Modeling and Analysis of Dynamic Systems

, by Close, Charles M.; Frederick, Dean K.; Newell, Jonathan C.

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ISBN: 9780471394426 | 0471394424
Cover: Paperback
Copyright: 8/20/2001

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The book presents the methodology applicable to the modeling and analysis of a variety of dynamic systems, regardless of their physical origin. It includes detailed modeling of mechanical, electrical, electro-mechanical, thermal, and fluid systems. Models are developed in the form of state-variable equations, input-output differential equations, transfer functions, and block diagrams. The Laplace-transform is used for analytical solutions. Computer solutions are based on MATLAB and Simulink.

Introduction

(13)

Rationale

(1)

Analysis of Dynamic Systems

(3)

Modeling the System

(2)

Solving the Model

(1)

Classification of Variables

(1)

Classification of Systems

(6)

Spatial Characteristics

(1)

Continuity of the Time Variable

(1)

Quantization of the Dependent Variable

(1)

Parameter Variation

(1)

Superposition Property

(1)

Analogous Systems

(1)

Computer Tools

(1)

Scope and Objectives

(2)

Translational Mechanical Systems

(34)

Variables

(2)

Element Laws

(4)

Mass

(1)

Friction

(2)

Stiffness

(1)

Interconnection Laws

(3)

D'Alembert's Law

(1)

The Law of Reaction Forces

(1)

The Law for Displacements

(2)

Obtaining the System Model

(25)

Free-Body Diagrams

(4)

Relative Displacements

(4)

The Ideal Pulley

(2)

Parallel Combinations

(3)

Series Combinations

(2)

Summary

(1)

Problems

(9)

Standard Forms for System Models

(25)

State-Variable Equations

(12)

Input-Output Equations

(3)

Reduction of Simultaneous Differential Equations

(1)

Comparison with the State-Variable Method

(1)

Matrix Formulation of State-Variable Equations

(10)

Summary

(1)

Problems

(4)

Block Diagrams And Computer Simulation

(22)

Diagram Blocks

(2)

Summer

(1)

Gain

(1)

Integrator

(1)

Constant

(1)

Combining Blocks to Solve Modeling Equations

(5)

Diagrams for Input-Output Equations

(2)

Diagrams for the Original Modeling Equations

(1)

Diagrams for State-Variable Models

(1)

Structure of Block Diagrams

(1)

Running Simulink with MATLAB

(10)

Blocks

(2)

Inputs

(1)

Running the Simulation

(4)

M-files

(4)

Repetitive Inputs

(5)

Signal Generator

(1)

Scope

(2)

Summary

(1)

Problems

(3)

Rotational Mechnical Systems

(43)

Variables

(1)

Element Laws

(6)

Moment of Inertia

(1)

Friction

(1)

Stiffness

(2)

The Lever

100

(1)

Gears

100

(2)

Interconnection Laws

102

(2)

D'Alembert's Law

103

(1)

The Law of Reaction Torques

103

(1)

The Law for Angular Displacements

103

(1)

Obtaining the System Model

104

(20)

Computer Simulation

124

(14)

Summary

125

(1)

Problems

126

(12)

Electrical Systems

138

(49)

Variables

138

(2)

Element Laws

140

(4)

Resistor

140

(1)

Capacitor

141

(1)

Inductor

142

(1)

Sources

142

(1)

Open and Short Circuits

143

(1)

Interconnection Laws

144

(4)

Kirchhoff's Voltage Law

144

(1)

Kirchhoff's Current Law

144

(4)

Obtaining the Input-Output Model

148

(6)

Resistive Circuits

154

(5)

Resistors in Series

155

(1)

Resistors in Parallel

156

(2)

The Steady-State Response

158

(1)

Obtaining the State-Variable Model

159

(7)

Operational Amplifiers

166

(7)

Computer Simulation

173

(14)

Summary

177

(1)

Problems

177

(10)

Transform Solutions of Linear Models

187

(55)

Basic Considerations

187

(2)

State-Variable Solutions

187

(1)

Solution of the Input-Output Differential Equation

188

(1)

Laplace Transform Solutions

188

(1)

Transforms of Functions

189

(3)

Step Function

189

(1)

Exponential Function

190

(1)

Ramp Function

191

(1)

Trigonometric Functions

191

(1)

Rectangular Pulse

192

(1)

Transform Properties

192

(5)

Multiplication by a Constant

193

(1)

Superposition

193

(1)

Multiplication of Functions

193

(1)

Multiplication by an Exponential

194

(1)

Multiplication by Time

194

(1)

Differentiation

195

(1)

Integration

196

(1)

First-Order Systems

197

(10)

General Procedure

199

(1)

General First-Order Model

199

(1)

Part of the Solution

200

(3)

Initial Conditions

203

(4)

The Step Function and Impulse

207

(13)

The Unit Step Function

207

(3)

The Unit Impulse

210

(4)

The Transform of the Unit Impulse

216

(4)

Transform Inversion

220

(9)

Distinct Poles

221

(1)

Repeated Poles

222

(2)

Complex Poles

224

(4)

Preliminary Step of Long Division

228

(1)

Additional Transform Properties

229

(13)

Time Delay

229

(3)

Inversion of Some Irrational Transforms

232

(1)

Initial-Value and Final-Value Theorems

233

(3)

Problems

236

(6)

Transform Function Analysis

242

(57)

The Complete Solution

242

(10)

Parts of the Solution

249

(3)

The Zero-Input Response

252

(12)

Second-Order Systems

253

(1)

The Complex Plane

253

(3)

A Property of Stable Systems

256

(2)

Damping Ratio and Undamped Natural Frequency

258

(5)

Mode Functions

263

(1)

The Zero-State Response

264

(10)

The Transfer Function

265

(1)

Poles and Zeros

265

(2)

Transient and Steady-State Components

267

(2)

The Impulse Response

269

(2)

The Step Response

271

(2)

Differentiating the Input

273

(1)

Frequency Response

274

(6)

Properties of the Transfer Function

280

(3)

Impedances

283

(16)

Summary

287

(1)

Problems

288

(11)

Developing a Linear Model

299

(37)

Linearization of an Element Law

299

(6)

Graphical Approach

300

(2)

Series-Expansion Approach

302

(3)

Linerarization of the Model

305

(11)

Circuits with Nonlinear Resistors

311

(5)

Computer Simulation

316

(6)

Piecewise Linear Systems

322

(14)

Summary

325

(1)

Problems

326

(10)

Electromechanical Systems

336

(33)

Resistive Coupling

336

(3)

Loading Effect

338

(1)

Coupling by a Magnetic Field

339

(3)

Devices Coupled by Magnetic Fields

342

(11)

The Galvanometer

342

(3)

The Microphone

345

(2)

A Direct-Current Motor

347

(6)

A Device for Measuring Acceleration

353

(4)

System Description

353

(1)

System Model

354

(1)

Transfer Function

355

(1)

Frequency Response

356

(1)

Computer Simulation

357

(12)

Summary

360

(1)

Problems

361

(8)

Thermal Systems

369

(27)

Variables

369

(1)

Element Laws

370

(3)

Thermal Capacitance

370

(1)

Thermal Resistance

371

(2)

Thermal Sources

373

(1)

Dynamic Models of Thermal Systems

373

(14)

A Thermal System

387

(9)

System Description

384

(1)

System Model

385

(1)

System Response

386

(3)

Summary

389

(1)

Problems

390

(6)

Fluid Systems

396

(21)

Variables

396

(1)

Element Laws

397

(7)

Capacitance

397

(2)

Resistance

399

(4)

Sources

403

(1)

Dynamic Models of Hydraulic Systems

404

(13)

Summary

410

(1)

Problems

411

(6)

Block Diagrams for Dynamic Systems

417

(38)

Rules for Altering Diagram Structure

417

(6)

Series Combination

418

(1)

Parallel Combination

418

(2)

Moving a Pick-Off Point

420

(1)

Moving a Simming Junction

421

(2)

Reducing Diagrams for Feedback Systems

423

(8)

Diagrams for Input-Output Models

431

(9)

Second-Order Systems

432

(5)

Higher-Order Systems

437

(3)

Application to a Control System

440

(15)

System Description

441

(2)

System Model

443

(1)

Closed-Loop Transfer Function

444

(1)

Design for Specified Damping Ratio

445

(1)

Proportional-Plus-Derivative Feedback

445

(3)

Summary

448

(1)

Problems

448

(7)

Modeling, Analysis, and Design Tools

455

(43)

Building Linear Models

455

(11)

Transfer-Function Form

456

(1)

Zero-Pole-Gain Form

456

(1)

State-Space Form

457

(1)

Extracting Data and Changing Forms

458

(3)

Series Connection

461

(3)

Parallel Connection

464

(2)

Time-Domain Analysis

466

(4)

Step and Impulse Responses

466

(1)

Responses to Arbitrary Inputs and Initial Conditions

467

(3)

Frequency-Domain Analysis

470

(9)

Using MATLAB to Construct Bode Diagrams

475

(2)

Using MATLAB to Construct Linear Plots

477

(2)

Models for Feedback Systems

479

(2)

Constructing MATLAB Models

479

(2)

Stability

481

(1)

Root-Locus Plots

481

(8)

Using MATLAB to Construct the Locus

486

(2)

Other Applications of the Root Locus

488

(1)

Stability Criteria

489

(9)

Summary

492

(1)

Problems

492

(6)

Feedback Design With Matlab

498

(35)

Design Guidelines

498

(13)

Proportional Control

500

(4)

Proportional-Plus-Derivative Control

504

(2)

Proportional-Plus-Integral Control

506

(2)

Other Types of Control

508

(2)

Additional Concerns

510

(1)

Applications

511

(22)

Summary

525

(1)

Problems

526

(7)

APPENDIX A UNITS

533

(2)

APPENDIX B MATRICES

535

(2)

APPENDIX C COMPLEX ALGEBRA

537

(5)

APPENDIX D CLASSICAL SOLUTION OF DIFFERENTIAL EQUATIONS

542

(5)

D.1 Homogeneous Differential Equations

542

(2)

D.2 Nonhomogeneous Differential Equations

544

(3)

APPENDIX E LAPLACE TRANSFORMS

547

(3)

APPENDIX F SELECTED READING

550

(3)

APPENDIX G ANSWERS TO SELECTED PROBLEMS

553

(18)

Index

571

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Modeling and Analysis of Dynamic Systems

Summary

Author Biography

Table of Contents

Supplemental Materials