An Introduction to System Modeling and Control 1st Edition by John Chiasson ISBN 9781119842897 1119842891

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ISBN 10: 1119842891
ISBN 13: 9781119842897
Author: John Chiasson

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

An Introduction to System Modeling and Control 1st Edition Table of contents:

1 Introduction

1.1 Aircraft

1.2 Quadrotors

1.3 Inverted Pendulum

1.4 Magnetic Levitation

1.5 General Control Problem

Notes

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

Notes

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

Notes

4 Mass–Spring–Damper Systems

4.1 Mechanical Work

4.2 Modeling Mass–Spring–Damper Systems

4.3 Simulation

Problems

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

Notes

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

Notes

7 Block Diagrams

7.1 Block Diagram for a DC Motor

7.2 Block Diagram Reduction

Problems

Note

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

Note

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

Notes

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

Notes

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

Appendix: Bode and Nyquist Plots in Matlab

Problems

Notes

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

Note

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

Notes

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

14.5 Solution of the Statespace Equation*

14.6 Discretization of a Statespace Model*

Problems

Note

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

Notes

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

Note

17 Robustness and Sensitivity of Feedback

17.1 Inverted Pendulum with Output x

17.2 Inverted Pendulum with Output

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

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Tags: John Chiasson, System Modeling, Control