Fundamentals of Modeling and Analyzing Engineering Systems

, by Philip D. Cha , James J. Rosenberg , Clive L. Dym

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ISBN: 9780521594431 | 052159443X
Cover: Hardcover
Copyright: 4/13/2000

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System modeling and analysis is a standard activity in every engineering discipline. This text offers a broad-based introduction to systems engineering that incorporates material from mechanical, electrical, aerospace, and chemical engineering. The overall theme that distinguishes it from other texts is its unified treatment of disparate physical systems, emphasizing similarities in both the modeling and behavior of lumped-element systems. Every chapter includes a wide variety of examples, as well as exercise problems, drawn from real-world mechanical, electrical, hydraulic, chemical, and thermal systems. Aimed at second- and third-year undergraduates, this introductory text offers a unified entry into the multidisciplinary world of engineering. Solutions manual available.

Examples

xiii

Preface

xix

Fundamental Concepts in Mathematical Modeling

(17)

Systems, Modeling, and Analysis

(2)

Abstraction

(1)

Physical Dimensions and Units

(1)

Linearity and Superposition

(2)

A Gentle Introduction to Differential Equations

(2)

Scaling in Elementary Differential Equations

(2)

Balance and Conservation Laws and the System Boundary Approach

(5)

Balance Equations

(1)

Conservation Laws

(1)

Examples

(3)

Summary

(1)

Problems

(1)

Lumped-Element Modeling

(49)

Introduction

(1)

One-Dimensional Translational Mechanical Systems

(18)

The Elements Comprising Simple Mechanical Systems

(1)

Translational Springs

(4)

Translational Dampers

(1)

Mass Elements in Translational Motion

(1)

The Ideal Force and the Ideal Displacement Inputs

(1)

The Interrelationship Between Forces in Different Elements in a System: Newton's Second Law

(2)

The Interrelationship Between Deformations of Different Elements in a System: Consistency of Displacements

(1)

Simplifying Models Through Combination of Elements

(3)

Examples

(5)

Summary

(1)

RLC Electrical Systems

(21)

Some Electrical Basics: Charge, Voltage, and Current

(1)

The Inductive, Resistive, and Capacitive Elements

(1)

The Ideal Inductor Element

(1)

The Ideal Resistor Element

(1)

The Ideal Capacitor Element

(1)

The Ideal Current and Ideal Voltage Sources

(1)

The Interrelationship Between Currents in Different Elements in a System

(2)

The Interrelationships Between the Voltage Differences Across Elements in a System

(1)

Simplifying Models Through Combination of Elements

(5)

Examples

(7)

Summary

(1)

Summary

(1)

Appendix 2-A: Faraday's Law

(1)

Appendix 2-B: Thevenin and Norton Equivalents

(2)

Problems

(6)

Generalizing Lumped-Element Modeling

(58)

Introduction

(1)

A Framework for Unifying Lumped-Element Models

(18)

Some Common Approaches: Virtues and Shortcomings

(1)

``Basic'' Linear Graph Theory

(5)

Relating Linear Graph Theory to Lumped-Element Models of Physical Systems

(1)

Manipulation of Graph Theory Rules

(5)

Examples

(5)

Summary

(1)

Rotational Mechanical Systems

(11)

The Basics of Rotational Mechanics

(1)

Rotational Mechanical System Elements

(1)

Torsional Springs

(1)

Torsional Damper Elements

(1)

The Mass Moment of Inertia Element

(1)

The Ideal Torque and the Ideal Angular Displacement Inputs

(1)

The Rules Governing Rotational Mechanical Systems

(3)

Examples

(3)

Summary

(1)

Hydraulic Systems

(9)

Basic Physics of Incompressible Fluids

(2)

Hydraulic System Elements

(1)

The Pipe Element

(1)

The Tank Element

(2)

Ideal Flow Rate and Ideal Pressure Sources

101

(1)

The Rules Governing the Hydraulic Model

101

(1)

Examples

102

(2)

Summary

104

(1)

Thermal Systems

105

(5)

Basic Concepts in Heat Transfer

105

(1)

Thermal System Elements

106

(1)

The Thermal Resistance Element

106

(1)

The Thermal Mass Element

106

(1)

Ideal Heat Transfer Rate and Ideal Temperature Inputs

107

(1)

The Rules Governing the Thermal Model

108

(1)

Examples

108

(2)

Summary

110

(1)

Drawing Analogies

110

(7)

Summary

117

(1)

Problems

117

(8)

First-Order System Models

125

(30)

Governing Equations for First-Order Systems

125

(7)

Canonical Form of First-Order Systems

132

(3)

Classification of Responses and Systems

135

(1)

Solution of Governing Equations

135

(9)

Free Response

136

(2)

Forced Response

138

(6)

Transient Response Specifications

144

(1)

Experimental Determination of τ

145

(1)

Free Response

145

(1)

Forced Response

145

(1)

Applications of Superposition in First-Order System Models

146

(5)

Summary

151

(1)

Problems

152

(3)

Second-Order Models of Systems

155

(30)

Governing Equations for Second-Order Systems

155

(8)

Canonical Form and Classification of Response

163

(3)

Solution of Governing Equations

166

(6)

Free Response

166

(4)

Forced Response

170

(2)

Transient Response Specifications

172

(4)

Experimental Determination of ζ

176

(2)

Using Free Response to Determine ζ

176

(2)

Using Step Response to Determine ζ

178

(1)

Summary

178

(1)

Problems

178

(7)

Laplace Transform

185

(31)

Definition of the Laplace Transform

186

(2)

Properties of the Laplace Transform

188

(6)

Superposition

188

(1)

Shift in t or Time Delay

188

(1)

Shift in s

189

(1)

Time Derivatives

189

(1)

Time Integral

190

(1)

Final Value Theorem

191

(3)

The Inverse Laplace Transform

194

(6)

Response of First-Order Systems Using the Laplace Transforms

200

(4)

Solution of RC Free Response

201

(1)

Solution of RC Step Response

202

(1)

Solution of RC Sinusoidal Response

203

(1)

Response of Second-Order Systems Using the Laplace Transform

204

(5)

Free Response

204

(4)

Forced Unit Step Response

208

(1)

Summary

209

(1)

Appendix 6-A: Complex Arithmetic

209

(2)

Problems

211

(5)

Frequency Response of Linear, Time-Invariant Systems

216

(72)

Transfer Functions and the Sinusoidal Steady State

217

(7)

Steady-State Sinusoidal Response of First-Order Systems

217

(1)

The Transfer Function and Its Relation to the Governing Equation

218

(3)

The Relationship Between T(jω) and Sinusoidal Steady-State Response

221

(3)

Mathematical Features of the Transfer Function

224

(1)

Poles and Zeros

224

(1)

First- and Second-Order Factors and Delay Factors

224

(1)

Bode Plots

225

(13)

The General Frequency Response Function and Its Factors

226

(1)

Gain Factor: k

227

(1)

Integral and Derivative Factors: 1/jωτ and jωτ

228

(3)

First-Order Factor: 1 + jωτ

231

(3)

Quadratic Factor: 1 - (ω/ωn)2 + j2ζ(&omega/ωn)

234

(3)

Delay Factor: e-jωto

237

(1)

Frequency Response of First-Order and Second-Order Systems

238

(29)

First-Order Low-Pass Frequency Response Function

239

(1)

First-Order High-Pass Frequency Response Function

239

(1)

Second-Order Low-Pass Frequency Response Function

240

(4)

Second-Order High-Pass Frequency Response Function

244

(2)

Second-Order Band-Pass Frequency Response Function

246

(2)

Resonance

248

(2)

Transfer Functions for Systems with Delay

250

(1)

Examples

251

(16)

Impedance

267

(11)

Passing the Transform Through the Node and Loop Rule Summations

268

(1)

Impedance in Electrical and Mechanical Systems

269

(3)

Application of Impedance Techniques

272

(6)

Summary

278

(1)

Summary

278

(1)

Problems

279

(9)

State Space Formulations of Systems Problems

288

(38)

Examples of State Variables and State Equations

288

(5)

Matrix Formulation

293

(2)

Free Response and the Eigenvalue Problem

295

(3)

Stability

298

(1)

Graphical Solution

298

(1)

Forced Response and Response to a Step Input

299

(1)

Examples of State Space Formulations and Solutions

300

(17)

Phase Plane and Stability Considerations

317

(2)

Summary

319

(1)

Appendix 8-A: A Short Introduction to Matrix Manipulation

320

(3)

Problems

323

(3)

Relating the Time Domain, Frequency Domain, and State Space

326

(33)

Introduction

326

(1)

The Pole-Zero Plot

326

(5)

Relating the Pole-Zero Plot to the Transfer Function, the Governing Equation, and the State Matrix Eigenvalues

327

(1)

Relating Pole Locations to System Parameters

328

(1)

Examples

329

(2)

Relating Frequency Response to Pole Location

331

(11)

The Relationship Between the |T(s)| Surface and the Frequency Response Function

331

(3)

Higher-Order Systems and Dominant Poles

334

(1)

Examples

335

(7)

Transient Response, Poles, and Frequency Response

342

(12)

The Relationship Between the Mathematical Form of the Free Response, Pole Location, and System Parameters

342

(3)

The Effect of Nondominant Poles on Transient Behavior

345

(3)

Examples

348

(6)

State Space Trajectories, Poles, and Transient Response

354

(2)

Summary

356

(1)

Problems

356

(3)

Feedback Systems

359

(98)

Systems with Feedback

359

(6)

What Is Feedback?

359

(1)

Some Examples of Systems with Feedback

360

(5)

Representing Systems and Subsystems Using Transfer Functions

365

(7)

Representing Inputs, Outputs, and System Behavior in the s-Domain

365

(4)

Subsystem Interaction and Loading

369

(3)

Block Diagrams

372

(11)

Block Diagram Elements and Structure

372

(2)

Simplifying Block Diagrams

374

(4)

Examples

378

(5)

Properties of Feedback Systems

383

(5)

Effect of Feedback on Overall Gain

383

(1)

Effect of Feedback on Parameter Sensitivity

383

(1)

Effect of Feedback on External Disturbance or Noise

384

(2)

Effect of Feedback on Stability

386

(2)

Relative Stability and the Phase and Gain Margins

388

(11)

Relative Stability

388

(1)

Phase Margin and Gain Margin

388

(11)

Design of Controllers

399

(40)

Feedback Control Systems: General Configuration and Terminology

399

(8)

Proportional Control

407

(13)

Derivative Control and PD Control

420

(7)

Integral Control and PI Control

427

(8)

PID Control

435

(4)

Summary

439

(1)

Appendix 10-A: Feedback Circuits Based on Operational Amplifiers

440

(5)

Noninverting Amplifier

440

(2)

Inverting Amplifier

442

(3)

Appendix 10-B: DC Servomotors and Tachometers

445

(6)

DC Servomotors

445

(5)

Tachometers

450

(1)

Problems

451

(6)

Index

457

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Fundamentals of Modeling and Analyzing Engineering Systems

Summary

Table of Contents

Supplemental Materials