## Table of Contents

1. Introduction

1.1 Introduction

1.2 A history of control systems

1.3 System configurations

1.4 Analysis and design objectives

1.5 The design process

1.6 Computer-aided design

1.7 The control systems engineer

1.8 Summary

1.9 Review questions

1.10 Cyber exploration laboratory

1.11 Bibliography

1.12 Problems

1.13 LAB: Getting started with MATLAB Grader

2. Modeling in the Frequency Domain

2.1 Introduction

2.2 Laplace transform review

2.3 The transfer function

2.4 Electrical network transfer functions, Part 1

2.5 Electrical network transfer functions, Part 2

2.6 Translational mechanical system transfer functions

2.7 Rotational mechanical system transfer functions

2.8 Transfer functions for systems with gears

2.9 Electromechanical system transfer functions

2.10 Electric circuit analogs

2.11 Nonlinearities

2.12 Linearization

2.13 Summary

2.14 Review questions

2.15 Cyber exploration laboratory

2.16 Hardware interface laboratory

2.17 Bibliography

2.18 Problems

2.19 LAB: Partial fraction expansion and inverse Laplace transforms

2.20 LAB: Solving mesh equations with symbolic variables

3. Modeling in the Time Domain

3.1 Introduction

3.2 Some observations

3.3 The general state-space representation

3.4 Applying the state-space representation

3.5 Converting a transfer function to state space

3.6 Converting from state space to a transfer function

3.7 Linearization

3.8 Summary

3.9 Review questions

3.10 Cyber exploration laboratory

3.11 Bibliography

3.12 Problems

3.13 LAB: State space and transfer function representations of a two mass system

4. Time Response

4.1 Introduction

4.2 Poles, zeros, and system response

4.3 First-order systems

4.4 Second-order systems: introduction

4.5 The general second-order system

4.6 Underdamped second-order systems

4.7 System response with additional poles

4.8 System response with zeros

4.9 Effects of nonlinearities upon time response

4.10 Laplace transform solution of state equations

4.11 Time domain solution of state equations

4.12 Summary

4.13 Review questions

4.14 Cyber exploration laboratory

4.15 Hardware interface laboratory

4.16 Bibliography

4.17 Problems

4.18 LAB: First order response characteristics of an RC circuit

4.19 LAB: Second order response characteristics of a mass-spring-damper system

5. Reduction of Multiple Subsystems

5.1 Introduction

5.2 Block diagrams

5.3 Analysis and design of feedback systems

5.4 Signal-flow graphs

5.5 Mason’s rule

5.6 Signal-flow graphs of state equations

5.7 Alternative representations in state space

5.8 Similarity transformations

5.9 Summary

5.10 Review questions

5.11 Cyber exploration laboratory

5.12 Bibliography

5.13 Problems

5.14 LAB: Block diagram algebra and transient responses for higher order systems

5.15 LAB: State space models of a double mass-spring-damper system

6. Stability

6.1 Introduction

6.2 Routh-Hurwitz criterion

6.3 Routh-Hurwitz criterion: special cases

6.4 Routh-Hurwitz criterion: additional examples

6.5 Stability in state space

6.6 Summary

6.7 Review questions

6.8 Cyber exploration laboratory

6.9 Bibliography

6.10 Problems

6.11 LAB: Stability of a DC motor with position control

7. Steady-State Errors

7.1 Introduction

7.2 Steady-state error for unity-feedback systems

7.3 Static error constants and system type

7.4 Steady-state error specifications

7.5 Steady-state error for disturbances

7.6 Steady-state error for nonunity-feedback systems

7.7 Sensitivity

7.8 Steady-state error for systems in state space

7.9 Summary

7.10 Review questions

7.11 Cyber exploration laboratory

7.12 Bibliography

7.13 Problems

7.14 LAB: Steady-state analysis of a motor speed controller

8. Root Locus Techniques

8.1 Introduction

8.2 Defining the root locus

8.3 Properties of the root locus

8.4 Sketching the root locus

8.5 Refining the sketch

8.6 An example

8.7 Transient response design via gain adjustment

8.8 Generalized root locus

8.9 Root locus for positive-feedback systems

8.10 Pole sensitivity

8.11 Summary

8.12 Review questions

8.13 Cyber exploration laboratory

8.14 Hardware interface laboratory

8.15 Bibliography

8.16 Problems

8.17 LAB: Using root locus to select feedback gains and evaluate system stability

9. Design via Root Locus

9.1 Introduction

9.2 Improving steady-state error via cascade compensation

9.3 Improving transient response via cascade compensation

9.4 Improving steady-state error and transient response

9.5 Feedback compensation

9.6 Physical realization of compensation

9.7 Summary

9.8 Review questions

9.9 Cyber exploration laboratory

9.10 Hardware interface laboratory

9.11 Bibliography

9.12 Problems

9.13 LAB: PI compensator design using root locus

10. Frequency Response Techniques

10.1 Introduction

10.2 Asymptotic approximations: Bode plots, Part 1

10.3 Asymptotic approximations: Bode plots, Part 2

10.4 Introduction to the Nyquist criterion

10.5 Sketching the Nyquist diagram

10.6 Stability via the Nyquist diagram

10.7 Gain margin and phase margin via the Nyquist diagram

10.8 Stability, gain margin, and phase margin via Bode plots

10.9 Relation between closed-loop transient and closed-loop frequency responses

10.10 Relation between closed- and open-loop frequency responses

10.11 Relation between closed-loop transient and open-loop frequency responses

10.12 Steady-state error characteristics from frequency response

10.13 Systems with time delay

10.14 Obtaining transfer functions experimentally

10.15 Summary

10.16 Review questions

10.17 Cyber exploration laboratory

10.18 Bibliography

10.19 Problems

10.20 LAB: Frequency response of a flexible link

11. Design via Frequency Response

11.1 Introduction

11.2 Transient response via gain adjustment

11.3 Lag compensation

11.4 Lead compensation

11.5 Lag-lead compensation

11.6 Summary

11.7 Review questions

11.8 Cyber exploration laboratory

11.9 Bibliography

11.10 Problems

11.11 LAB: Lag compensator design via Bode plots

12. Design via State Space

12.1 Introduction

12.2 Controller design

12.3 Controllability

12.4 Alternative approaches to controller design

12.5 Observer design

12.6 Observability

12.7 Alternative approaches to observer design

12.8 Steady-state error design via integral control

12.9 Summary

12.10 Review questions

12.11 Cyber exploration laboratory

12.12 Bibliography

12.13 Problems

12.14 LAB: State feedback using an observer

13. Digital Control Systems

13.1 Introduction

13.2 Modeling the digital computer

13.3 The z-transform

13.4 Transfer functions

13.5 Block diagram reduction

13.6 Stability

13.7 Steady-state errors

13.8 Transient response on the z-plane

13.9 Gain design on the z-plane

13.10 Cascade compensation via the s-plane

13.11 Implementing the digital compensator

13.12 Summary

13.13 Review questions

13.14 Cyber exploration laboratory

13.15 Bibliography

13.16 Problems

13.17 LAB: Digital controller design using the Tustin transformation

14. Appendix A1: List of Symbols

14.1 List of symbols

15. Appendix A2: Antenna Azimuth Position Control System

15.1 Antenna azimuth position control system

16. Appendix A3: Unmanned Free-Swimming Submersible Vehicle

16.1 Unmanned free-swimming submersible vehicle

17. Appendix A4: Key Equations

17.1 Key equations

18. Appendix B: MATLAB Tutorial

18.1 Introduction

18.2 MATLAB examples

18.3 Command summary

18.4 Bibliography

19. Appendix C: Simulink Tutorial

19.1 Introduction

19.2 Using Simulink

19.3 Examples

19.4 Using Simulink for control system design

19.5 Summary

19.6 Bibliography

20. Appendix D: LabVIEW Tutorial

20.1 Introduction

20.2 Control systems analysis, design, and simulation

20.3 Using LabVIEW

20.4 Analysis and design examples

20.5 Simulation examples

20.6 Interfacing with external hardware

20.7 Summary

20.8 Bibliography

21. Appendix E: MATLAB’s GUI Tools Tutorial

21.1 Introduction

21.2 The Linear System Analyzer: description

21.3 Using the Linear System Analyzer

21.4 Linear System Analyzer examples

21.5 Simulink and the Linear Analysis Tool

21.6 Using the Linear Analysis Tool with Simulink to analyze a response

21.7 The Control System Designer: description

21.8 Using the Control System Designer

21.9 Summary

21.10 Bibliography

22. Appendix F: MATLAB’s Symbolic Math Toolbox Tutorial

22.1 Introduction

22.2 Symbolic Math Toolbox examples

22.3 Command summary

22.4 Bibliography

23. Appendix G: Matrices, Determinants, and Systems of Equations

23.1 Matrix definitions and notations

23.2 Matrix operations

23.3 Matrix and determinant identities

23.4 Systems of equations

23.5 Bibliography

24. Appendix H: Control System Computational Aids

24.1 Step response of a system represented in state space

24.2 Root locus and frequency response

25. Appendix I: Derivation of a Schematic for a DC Motor

25.1 Derivation of a schematic for a DC motor

25.2 Bibliography

26. Appendix J: Derivation of the Time Domain Solution of State Equations

26.1 Derivation of the time domain solution of state equations

26.2 Bibliography

27. Appendix K: Solution of State Equations for a Different Initial Time

27.1 Solution of state equations for a different initial time

27.2 Bibliography

28. Appendix L: Derivation of Similarity Transformations

28.1 Introduction

28.2 Expressing any vector in terms of basis vectors

28.3 Vector transformations

28.4 Finding the transformation matrix, P

28.5 Transforming the state equations

28.6 Bibliography

29. Appendix M: Root Locus Rules: Derivations

29.1 Derivation of the behavior of the root locus at infinity (Kuo, 1987)

29.2 Derivation of transition method for breakaway and break-in points

29.3 Bibliography

## Same Text, More Action

Highly regarded for its accessibility and focus on practical applications, Control Systems Engineering offers students a comprehensive introduction to the design and analysis of feedback systems that support modern technology. Now available in a zyVersion, **Control Systems Engineering** features:

- Over 100 animations bring hard-to-visualize concepts to life
- More than 700 individual questions make up learning question sets that will help students understand topics through incremental steps providing thorough explanations of both right and wrong answers
- 80 Challenge Activities (“auto-graded homework problems”) provide algorithmic, auto-graded versions of the end-of-chapter problems in the original text
- An additional 21 Challenge Activities using MATLAB® GraderTM are available for a modest extra cost

### Optional Challenge Activities

As an instructor, you have the ability to mark Challenge Activities as optional, which means you can indicate which Challenge Activities your students need to complete in order to meet your course requirements. Those marked as optional won’t contribute to point totals in reports or assignments.

### Also available – zyLabs with MATLAB® GraderTM

Available for a modest extra cost, MATLAB® zyLabs is a program submission and auto-grading system. MATLAB® zyLabs is an implementation of MATLAB® GraderTM within the zyVersion through our partnership with MathWorks.

- Instructors can create labs and assessments using features built into MATLAB® zyLabs and write scripts for custom assessments – no software installation required
- MATLAB® zyLabs are fully integrated into the zyVersion and provide students access to MATLAB’s industry standard toolboxes
- Students can run MATLAB commands directly in zyLabs, avoiding the complexity of using external tools
- Students receive immediate feedback on their submissions and can correct and resubmit their solutions, increasing student learning and motivation

## What is a zyVersion?

zyVersions are leading print titles converted and adapted to zyBooks’ interactive learning platform, allowing for a quick and easy transition to an engaging digital experience for instructors and students.

zyBooks’ web-native content helps students visualize concepts to learn faster and more effectively than with a traditional textbook.

This zyVersion of **Control Systems Engineering (8e)** benefits both students and instructors:

- Instructor benefits
- Customize your course by reorganizing existing content, or adding your own content
- Continuous publication model updates your course with the latest content and technologies
- Robust reporting gives you insight into students’ progress, reading and participation

- Student benefits
- Learning questions and other content serve as an interactive form of reading and provide instant feedback
- Concepts come to life through extensive animations embedded into the interactive content
- Save chapters as PDFs to reference material at any time, even after the course has been completed

### Control Systems Engineering in Action

In the video below, University of South Wales instructor Selim Tudgey discusses how she teaches with the Control Systems Engineering zyVersion:

## Author

**Norman S. Nise**

*California State Polytechnic University, Pomona*

## Key Contributors

**Yasaman Adibi**

*Content Developer at zyBooks*

**Mark Atkins**

*Associate Professor of Electrical Engineering (retired), Ivy Tech Community College*

**Greg Mason**

*Content Developer at zyBooks / Professor Emeritus, Mechanical Engineering, Seattle University*

**Oscar Rios**

*Content Developer at zyBooks*

**Mohsen Sarraf**

*Senior lecturer in Electrical Engineering, University of New Haven*