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Digital Control of Dynamic Systems

by: Franklin, Gene F.; Powell, J. David; Workman, Michael L.

Digital Control of Dynamic Systems

by: Franklin, Gene F.; Powell, J. David; Workman, Michael L.

ISBN 13:
9780201820546
ISBN 10:
0201820544
Edition: 3rd
Format: Hardcover
Copyright: 01/01/1998
Publisher: Prentice Hall

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Summary

This well-respected, market-leading text discusses the use of digital computers in the real-time control of dynamic systems. The emphasis is on the design of digital controls that achieve good dynamic response and small errors while using signals that are sampled in time and quantized in amplitude. Both classical and modern control methods are described and applied to illustrative examples. The strengths and limitations of each method are explored to help the reader develop solid designs with the least effort. Two new chapters have been added to the third edition offering a review of feedback control systems and an overview of digital control systems. Updated to be fully compatible with MATLAB versions 4 and 5, the text thoroughly integrates MATLAB statements and problems to offer readers a complete design picture. The new edition contains up-to-date material on state-space design and twice as many end- of-chapter problems to give students more opportunities to practice the material.

Preface

xix

1 Introduction

(10)

1.1 Problem Definition

(4)

1.2 Overview of Design Approach

(2)

1.3 Computer-Aided Design

(1)

1.4 Suggestions for Further Reading

(1)

1.5 Summary

(1)

1.6 Problems

(3)

2 Review of Continuous Control

(46)

2.1 Dynamic Response

(11)

2.1.1 Differential Equations

(1)

2.1.2 Laplace Transforms and Transfer Functions

(2)

2.1.3 Output Time Histories

(1)

2.1.4 The Final Value Theorem

(1)

2.1.5 Block Diagrams

(1)

2.1.6 Response versus Pole Locations

(4)

2.1.7 Time-Domain Specifications

(2)

2.2 Basic Properties of Feedback

(2)

2.2.1 Stability

(1)

2.2.2 Steady-State Errors

(1)

2.2.3 PID Control

(1)

2.3 Root Locus

(7)

2.3.1 Problem Definition

(1)

2.3.2 Root Locus Drawing Rules

(2)

2.3.3 Computer-Aided Loci

(3)

2.4 Frequency Response Design

(8)

2.4.1 Specifications

(2)

2.4.2 Bode Plot Techniques

(1)

2.4.3 Steady-State Errors

(1)

2.4.4 Stability Margins

(1)

2.4.5 Bode's Gain-Phase Relationship

(1)

2.4.6 Design

(1)

2.5 Compensation

(2)

2.6 State-Space Design

(9)

2.6.1 Control Law

(4)

2.6.2 Estimator Design

(2)

2.6.3 Compensation: Combined Control and Estimation

(1)

2.6.4 Reference Input

(1)

2.6.5 Integral Control

(1)

2.7 Summary

(2)

2.8 Problems

(5)

3 Introductory Digital Control

(16)

3.1 Digitization

(5)

3.2 Effect of Sampling

(3)

3.3 PID Control

(2)

3.4 Summary

(1)

3.5 Problems

(4)

4 Discrete Systems Analysis

(82)

4.1 Linear Difference Equations

(5)

4.2 The Discrete Transfer Function

(18)

4.2.1 The z-Transform

(1)

4.2.2 The Transfer Function

(2)

4.2.3 Block Diagrams and State-Variable Descriptions

(8)

4.2.4 Relation of Transfer Function to Pulse Response

(3)

4.2.5 External Stability

(3)

4.3 Discrete Models of Sampled-Data Systems

(23)

4.3.1 Using the z-Transform

(3)

4.3.2 (*)Continuous Time Delay

(2)

4.3.3 State-Space Form

101

(9)

4.3.4 (*)State-Space Models for Systems with Delay

110

(4)

4.3.5 (*)Numerical Considerations in Computing XXX and XXX

114

(3)

4.3.6 (*)Nonlinear Models

117

(2)

4.4 Signal Analysis and Dynamic Response

119

(12)

4.4.1 The Unit Pulse

120

(1)

4.4.2 The Unit Step

120

(1)

4.4.3 Exponential

121

(1)

4.4.4 General Sinusoid

122

(3)

4.4.5 Correspondence with Continuous Signals

125

(3)

4.4.6 Step Response

128

(3)

4.5 Frequency Response

131

(6)

4.5.1 (*)The Discrete Fourier Transform (DFT)

134

(3)

4.6 Properties of the z-Transform

137

(11)

4.6.1 Essential Properties

137

(5)

4.6.2 (*)Convergence of z-Transform

142

(4)

4.6.3 (*)Another Derivation of the Transfer Function

146

(2)

4.7 Summary

148

(1)

4.8 Problems

149

(6)

5 Sampled-Data Systems

155

(32)

5.1 Analysis of the Sample and Hold

156

(4)

5.2 Spectrum of a Sampled Signal

160

(4)

5.3 Data Extrapolation

164

(6)

5.4 Block-Diagram Analysis of Sampled-Data Systems

170

(10)

5.5 Calculating the System Output Between Samples: The Ripple

180

(2)

5.6 Summary

182

(1)

5.7 Problems

183

(3)

5.8 Appendix

186

(1)

6 Discrete Equivalents

187

(24)

6.1 Design of Discrete Equivalents via Numerical Integration

189

(11)

6.2 Zero-Pole Matching Equivalents

200

(2)

6.3 Hold Equivalents

202

(6)

6.3.1 Zero-Order Hold Equivalent

203

(1)

6.3.2 A Non-Causal First-Order-Hold Equivalent: The Triangle-Hold Equivalent

204

(4)

6.4 Summary

208

(1)

6.5 Problems

209

(2)

7 Design Using Transform Techniques

211

(68)

7.1 System Specifications

212

(2)

7.2 Design by Emulation

214

(8)

7.2.1 Discrete Equivalent Controllers

215

(3)

7.2.2 Evaluation of the Design

218

(4)

7.3 Direct Design by Root Locus in the z-Plane

222

(12)

7.3.1 z-Plane Specifications

222

(5)

7.3.2 The Discrete Root Locus

227

(7)

7.4 Frequency Response Methods

234

(30)

7.4.1 Nyquist Stability Criterion

238

(5)

7.4.2 Design Specifications in the Frequency Domain

243

(16)

7.4.3 Low Frequency Gains and Error Coefficients

259

(1)

7.4.4 Compensator Design

260

(4)

7.5 Direct Design Method of Ragazzini

264

(5)

7.6 Summary

269

(1)

7.7 Problems

270

(9)

8 Design Using State-Space Methods

279

(80)

8.1 Control Law Design

280

(9)

8.1.1 Pole Placement

282

(3)

8.1.2 Controllability

285

(1)

8.1.3 Pole Placement Using CACSD

286

(3)

8.2 Estimator Design

289

(13)

8.2.1 Prediction Estimators

290

(3)

8.2.2 Observability

293

(1)

8.2.3 Pole Placement Using CACSD

294

(1)

8.2.4 Current Estimators

295

(4)

8.2.5 Reduced-Order Estimators

299

(3)

8.3 Regulator Design: Combined Control Law and Estimator

302

(8)

8.3.1 The Separation Principle

302

(6)

8.3.2 Guidelines for Pole Placement

308

(2)

8.4 Introduction of the Reference Input

310

(12)

8.4.1 Reference Inputs for Full-State Feedback

310

(4)

8.4.2 Reference Inputs with Estimators: The State-Command Structure

314

(3)

8.4.3 Output Error Command

317

(2)

8.4.4 A Comparison of the Estimator Structure and Classical Methods

319

(3)

8.5 Integral Control and Disturbance Estimation

322

(15)

8.5.1 Integral Control by State Augmentation

323

(5)

8.5.2 Disturbance Estimation

328

(9)

8.6 Effect of Delays

337

(8)

8.6.1 Sensor Delays

338

(3)

8.6.2 Actuator Delays

341

(4)

8.7 (*)Controllability and Observability

345

(6)

8.8 Summary

351

(1)

8.9 Problems

352

(7)

9 Multivariable and Optimal Control

359

(66)

9.1 Decoupling

360

(4)

9.2 Time-Varying Optimal Control

364

(7)

9.3 LQR Steady-State Optimal Control

371

(11)

9.3.1 Reciprocal Root Properties

372

(1)

9.3.2 Symmetric Root Locus

373

(1)

9.3.3 Eigenvector Decomposition

374

(5)

9.3.4 Cost Equivalents

379

(1)

9.3.5 Emulation by Equivalent Cost

380

(2)

9.4 Optimal Estimation

382

(18)

9.4.1 Least-Squares Estimation

383

(6)

9.4.2 The Kalman Filter

389

(5)

9.4.3 Steady-State Optimal Estimation

394

(2)

9.4.4 Noise Matrices and Discrete Equivalents

396

(4)

9.5 Multivariable Control Design

400

(19)

9.5.1 Selection of Weighting Matrices XXX(1) and XXX(2)

400

(1)

9.5.2 Pincer Procedure

401

(2)

9.5.3 Paper-Machine Design Example

403

(4)

9.5.4 Magnetic-Tape-Drive Design Example

407

(12)

9.6 Summary

419

(1)

9.7 Problems

420

(5)

10 Quantization Effects

425

(24)

10.1 Analysis of Round-Off Error

426

(11)

10.2 Effects of Parameter Round-Off

437

(3)

10.3 Limit Cycles and Dither

440

(5)

10.4 Summary

445

(1)

10.5 Problems

445

(4)

11 Sample Rate Selection

449

(30)

11.1 The Sampling Theorem's Limit

450

(1)

11.2 Time Response and Smoothness

451

(3)

11.3 Errors Due to Random Plant Disturbances

454

(7)

11.4 Sensitivity to Parameter Variations

461

(4)

11.5 Measurement Noise and Antialiasing Filters

465

(4)

11.6 Multirate Sampling

469

(5)

11.7 Summary

474

(2)

11.8 Problems

476

(3)

12 System Identification

479

(64)

12.1 Defining the Model Set for Linear Systems

481

(3)

12.2 Identification of Nonparametric Models

484

(11)

12.3 Models and Criteria for Parametric Identification

495

(7)

12.3.1 Parameter Selection

496

(2)

12.3.2 Error Definition

498

(4)

12.4 Deterministic Estimation

502

(8)

12.4.1 Least Squares

503

(3)

12.4.2 Recursive Least Squares

506

(4)

12.5 Stochastic Least Squares

510

(11)

12.6 Maximum Likelihood

521

(5)

12.7 Numerical Search for the Maximum-Likelihood Estimate

526

(9)

12.8 Subspace Identification Methods

535

(3)

12.9 Summary

538

(1)

12.10 Problems

539

(4)

13 Nonlinear Control

543

(106)

13.1 Analysis Techniques

544

(38)

13.1.1 Simulation

545

(5)

13.1.2 Linearization

550

(9)

13.1.3 Describing Functions

559

(14)

13.1.4 Equivalent Gains

573

(4)

13.1.5 Circle Criterion

577

(2)

13.1.6 Lyapunov's Second Method

579

(3)

13.2 Nonlinear Control Structures: Design

582

(53)

13.2.1 Large Signal Linearization: Inverse Nonlinearities

582

(17)

13.2.2 Time-Optimal Servomechanisms

599

(12)

13.2.3 Extended PTOS for Flexible Structures

611

(4)

13.2.4 Introduction to Adaptive Control

615

(20)

13.3 Design with Nonlinear Cost Functions

635

(7)

13.3.1 Random Neighborhood Search

635

(7)

13.4 Summary

642

(1)

13.5 Problems

643

(6)

14 Design of a Disk Drive Servo: A Case Study

649

(40)

14.1 Overview of Disk Drives

650

(5)

14.1.1 High Performance Disk Drive Servo Profile

652

(2)

14.1.2 The Disk-Drive Servo

654

(1)

14.2 Components and Models

655

(11)

14.2.1 Voice Coil Motors

655

(3)

14.2.2 Shorted Turn

658

(1)

14.2.3 Power Amplifier Saturation

659

(1)

14.2.4 Actuator and HDA Dynamics

660

(3)

14.2.5 Position Measurement Sensor

663

(1)

14.2.6 Runout

664

(2)

14.3 Design Specifications

666

(4)

14.3.1 Plant Parameters for Case Study Design

667

(2)

14.3.2 Goals and Objectives

669

(1)

14.4 Disk Servo Design

670

(16)

14.4.1 Design of the Linear Response

671

(3)

14.4.2 Design by Random Numerical Search

674

(4)

14.4.3 Time-Domain Response of XPTOS Structure

678

(5)

14.4.4 Implementation Considerations

683

(3)

14.5 Summary

686

(1)

14.6 Problems

687

(2)

Appendix A Examples

689

(12)

A.1 Single-Axis Satellite Attitude Control

689

(2)

A.2 A Servomechanism for Antenna Azimuth Control

691

(3)

A.3 Temperature Control of Fluid in a Tank

694

(3)

A.4 Control Through a Flexible Structure

697

(2)

A.5 Control of a Pressurized Flow Box

699

(2)

Appendix B Tables

701

(4)

B.1 Properties of z-Transforms

701

(1)

B.2 Table of z-Transforms

702

(3)

Appendix C A Few Results from Matrix Analysis

705

(8)

C.1 Determinants and the Matrix Inverse

705

(2)

C.2 Eigenvalues and Eigenvectors

707

(2)

C.3 Similarity Transformations

709

(2)

C.4 The Cayley-Hamilton Theorem

711

(2)

Appendix D Summary of Facts from the Theory of Probability and Stochastic Processes

713

(12)

D.1 Random Variables

713

(2)

D.2 Expectation

715

(2)

D.3 More Than One Random Variable

717

(2)

D.4 Stochastic Processes

719

(6)

Appendix E MATLAB Functions

725

(2)

Appendix F Differences Between MATLAB v5 and v4

727

(4)

F.1 System Specification

727

(2)

F.2 Continuous to Discrete Conversion

729

(1)

F.3 Optimal Estimation

730

(1)

References

731

(6)

Index

737

Amazon no longer offers textbook rentals. We do!

Digital Control of Dynamic Systems

Digital Control of Dynamic Systems

9780201820546

0201820544

Summary

Table of Contents

Supplemental Materials

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