An Introduction to System Modeling and Control

An Introduction to System Modeling and Control

by John Chiasson
Released March 2022
Publisher(s): Wiley
ISBN: 9781119842897

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Book description

A practical and straightforward exploration of the basic tools for the modeling, analysis, and design of control systems

In An Introduction to System Modeling and Control, Dr. Chiasson delivers an accessible and intuitive guide to understanding modeling and control for students in electrical, mechanical, and aerospace/aeronautical engineering. The book begins with an introduction to the need for control by describing how an aircraft flies complete with figures illustrating roll, pitch, and yaw control using its ailerons, elevators, and rudder, respectively. The book moves on to rigid body dynamics about a single axis (gears, cart rolling down an incline) and then to modeling DC motors, DC tachometers, and optical encoders. Using the transfer function representation of these dynamic models, PID controllers are introduced as an effective way to track step inputs and reject constant disturbances.

It is further shown how any transfer function model can be stabilized using output pole placement and on how two-degree of freedom controllers can be used to eliminate overshoot in step responses. Bode and Nyquist theory are then presented with an emphasis on how they give a quantitative insight into a control system's robustness and sensitivity. An Introduction to System Modeling and Control closes with chapters on modeling an inverted pendulum and a magnetic levitation system, trajectory tracking control using state feedback, and state estimation. In addition the book offers:

  • A complete set of MATLAB/SIMULINK files for examples and problems included in the book.
  • A set of lecture slides for each chapter.
  • A solutions manual with recommended problems to assign.
  • An analysis of the robustness and sensitivity of four different controller designs for an inverted pendulum (cart-pole).

Perfect for electrical, mechanical, and aerospace/aeronautical engineering students, An Introduction to System Modeling and Control will also be an invaluable addition to the libraries of practicing engineers.

Table of contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Preface
  5. About the Companion Website
  6. 1 Introduction
    1. 1.1 Aircraft
    2. 1.2 Quadrotors
    3. 1.3 Inverted Pendulum
    4. 1.4 Magnetic Levitation
    5. 1.5 General Control Problem
    6. Notes
  7. 2 Laplace Transforms
    1. 2.1 Laplace Transform Properties
    2. 2.2 Partial Fraction Expansion
    3. 2.3 Poles and Zeros
    4. 2.4 Poles and Partial Fractions
    5. Appendix: Exponential Function
    6. Problems
    7. Notes
  8. 3 Differential Equations and Stability
    1. 3.1 Differential Equations
    2. 3.2 Phasor Method of Solution
    3. 3.3 Final Value Theorem
    4. 3.4 Stable Transfer Functions
    5. 3.5 Routh–Hurwitz Stability Test
    6. Problems
    7. Notes
  9. 4 Mass–Spring–Damper Systems
    1. 4.1 Mechanical Work
    2. 4.2 Modeling Mass–Spring–Damper Systems
    3. 4.3 Simulation
    4. Problems
  10. 5 Rigid Body Rotational Dynamics
    1. 5.1 Moment of Inertia
    2. 5.2 Newton's Law of Rotational Motion
    3. 5.3 Gears
    4. 5.4 Rolling Cylinder
    5. Problems
    6. Notes
  11. 6 The Physics of the DC Motor
    1. 6.1 Magnetic Force
    2. 6.2 Single‐Loop Motor
    3. 6.3 Faraday's Law
    4. 6.4 Dynamic Equations of the DC Motor
    5. 6.5 Optical Encoder Model
    6. 6.6 Tachometer for a DC Machine*
    7. 6.7 The Multiloop DC Motor*
    8. Problems
    9. Notes
  12. 7 Block Diagrams
    1. 7.1 Block Diagram for a DC Motor
    2. 7.2 Block Diagram Reduction
    3. Problems
    4. Note
  13. 8 System Responses
    1. 8.1 First‐Order System Response
    2. 8.2 Second‐Order System Response
    3. 8.3 Second‐Order Systems with Zeros
    4. 8.4 Third‐Order Systems
    5. Appendix: Root Locus Matlab File
    6. Problems
    7. Note
  14. 9 Tracking and Disturbance Rejection
    1. 9.1 Servomechanism
    2. 9.2 Control of a DC Servo Motor
    3. 9.3 Theory of Tracking and Disturbance Rejection
    4. 9.4 Internal Model Principle
    5. 9.5 Design Example: PI‐D Control of Aircraft Pitch
    6. 9.6 Model Uncertainty and Feedback*
    7. Problems
    8. Notes
  15. 10 Pole Placement, 2 DOF Controllers, and Internal Stability
    1. 10.1 Output Pole Placement
    2. 10.2 Two Degrees of Freedom Controllers
    3. 10.3 Internal Stability
    4. 10.4 Design Example: 2 DOF Control of Aircraft Pitch
    5. 10.5 Design Example: Satellite with Solar Panels (Collocated Case)
    6. Appendix: Output Pole Placement
    7. Appendix: Multinomial Expansions
    8. Appendix: Overshoot
    9. Appendix: Unstable Pole‐Zero Cancellation
    10. Appendix: Undershoot
    11. Problems
    12. Notes
  16. 11 Frequency Response Methods
    1. 11.1 Bode Diagrams
    2. 11.2 Nyquist Theory
    3. 11.3 Relative Stability: Gain and Phase Margins
    4. 11.4 Closed‐Loop Bandwidth
    5. 11.5 Lead and Lag Compensation
    6. 11.6 Double Integrator Control via Lead‐Lag Compensation
    7. 11.7 Inverted Pendulum with Output
    8. Appendix: Bode and Nyquist Plots in Matlab
    9. Problems
    10. Notes
  17. 12 Root Locus
    1. 12.1 Angle Condition and Root Locus Rules
    2. 12.2 Asymptotes and Their Real Axis Intersection
    3. 12.3 Angles of Departure
    4. 12.4 Effect of Open‐Loop Poles on the Root Locus
    5. 12.5 Effect of Open‐Loop Zeros on the Root Locus
    6. 12.6 Breakaway Points and the Root Locus
    7. 12.7 Design Example: Satellite with Solar Panels (Noncollocated)
    8. Problems
    9. Note
  18. 13 Inverted Pendulum, Magnetic Levitation, and Cart on a Track
    1. 13.1 Inverted Pendulum
    2. 13.2 Linearization of Nonlinear Models
    3. 13.3 Magnetic Levitation
    4. 13.4 Cart on a Track System
    5. Problems
    6. Notes
  19. 14 State Variables
    1. 14.1 Statespace Form
    2. 14.2 Transfer Function to Statespace
    3. 14.3 Laplace Transform of the Statespace Equations
    4. 14.4 Fundamental Matrix
    5. 14.5 Solution of the Statespace Equation*
    6. 14.6 Discretization of a Statespace Model*
    7. Problems
    8. Note
  20. 15 State Feedback
    1. 15.1 Two Examples
    2. 15.2 General State Feedback Trajectory Tracking
    3. 15.3 Matrix Inverses and the Cayley–Hamilton Theorem
    4. 15.4 Stabilization and State Feedback
    5. 15.5 State Feedback and Disturbance Rejection
    6. 15.6 Similarity Transformations
    7. 15.7 Pole Placement
    8. 15.8 Asymptotic Tracking of Equilibrium Points
    9. 15.9 Tracking Step Inputs via State Feedback
    10. 15.10 Inverted Pendulum on an Inclined Track*
    11. 15.11 Feedback Linearization Control*
    12. Appendix: Disturbance Rejection in the Statespace
    13. Problems
    14. Notes
  21. 16 State Estimators and Parameter Identification
    1. 16.1 State Estimators
    2. 16.2 State Feedback and State Estimation in the Laplace Domain*
    3. 16.3 Multi‐Output Observer Design for the Inverted Pendulum*
    4. 16.4 Properties of Matrix Transpose and Inverse
    5. 16.5 Duality*
    6. 16.6 Parameter Identification
    7. Problems
    8. Note
  22. 17 Robustness and Sensitivity of Feedback
    1. 17.1 Inverted Pendulum with Output x
    2. 17.2 Inverted Pendulum with Output
    3. 17.3 Inverted Pendulum with State Feedback
    4. 17.4 Inverted Pendulum with an Integrator and State Feedback
    5. 17.5 Inverted Pendulum with State Feedback via State Estimation
    6. Problems
    7. Notes
  23. References
  24. Index
  25. Wiley End User License Agreement

Product information

  • Title: An Introduction to System Modeling and Control
  • Author(s): John Chiasson
  • Release date: March 2022
  • Publisher(s): Wiley
  • ISBN: 9781119842897