An Introduction to System Modeling and Control

✍ Scribed by John Chiasson

• Publisher: Wiley
• Year: 2022
• Tongue: English
• Leaves: 755
• Edition: 1
• Category: Library

✦ Synopsis

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

Cover
Title Page
Copyright
Contents
Preface
About the Companion Website
Chapter 1 Introduction
1.1 Aircraft
1.2 Quadrotors
1.3 Inverted Pendulum
1.4 Magnetic Levitation
1.5 General Control Problem
Chapter 2 Laplace Transforms
2.1 Laplace Transform Properties
2.2 Partial Fraction Expansion
2.3 Poles and Zeros
2.4 Poles and Partial Fractions
Appendix: Exponential Function
Problems
Chapter 3 Differential Equations and Stability
3.1 Differential Equations
3.2 Phasor Method of Solution
3.3 Final Value Theorem
3.4 Stable Transfer Functions
3.5 Routh–Hurwitz Stability Test
Problems
Chapter 4 Mass–Spring–Damper Systems
4.1 Mechanical Work
4.2 Modeling Mass–Spring–Damper Systems
4.3 Simulation
Problems
Chapter 5 Rigid Body Rotational Dynamics
5.1 Moment of Inertia
5.2 Newton's Law of Rotational Motion
5.3 Gears
5.4 Rolling Cylinder
Problems
Chapter 6 The Physics of the DC Motor
6.1 Magnetic Force
6.2 Single‐Loop Motor
6.3 Faraday's Law
6.4 Dynamic Equations of the DC Motor
6.5 Optical Encoder Model
6.6 Tachometer for a DC Machine
6.7 The Multiloop DC Motor
Problems
Chapter 7 Block Diagrams
7.1 Block Diagram for a DC Motor
7.2 Block Diagram Reduction
Problems
Chapter 8 System Responses
8.1 First‐Order System Response
8.2 Second‐Order System Response
8.3 Second‐Order Systems with Zeros
8.4 Third‐Order Systems
Appendix: Root Locus Matlab File
Problems
Chapter 9 Tracking and Disturbance Rejection
9.1 Servomechanism
9.2 Control of a DC Servo Motor
9.3 Theory of Tracking and Disturbance Rejection
9.4 Internal Model Principle
9.5 Design Example: PI‐D Control of Aircraft Pitch
9.6 Model Uncertainty and Feedback
Problems
Chapter 10 Pole Placement, 2 DOF Controllers, and Internal Stability
10.1 Output Pole Placement
10.2 Two Degrees of Freedom Controllers
10.3 Internal Stability
10.4 Design Example: 2 DOF Control of Aircraft Pitch
10.5 Design Example: Satellite with Solar Panels (Collocated Case)
Appendix: Output Pole Placement
Appendix: Multinomial Expansions
Appendix: Overshoot
Appendix: Unstable Pole‐Zero Cancellation
Appendix: Undershoot
Problems
Chapter 11 Frequency Response Methods
11.1 Bode Diagrams
11.2 Nyquist Theory
11.3 Relative Stability: Gain and Phase Margins
11.4 Closed‐Loop Bandwidth
11.5 Lead and Lag Compensation
11.6 Double Integrator Control via Lead‐Lag Compensation
11.7 Inverted Pendulum with Output Y(s)=X(s)+ℓ+Jmℓθ(s)
Appendix: Bode and Nyquist Plots in Matlab
Problems
Chapter 12 Root Locus
12.1 Angle Condition and Root Locus Rules
12.2 Asymptotes and Their Real Axis Intersection
12.3 Angles of Departure
12.4 Effect of Open‐Loop Poles on the Root Locus
12.5 Effect of Open‐Loop Zeros on the Root Locus
12.6 Breakaway Points and the Root Locus
12.7 Design Example: Satellite with Solar Panels (Noncollocated)
Problems
Chapter 13 Inverted Pendulum, Magnetic Levitation, and Cart on a Track
13.1 Inverted Pendulum
13.2 Linearization of Nonlinear Models
13.3 Magnetic Levitation
13.4 Cart on a Track System
Problems
Chapter 14 State Variables
14.1 Statespace Form
14.2 Transfer Function to Statespace
14.3 Laplace Transform of the Statespace Equations
14.4 Fundamental Matrix &rmPhi;
14.5 Solution of the Statespace Equation
14.6 Discretization of a Statespace Model
Problems
Chapter 15 State Feedback
15.1 Two Examples
15.2 General State Feedback Trajectory Tracking
15.3 Matrix Inverses and the Cayley–Hamilton Theorem
15.4 Stabilization and State Feedback
15.5 State Feedback and Disturbance Rejection
15.6 Similarity Transformations
15.7 Pole Placement
15.8 Asymptotic Tracking of Equilibrium Points
15.9 Tracking Step Inputs via State Feedback
15.10 Inverted Pendulum on an Inclined Track
15.11 Feedback Linearization Control
Appendix: Disturbance Rejection in the Statespace
Problems
Chapter 16 State Estimators and Parameter Identification
16.1 State Estimators
16.2 State Feedback and State Estimation in the Laplace Domain
16.3 Multi‐Output Observer Design for the Inverted Pendulum
16.4 Properties of Matrix Transpose and Inverse
16.5 Duality
16.6 Parameter Identification
Problems
Chapter 17 Robustness and Sensitivity of Feedback
17.1 Inverted Pendulum with Output x
17.2 Inverted Pendulum with Output y(t)=x(t)+ℓ+Jmℓθ(t)
17.3 Inverted Pendulum with State Feedback
17.4 Inverted Pendulum with an Integrator and State Feedback
17.5 Inverted Pendulum with State Feedback via State Estimation
Problems
References
Index
EULA