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 timeÂ
   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
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Norman S. Nise
California State Polytechnic University, Pomona
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