GLOBAL EDITION

Feedback Control of Dynamic SystemsS E V E N T H E D IT IO N

Gene F. Franklin • J. David Powell • Abbas Emami-Naeini

r is j . . . é î J J

Feedback Control of Dynamic Systems

Seventh Edition

Global Edition

Gene F. FranklinStanford University

J. David PowellStanford University

Abbas Emami-NaeiniSC Solutions, Inc.

Global Edition contributions by

Sanjay H.S.M.S. Ramaiah College of Engineering

PEARSON

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ContentsPreface 13

L An Overview and Brief History of Feedback Control 21A Perspective on Feedback Control 21 Chapter Overview 221.1 A Simple Feedback System 231.2 A First Analysis o f Feedback 261.3 Feedback System Fundamentals 301.4 A Brief History 311.5 An Overview of the Book 37Summary 39Review Questions 39 Problems 40

! Dynamic Models 43A Perspective on Dynamic M odels 43 Chapter Overview 442.1 Dynamics of M echanical Systems 44

2.1.1 Translational Motion 442.1.2 Rotational Motion 512.1.3 Combined Rotation and Translation 592.1.4 Complex M echanical Systems (W )** 622.1.5 Distributed Parameter Systems 622.1.6 Summary: Developing Equations of Motion

for Rigid Bodies 642.2 Models o f Electric Circuits 652.3 Models o f Electromechanical Systems 70

2.3.1 Loudspeakers 702.3.2 Motors 72

A 2.3.3 Gears 76A 2.4 Heat and Fluid-Flow Models 77

2.4.1 Heat Flow 782.4.2 Incompressible Fluid Flow 81

2.5 Historical Perspective 88 Summary 91Review Questions 91 Problems 92

**Sections with (W) indicates that additional material is located on the web at www.FPE7e.com.

5

6 Contents

Dynamic Response 104A Perspective on System Response 104 Chapter Overview 1053.1 Review o f Laplace Transforms 105

3.1.1 Response by Convolution 1063.1.2 Transfer Functions and Frequency Response 1113.1.3 The £ _ Laplace Transform 1213.1.4 Properties of Laplace Transforms 1233.1.5 Inverse Laplace Transform by Partial-Fraction

Expansion 1253.1.6 The Final Value Theorem 1273.1.7 Using Laplace Transforms to Solve Differential

Equations 1293.1.8 Poles and Zeros 1313.1.9 Linear System Analysis Using M atlab® 132

3.2 System M odeling Diagram s 1383.2.1 The Block D iagram 1383.2.2 Block-D iagram Reduction Using M atlab 1423.2.3 M ason’s Rule and the Signal Flow Graph (W) 143

3.3 Effect o f Pole Locations 1433.4 Tim e-Dom ain Specifications 151

3.4.1 Rise Time 1523.4.2 Overshoot and Peak Time 1523.4.3 Settling Time 154

3.5 Effects o f Zeros and Additional Poles 1573.6 Stability 166

3.6.1 Bounded Input-B ounded Output Stability 1673.6.2 Stability of LTI Systems 1683.6.3 R outh’s Stability Criterion 169

A 3.7 O btaining M odels from Experimental Data:System Identification (W) 176

A 3.8 Am plitude and Time Scaling (W) 1763.9 H istorical Perspective 176Sum m ary 177Review Questions 179 Problems 179

\ A First Analysis of Feedback 200A Perspective on the Analysis o f Feedback 200Chapter Overview 2014.1 The Basic Equations o f Control 202

4.1.1 Stability 2034.1.2 Tracking 2044.1.3 Regulation 2054.1.4 Sensitivity 206

Contents 7

4.2 Control o f Steady-State Error to Polynomial Inputs:System Type 208

4.2.1 System Type for Tracking 2094.2.2 System Type for Regulation and Disturbance

Rejection 2144.3 The Three-Term Controller: PID Control 216

4.3.1 Proportional Control (P) 2164.3.2 Integral Control (I) 2184.3.3 Derivative Control (D) 2214.3.4 Proportional Plus Integral Control (PI) 2214.3.5 PID Control 2224.3.6 Z iegler-N ichols Tuning of the PID

Controller 2264.4 Feedforward Control by Plant Model Inversion 232

A 4.5 Introduction to Digital Control (W) 234A 4.6 Sensitivity of Time Response to Parameter Change (W) 235

4.7 Historical Perspective 235Summary 237 Review Questions 238 Problems 238

J The Root-Locus Design Method 254A Perspective on the Root-Locus Design M ethod 254 Chapter Overview 2555.1 Root Locus of a Basic Feedback System 2555.2 Guidelines for Determining a Root Locus 260

5.2.1 Rules for Determining a Positive (180°)Root Locus 262

5.2.2 Summary of the Rules for Determining aRoot Locus 268

5.2.3 Selecting the Parameter Value 2695.3 Selected Illustrative Root Loci 2715.4 Design Using Dynamic Compensation 284

5.4.1 Design Using Lead Compensation 2865.4.2 Design Using Lag Com pensation 2905.4.3 Design Using Notch Compensation 292

A 5.4.4 Analog and Digital Implementations (W) 2945.5 A Design Example Using the Root Locus 2955.6 Extensions of the Root-Locus M ethod 301

5.6.1 Rules for Plotting a Negative (0°)Root Locus 301

A 5.6.2 Consideration of Two Parameters 304A 5.6.3 Time Delay (W) 306

5.7 Historical Perspective 307

Sum m ary 309 Review Questions 310 Problem s 311

The Frequency-Response Design Method 328A Perspective on the Frequency-Response Design M ethod 328 Chapter Overview 3296.1 Frequency Response 329

6.1.1 Bode Plot Techniques 3376.1.2 Steady-State Errors 350

6.2 Neutral Stability 3516.3 The N yquist Stability Criterion 353

6.3.1 The Argum ent Principle 3546.3.2 Application of The Argument Principle

to Control Design 3556.4 Stability M argins 3686.5 B ode’s G ain-Phase Relationship 3776.6 Closed-Loop Frequency Response 3816.7 Com pensation 383

6.7.1 PD Com pensation 3836.7.2 Lead Com pensation (W) 3846.7.3 PI Com pensation 3946.7.4 Lag Com pensation 3956.7.5 PID Com pensation 4016.7.6 Design Considerations 4076.7.7 Specifications in Terms of the Sensitivity

Function 4096.7.8 Lim itations on Design in Terms of the Sensitivity

Function 4146.8 Time Delay 418

6.8.1 Time Delay via the Nyquist Diagram (W) 4206.9 Alternative Presentation of Data 420

6.9.1 Nichols Chart 4206.9.2 The Inverse Nyquist Diagram (W) 424

6.10 H istorical Perspective 424 Sum m ary 425Review Questions 428 Problem s 428

State-Space Design 453

A Perspective on State-Space Design 453 C hapter Overview 4547.1 Advantages of State-Space 4547.2 System Description in State-Space 4567.3 Block Diagrams and State-Space 462