book

An Introduction to System Modeling and Control

Name: An Introduction to System Modeling and Control
Author: John Chiasson
ISBN: 9781119842897

by John Chiasson

March 2022

Intermediate to advanced

752 pages

24h 14m

English

Wiley

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Cover
Title Page
Copyright
Preface
About the Companion Website
1 Introduction
1.1 Aircraft1.2 Quadrotors1.3 Inverted Pendulum1.4 Magnetic Levitation1.5 General Control ProblemNotes
2 Laplace Transforms
2.1 Laplace Transform Properties2.2 Partial Fraction Expansion2.3 Poles and Zeros2.4 Poles and Partial FractionsAppendix: Exponential FunctionProblemsNotes
3 Differential Equations and Stability
3.1 Differential Equations3.2 Phasor Method of Solution3.3 Final Value Theorem3.4 Stable Transfer Functions3.5 Routh–Hurwitz Stability TestProblemsNotes
4 Mass–Spring–Damper Systems
4.1 Mechanical Work4.2 Modeling Mass–Spring–Damper Systems4.3 SimulationProblems
5 Rigid Body Rotational Dynamics
5.1 Moment of Inertia5.2 Newton's Law of Rotational Motion5.3 Gears5.4 Rolling CylinderProblemsNotes

6 The Physics of the DC Motor
6.1 Magnetic Force6.2 Single‐Loop Motor6.3 Faraday's Law6.4 Dynamic Equations of the DC Motor6.5 Optical Encoder Model6.6 Tachometer for a DC Machine*6.7 The Multiloop DC Motor*ProblemsNotes
7 Block Diagrams
7.1 Block Diagram for a DC Motor7.2 Block Diagram ReductionProblemsNote
8 System Responses
8.1 First‐Order System Response8.2 Second‐Order System Response8.3 Second‐Order Systems with Zeros8.4 Third‐Order SystemsAppendix: Root Locus Matlab FileProblemsNote
9 Tracking and Disturbance Rejection
9.1 Servomechanism9.2 Control of a DC Servo Motor9.3 Theory of Tracking and Disturbance Rejection9.4 Internal Model Principle9.5 Design Example: PI‐D Control of Aircraft Pitch9.6 Model Uncertainty and Feedback*ProblemsNotes
10 Pole Placement, 2 DOF Controllers, and Internal Stability
10.1 Output Pole Placement10.2 Two Degrees of Freedom Controllers10.3 Internal Stability10.4 Design Example: 2 DOF Control of Aircraft Pitch10.5 Design Example: Satellite with Solar Panels (Collocated Case)Appendix: Output Pole PlacementAppendix: Multinomial ExpansionsAppendix: OvershootAppendix: Unstable Pole‐Zero CancellationAppendix: UndershootProblemsNotes
11 Frequency Response Methods
11.1 Bode Diagrams11.2 Nyquist Theory11.3 Relative Stability: Gain and Phase Margins11.4 Closed‐Loop Bandwidth11.5 Lead and Lag Compensation11.6 Double Integrator Control via Lead‐Lag Compensation11.7 Inverted Pendulum with Output Appendix: Bode and Nyquist Plots in MatlabProblemsNotes
12 Root Locus
12.1 Angle Condition and Root Locus Rules12.2 Asymptotes and Their Real Axis Intersection12.3 Angles of Departure12.4 Effect of Open‐Loop Poles on the Root Locus12.5 Effect of Open‐Loop Zeros on the Root Locus12.6 Breakaway Points and the Root Locus12.7 Design Example: Satellite with Solar Panels (Noncollocated)ProblemsNote
13 Inverted Pendulum, Magnetic Levitation, and Cart on a Track
13.1 Inverted Pendulum13.2 Linearization of Nonlinear Models13.3 Magnetic Levitation13.4 Cart on a Track SystemProblemsNotes
14 State Variables
14.1 Statespace Form14.2 Transfer Function to Statespace14.3 Laplace Transform of the Statespace Equations14.4 Fundamental Matrix 14.5 Solution of the Statespace Equation*14.6 Discretization of a Statespace Model*ProblemsNote
15 State Feedback
15.1 Two Examples15.2 General State Feedback Trajectory Tracking15.3 Matrix Inverses and the Cayley–Hamilton Theorem15.4 Stabilization and State Feedback15.5 State Feedback and Disturbance Rejection15.6 Similarity Transformations15.7 Pole Placement15.8 Asymptotic Tracking of Equilibrium Points15.9 Tracking Step Inputs via State Feedback15.10 Inverted Pendulum on an Inclined Track*15.11 Feedback Linearization Control*Appendix: Disturbance Rejection in the StatespaceProblemsNotes
16 State Estimators and Parameter Identification
16.1 State Estimators16.2 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 Inverse16.5 Duality*16.6 Parameter IdentificationProblemsNote
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 Feedback17.4 Inverted Pendulum with an Integrator and State Feedback17.5 Inverted Pendulum with State Feedback via State EstimationProblemsNotes
References
Index
Wiley End User License Agreement

Content preview from An Introduction to System Modeling and Control

14State Variables

14.1 Statespace Form

Consider the mass–spring–damper system in Figure 14.1.

Schematic illustration of (a) Spring-mass-damper system. (b) Damper cross section. — Figure 14.1. (a) Spring–mass–damper system. (b) Damper cross section.

If then the spring is neither compressed nor stretched, which is to say the spring is relaxed. The force on the mass due to the spring is

Note that if the spring is pulling to the left while if the spring is pushing to the right. The damper (dashpot) is illustrated in more detail on Figure 14.1b. The force of the damper on is proportional to its velocity and is given by

Note that if then the mass along with the ...

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An Introduction to System Modeling and Control

by John Chiasson

14State Variables

14.1 Statespace Form

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