# Automatic Control Systems, Tenth Edition

by: Dr. Farid Golnaraghi, Dr. Benjamin C. Kuo

**Abstract:**A complete toolkit for teaching, learning, and understanding the essential concepts of automatic control systems. Edition after acclaimed edition, Automatic Control Systems has delivered up-to-date, real-world coverage designed to introduce students to the fundamentals of control systems. More than a comprehensive text, Automatic Control Systems includes innovative virtual labs that replicate physical systems and sharpen readers' problem-solving skills. The Tenth Edition introduces the concept of Control Lab, which includes two classes of experiments: SIMLab (model-based simulation) and LEGOLab (physical experiments using LEGO® robots). These experiments are intended to supplement, or replace, the experimental exposure of the students in a traditional undergraduate control course and will allow these students to do their work within the MATLAB® and Simulink® environment—even at home. This cost-effective approach may allow educational institutions to equip their labs with a number of LEGO test beds and maximize student access to the equipment at a fraction of the cost of currently available control-systems experiments. Alternatively, as a supplemental learning tool, students can take the equipment home and learn at their own pace. This new edition continues a tradition of excellence with: • A greater number of solved examples • Online labs using both LEGO MINDSTORMS® and MATLAB/SIMLab • Enhancements to the easy-to-use MATLAB GUI software (ACSYS) to allow interface with LEGO MINDSTORMS • A valuable introduction to the concept of Control Lab • A logical organization, with Chaps. 1 to 3 covering all background material and Chaps. 4 to 11 presenting material directly related to the subject of control • 10 online appendices, including Elementary Matrix Theory and Algebra, Control Lab, Difference Equations, and Mathematical Foundations • A full set of PowerPoint® slides and solutions manual available to instructors Adopted by hundreds of universities and translated into at least nine languages, Automatic Control Systems remains the single-best resource for students to gain a practical understanding of the subject and to prepare them for the challenges they will one day face. For practicing engineers, it represents a clear, thorough, and current self-study resource that they will turn to again and again throughout their career.

Full details

## Table of Contents

**A.**Dedication**B.**About the Authors**C.**In Memory of Professor Benjamin C. Kuo—A Visionary Pioneer and a Brilliant Teacher**D.**LEGO and MINDSTORMS are registered trademarks of the LEGO Group.**E.**Preface**1.**Introduction to Control Systems**2.**Modeling of Dynamic Systems**3.**Solution of Differential Equations of Dynamic Systems**4.**Block Diagrams and Signal-Flow Graphs**5.**Stability of Linear Control Systems**6.**Important Components of Feedback Control Systems**7.**Time-Domain Performance of Control Systems**8.**State-Space Analysis and Controller Design**9.**Root-Locus Analysis**10.**Frequency-Domain Analysis**11.**Design of Control Systems**A.**APPENDIX A: Elementary Matrix Theory and Algebra**B.**APPENDIX B: Mathematical Foundations**C.**APPENDIX C: Laplace Transform Table**D.**APPENDIX D: Control Lab**E.**APPENDIX E: ACSYS 2013: Description of the Software**F.**APPENDIX F: Properties and Construction of the Root Loci**G.**APPENDIX G: General Nyquist Criterion**H.**APPENDIX H: Discrete-Data Control Systems**I.**APPENDIX I: Difference Equations**J.**APPENDIX J: z-Transform Table

## Expanded Table of Contents

**A.**Dedication**B.**About the Authors**C.**In Memory of Professor Benjamin C. Kuo—A Visionary Pioneer and a Brilliant Teacher**D.**LEGO and MINDSTORMS are registered trademarks of the LEGO Group.**E.**Preface**1.**Introduction to Control Systems- CHAPTER PRELIMINARIES
- BASIC COMPONENTS OF A CONTROL SYSTEM
- EXAMPLES OF CONTROL-SYSTEM APPLICATIONS
- OPEN-LOOP CONTROL SYSTEMS (NONFEEDBACK SYSTEMS)
- CLOSED-LOOP CONTROL SYSTEMS (FEEDBACK CONTROL SYSTEMS)
- WHAT IS FEEDBACK, AND WHAT ARE ITS EFFECTS?
- TYPES OF FEEDBACK CONTROL SYSTEMS
- LINEAR VERSUS NONLINEAR CONTROL SYSTEMS
- TIME-INVARIANT VERSUS TIME-VARYING SYSTEMS
- CONTINUOUS-DATA CONTROL SYSTEMS
- DISCRETE-DATA CONTROL SYSTEMS
- CASE STUDY: INTELLIGENT VEHICLE OBSTACLE AVOIDANCE—LEGO MINDSTORMS
- SUMMARY

**2.**Modeling of Dynamic Systems- CHAPTER PRELIMINARIES
- MODELING OF SIMPLE MECHANICAL SYSTEMS
- INTRODUCTION TO MODELING OF SIMPLE ELECTRICAL SYSTEMS
- INTRODUCTION TO MODELING OF THERMAL AND FLUID SYSTEMS
- LINEARIZATION OF NONLINEAR SYSTEMS
- ANALOGIES
- PROJECT: INTRODUCTION TO LEGO MINDSTORMS NXT MOTOR—MECHANICAL MODELING
- SUMMARY
- REFERENCES
- PROBLEMS

**3.**Solution of Differential Equations of Dynamic Systems- CHAPTER PRELIMINARIES
- INTRODUCTION TO DIFFERENTIAL EQUATIONS
- LAPLACE TRANSFORM
- INVERSE LAPLACE TRANSFORM BY PARTIAL-FRACTION EXPANSION
- APPLICATION OF THE LAPLACE TRANSFORM TO THE SOLUTION OF LINEAR ORDINARY DIFFERENTIAL EQUATIONS
- IMPULSE RESPONSE AND TRANSFER FUNCTIONS OF LINEAR SYSTEMS
- SYSTEMS OF FIRST-ORDER DIFFERENTIAL EQUATIONS: STATE EQUATIONS
- SOLUTION OF THE LINEAR HOMOGENEOUS STATE EQUATION
- CASE STUDIES WITH MATLAB
- LINEARIZATION REVISITED—THE STATE-SPACE APPROACH
- SUMMARY
- REFERENCES
- PROBLEMS

**4.**Block Diagrams and Signal-Flow Graphs**5.**Stability of Linear Control Systems**6.**Important Components of Feedback Control Systems- CHAPTER PRELIMINARIES
- MODELING OF ACTIVE ELECTRICAL ELEMENTS: OPERATIONAL AMPLIFIERS
- SENSORS AND ENCODERS IN CONTROL SYSTEMS
- DC MOTORS IN CONTROL SYSTEMS
- SPEED AND POSITION CONTROL OF A DC MOTOR
- CASE STUDIES: PRACTICAL EXAMPLES
- THE CONTROL LAB: INTRODUCTION TO LEGO MINDSTORMS NXT MOTOR—MODELING AND CHARACTERIZATION
- SUMMARY
- REFERENCES
- PROBLEMS

**7.**Time-Domain Performance of Control Systems- CHAPTER PRELIMINARIES
- TIME RESPONSE OF CONTINUOUS-DATA SYSTEMS: INTRODUCTION
- TYPICAL TEST SIGNALS TO EVALUATE TIME-RESPONSE PERFORMANCE OF CONTROL SYSTEMS
- THE UNIT-STEP RESPONSE AND TIME-DOMAIN SPECIFICATIONS
- TIME RESPONSE OF A PROTOTYPE FIRST-ORDER SYSTEM
- TRANSIENT RESPONSE OF A PROTOTYPE SECOND-ORDER SYSTEM
- STEADY-STATE ERROR
- BASIC CONTROL SYSTEMS AND EFFECTS OF ADDING POLES AND ZEROS TO TRANSFER FUNCTIONS
- DOMINANT POLES AND ZEROS OF TRANSFER FUNCTIONS
- CASE STUDY: TIME-DOMAIN ANALYSIS OF A POSITION-CONTROL SYSTEM
- THE CONTROL LAB: INTRODUCTION TO LEGO MINDSTORMS NXT MOTOR—POSITION CONTROL
- SUMMARY
- REFERENCES
- PROBLEMS

**8.**State-Space Analysis and Controller Design- CHAPTER PRELIMINARIES
- STATE-VARIABLE ANALYSIS
- BLOCK DIAGRAMS, TRANSFER FUNCTIONS, AND STATE DIAGRAMS
- SYSTEMS OF FIRST-ORDER DIFFERENTIAL EQUATIONS: STATE EQUATIONS
- VECTOR-MATRIX REPRESENTATION OF STATE EQUATIONS
- STATE-TRANSITION MATRIX
- STATE-TRANSITION EQUATION
- RELATIONSHIP BETWEEN STATE EQUATIONS AND HIGH-ORDER DIFFERENTIAL EQUATIONS
- RELATIONSHIP BETWEEN STATE EQUATIONS AND TRANSFER FUNCTIONS
- CHARACTERISTIC EQUATIONS, EIGENVALUES, AND EIGENVECTORS
- SIMILARITY TRANSFORMATION
- DECOMPOSITIONS OF TRANSFER FUNCTIONS
- CONTROLLABILITY OF CONTROL SYSTEMS
- OBSERVABILITY OF LINEAR SYSTEMS
- RELATIONSHIP AMONG CONTROLLABILITY, OBSERVABILITY, AND TRANSFER FUNCTIONS
- INVARIANT THEOREMS ON CONTROLLABILITY AND OBSERVABILITY
- CASE STUDY: MAGNETIC-BALL SUSPENSION SYSTEM
- STATE-FEEDBACK CONTROL
- POLE-PLACEMENT DESIGN THROUGH STATE FEEDBACK
- STATE FEEDBACK WITH INTEGRAL CONTROL
- MATLAB TOOLS AND CASE STUDIES
- CASE STUDY: POSITION CONTROL OF THE LEGO MINDSTORMS ROBOTIC ARM SYSTEM
- SUMMARY
- REFERENCES
- PROBLEMS

**9.**Root-Locus Analysis**10.**Frequency-Domain Analysis- CHAPTER PRELIMINARIES
- INTRODUCTION TO FREQUENCY RESPONSE
- Mr, ωr, AND BANDWIDTH OF THE PROTOTYPE SECOND-ORDER SYSTEM
- EFFECTS OF ADDING POLES AND ZEROS TO THE FORWARD-PATH TRANSFER FUNCTION
- NYQUIST STABILITY CRITERION: FUNDAMENTALS
- NYQUIST CRITERION FOR SYSTEMS WITH MINIMUM-PHASE TRANSFER FUNCTIONS
- RELATION BETWEEN THE ROOT LOCI AND THE NYQUIST PLOT
- ILLUSTRATIVE EXAMPLES: NYQUIST CRITERION FOR MINIMUM-PHASE TRANSFER FUNCTIONS
- EFFECTS OF ADDING POLES AND ZEROS TO L(s) ON THE SHAPE OF THE NYQUIST PLOT
- RELATIVE STABILITY: GAIN MARGIN AND PHASE MARGIN
- STABILITY ANALYSIS WITH THE BODE PLOT
- RELATIVE STABILITY RELATED TO THE SLOPE OF THE MAGNITUDE CURVE OF THE BODE PLOT
- STABILITY ANALYSIS WITH THE MAGNITUDE-PHASE PLOT
- CONSTANT-M LOCI IN THE MAGNITUDE-PHASE PLANE: THE NICHOLS CHART
- NICHOLS CHART APPLIED TO NONUNITY-FEEDBACK SYSTEMS
- SENSITIVITY STUDIES IN THE FREQUENCY DOMAIN
- MATLAB TOOLS AND CASE STUDIES
- SUMMARY
- REFERENCES
- PROBLEMS

**11.**Design of Control Systems- CHAPTER PRELIMINARIES
- INTRODUCTION
- DESIGN WITH THE PD CONTROLLER
- DESIGN WITH THE PI CONTROLLER
- DESIGN WITH THE PID CONTROLLER
- DESIGN WITH PHASE-LEAD AND PHASE-LAG CONTROLLERS
- POLE-ZERO-CANCELLATION DESIGN: NOTCH FILTER
- FORWARD AND FEEDFORWARD CONTROLLERS
- DESIGN OF ROBUST CONTROL SYSTEMS
- MINOR-LOOP FEEDBACK CONTROL
- MATLAB TOOLS AND CASE STUDIES
- THE CONTROL LAB
- REFERENCES
- PROBLEMS

**A.**APPENDIX A: Elementary Matrix Theory and Algebra**B.**APPENDIX B: Mathematical Foundations- APPENDIX PRELIMINARIES
- COMPLEX-VARIABLE CONCEPT
- FREQUENCY-DOMAIN PLOTS
- STABILITY OF LINEAR CONTROL SYSTEMS
- BOUNDED-INPUT, BOUNDED-OUTPUT (BIBO) STABILITY—CONTINUOUS-DATA SYSTEMS
- RELATIONSHIP BETWEEN CHARACTERISTIC EQUATION ROOTS AND STABILITY
- ZERO-INPUT AND ASYMPTOTIC STABILITY OF CONTINUOUS-DATA SYSTEMS
- REFERENCES

**C.**APPENDIX C: Laplace Transform Table**D.**APPENDIX D: Control Lab**E.**APPENDIX E: ACSYS 2013: Description of the Software**F.**APPENDIX F: Properties and Construction of the Root Loci- APPENDIX PRELIMINARIES
- K = 0 AND K = ±∞ POINTS
- NUMBER OF BRANCHES ON THE ROOT LOCI
- SYMMETRY OF THE ROOT LOCI
- ANGLES OF ASYMPTOTES OF THE ROOT LOCI AND BEHAVIOR OF THE ROOT LOCI AT |S| → ∞
- INTERSECT OF THE ASYMPTOTES (CENTROID)
- ROOT LOCI ON THE REAL AXIS
- ANGLES OF DEPARTURE AND ANGLES OF ARRIVAL OF THE ROOT LOCI
- INTERSECTION OF THE ROOT LOCI WITH THE IMAGINARY AXIS
- BREAKAWAY POINTS (SADDLE POINTS)
- CALCULATION OF K ON THE ROOT LOCI

**G.**APPENDIX G: General Nyquist Criterion**H.**APPENDIX H: Discrete-Data Control Systems- APPENDIX PRELIMINARIES
- INTRODUCTION
- THE Z-TRANSFORM
- TRANSFER FUNCTIONS OF DISCRETE-DATA SYSTEMS
- STATE EQUATIONS OF LINEAR DISCRETE-DATA SYSTEMS
- STABILITY OF DISCRETE-DATA SYSTEMS
- TIME-DOMAIN PROPERTIES OF DISCRETE-DATA SYSTEMS
- STEADY-STATE ERROR ANALYSIS OF DISCRETE-DATA CONTROL SYSTEMS
- ROOT LOCI OF DISCRETE-DATA SYSTEMS
- FREQUENCY-DOMAIN ANALYSIS OF DISCRETE-DATA CONTROL SYSTEMS
- DESIGN OF DISCRETE-DATA CONTROL SYSTEMS
- DIGITAL CONTROLLERS
- DESIGN OF DISCRETE-DATA CONTROL SYSTEMS IN THE FREQUENCY DOMAIN AND THE Z-PLANE
- DESIGN OF DISCRETE-DATA CONTROL SYSTEMS WITH DEADBEAT RESPONSE
- POLE-PLACEMENT DESIGN WITH STATE FEEDBACK
- REFERENCES
- PROBLEMS

**I.**APPENDIX I: Difference Equations**J.**APPENDIX J: z-Transform Table

**Book Details**

**Title: **Automatic Control Systems, Tenth Edition

**Publisher: **McGraw-Hill Education: New York, Chicago, San Francisco, Athens, London, Madrid, Mexico City, Milan, New Delhi, Singapore, Sydney, Toronto

**Copyright / Pub. Date: **2017 McGraw-Hill Education

**ISBN: **9781259643835

**Authors:****Dr. Farid Golnaraghi**
has been a professor and the Director of Mechatronic Systems Engineering at Simon Fraser University in Vancouver since 2006. He also holds a Burnaby Mountain Endowed Chair at SFU, and his primary research focuses on intelligent vehicle systems. Prior to joining SFU, Dr. Golnaraghi was a professor of Mechanical and Mechatronics Engineering at the University of Waterloo. His pioneering research has resulted in two textbooks, more than 150 journal and conference papers, four patents, and two start-up companies.
**Dr. Benjamin C. Kuo**
was a member of the faculty of the Department of Electrical and Computer Engineering at the University of Illinois at Urbana-Champaign, which he joined in 1958 upon the completion of his Ph.D. and where he remained for 31 rewarding years. He was a true visionary pioneer in the field of automatic control, and the impact of his distinguished career as a researcher and educator cannot be overstated.

**Description: **
A complete toolkit for teaching, learning, and understanding the essential concepts of automatic control systems.
Edition after acclaimed edition, Automatic Control Systems has delivered up-to-date, real-world coverage designed to introduce students to the fundamentals of control systems. More than a comprehensive text, Automatic Control Systems includes innovative virtual labs that replicate physical systems and sharpen readers' problem-solving skills.
The Tenth Edition introduces the concept of Control Lab, which includes two classes of experiments: SIMLab (model-based simulation) and LEGOLab (physical experiments using LEGO® robots). These experiments are intended to supplement, or replace, the experimental exposure of the students in a traditional undergraduate control course and will allow these students to do their work within the MATLAB® and Simulink® environment—even at home. This cost-effective approach may allow educational institutions to equip their labs with a number of LEGO test beds and maximize student access to the equipment at a fraction of the cost of currently available control-systems experiments. Alternatively, as a supplemental learning tool, students can take the equipment home and learn at their own pace.
This new edition continues a tradition of excellence with:
• A greater number of solved examples
• Online labs using both LEGO MINDSTORMS® and MATLAB/SIMLab
• Enhancements to the easy-to-use MATLAB GUI software (ACSYS) to allow interface with LEGO MINDSTORMS
• A valuable introduction to the concept of Control Lab
• A logical organization, with Chaps. 1 to 3 covering all background material and Chaps. 4 to 11 presenting material directly related to the subject of control
• 10 online appendices, including Elementary Matrix Theory and Algebra, Control Lab, Difference Equations, and Mathematical Foundations
• A full set of PowerPoint® slides and solutions manual available to instructors
Adopted by hundreds of universities and translated into at least nine languages, Automatic Control Systems remains the single-best resource for students to gain a practical understanding of the subject and to prepare them for the challenges they will one day face. For practicing engineers, it represents a clear, thorough, and current self-study resource that they will turn to again and again throughout their career.