow Graphs and Mason’s Theorem

2.15.  Reduction of the Signal-Flow Graph

2.16.  Application of Mason’s Theorem and the Signal-Flow Graph to Multiple-Feeback Systems

2.17.  Disturbance Signals in Feedback Control Systems

2.18.  Operational Amplifiers

2.19.  Simulation Diagrams

2.20.  Review of Matrix Algebra

2.21.  State-Variable Concepts

2.22.  State-Variable Diagram

2.23.  Transformation Between the State-Space Form and the Transfer Function Form using MATLAB

2.24.  Digital Computer Evaluation of the Time Response

2.25.  Obtaining the Transient Response of Systems Using MATLAB

2.26.  State Transition Matrix

2.27.  Total Solution of the State Equation

2.28.  Evaluation of the State Transition Matrix from an Exponential Series

2.29.  Summary

2.30.  Illustrative Problems and Solutions

Problems

References

3    State Equations and Transfer-Function Representation of Physical Linear Control-System elements

3.1.    Introduction

3.2.    State Equations of Electrical Networks

3.3.    Transfer-Function and State-Variable Representation of Typical Mechanical Control-System Devices

3.4.    Transfer-Function and State-Variable Representation of Typical Electromechanical Control-System Devices

3.5.    Transfer-Function and State-Variable Representation of Typical Hydraulic Devices

3.6.    Transfer-Function Representation of Thermal Systems

3.7.    A Generalized Approach for Modeling—the Principles of Conservation and Analogy

3.8.    Illustrative Problems and Solutions

Problems

References

4    Second-Order Systems

4.1.    Introduction

4.2.    Characteristic Responses of Second-Order Control Systems

4.3.    Relation Between Location of Roots in the s-Plane and the Transient Response

4.4.    State-Variable Signal-Flow Graph of a Second-Order System

4.5.    What is the Best Damping Ratio to Use?

4.6.    Modeling the Transfer Functions of Control Systems

4.7.    Illustrative Problems and Solutions

Problems

References

5    Performance Criteria

5.1.    Introduction

5.2.    Stability

5.3.    Sensitivity

5.4.    Static Accuracy

5.5.    Transient Response

5.6.    Performance Indices

5.7.    Zero-Error Systems

5.8.    The ITAE Performance Criterion for Optimizing the Transient Response

5.9.    Other Practical Considerations

5.10.  Illustrative Problems and Solutions

Problems

References

6    Techniques for Determining Control-System Stability

6.1.    Introduction

6.2.    Determining the Characteristic Equation using Conventional and State-Variable Methods

6.3.    Routh—Hurwitz Stability Criterion

6.4.    Mapping Contours From the s-Plane to the F(s)-Plane

6.5.    Nyquist Stability Criterion

6.6.    Nyquist Diagrams Using MATLAB

6.7.    Bode-Diagram Approach

6.8.    Bode Diagrams Using MATLAB

6.9.    Digital Computer Programs for Obtaining the Open-Loop and Closed-Loop Frequency Responses and the Time-Domain Response

6.10.  Nichols Chart

6.11.  Nichols Chart Using MATLAB

6.12.  Relationship between Closed-Loop Frequency Response and the Time-Domain Response

6.13.  Closed-Loop Frequency Bandwidth and Cutoff Frequency

6.14.  Root-Locus Method for Negative-Feedback Systems

6.15.  Root Locus of Time-Delay Factors

6.16.  Root-Locus Method for Positive-Feedback Systems

6.17.  Root-Locus Method for Control Systems Using MATLAB

6.18.  Digital Computer Program for Obtaining the Root Locus

6.19.  Control Systems Containing Multiple Gain Margins

6.20.  Comparison of the Nyquist Diagram, Bode Diagram, Nichols Chart, and Root Locus for 12 Commonly Used Transfer Functions

6.21.  Commercially Available Software Packages for Computer-Aided Control-System Design

6.22.  What is the “Best” Stability Analysis Technique? Guidelines for using the Analysis Techniques Presented

6.23.  Illustrative Problems and Solutions

Problems

References

7    Linear Control-System Compensation and Design

7.1.    Introduction

7.2.    Cascade-Compensation Techniques

7.3.    Minor-Loop Feedback-Compensation Techniques

7.4.    Proportional-Plus-Integral-Plus Derivative (PID) Compensators

7.5.    Example for the Design of a Second-Order Control System

7.6.    Compensation and Design using the Bode-Diagram Method

7.7.    Approximate Methods for Preliminary Compensation and Design using the Bode Diagram

7.8.    Compensation and Design using the Nichols Chart

7.9.    Compensation and Design using the Root-Locus Method

7.10.  Tradeoffs of using Various Cascade-Compensation Methods and Minor-Loop Feedback

7.11.  Illustrative Problems and Solutions

Problems

References

8    Modern Control-System Design using State-Space, Pole Placement, Ackermann’s Formula, Estimation, Robust Control, and H^∞ Techniques

8.1.    Introduction

8.2.    Pole-Placement Design using Linear-State-Variable Feedback

8.3.    Controller Design using Pole Placement and Linear-State-Variable Feedback Techniques

8.4.    Controllability

8.5.    Observability

8.6.    Ackermann’s Formula for Design using Pole Placement

8.7.    Estimator Design in Conjunction with the Pole Placement Approach using Linear-State-Variable Feedback

8.8.    Combined Compensator Design Including a Controller and an Estimator for a Regulator System

8.9.    Extension of Combined Compensator Design Including a Controller and an Estimator for Systems Containing a Reference Input

8.10.  Robust Control Systems

8.11.  An Introduction to H^∞ Control Concepts

8.12.  Foundations of H^∞ Control Theory

8.13.  Linear Algebraic Aspects of Control-System Design Computations

8.14.  Illustrative Problems and Solutions

Problems

References

Appendix A    Laplace-Transform Table

Appendix B    Proof of the Nyquist Stability Criterion

Answers to Selected Problems

Index