Pid Control

, by Johnson, Michael A.; MORADI, MOHAMMAD H.; CROWE, J.

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ISBN: 9781852337025 | 1852337028
Cover: Hardcover
Copyright: 7/20/2005

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The effectiveness of proportional-integral-derivative (PID) controllers for a large class of process systems has ensured their continued and widespread use in industry. Similarly there has been a continued interest from academia in devising new ways of approaching the PID tuning problem. To the industrial engineer and many control academics this work has previously appeared fragmented but a key determinant of this literature is the type of process model information used in the PID tuning methods. PID Control presents a set of coordinated contributions illustrating methods, old and new, that cover the range of process model assumptions systematically. After a review of PID technology, these contributions begin with model-free methods, progress through non-parametric model methods (relay experiment and phase-locked-loop procedures), visit fuzzy-logic- and genetic-algorithm-based methods; introduce a novel subspace identification method before closing with an interesting set of parametric model techniques including a chapter on predictive PID controllers. Highlights of PID Control include: an introduction to PID control technology features and typical industrial implementations; chapter contributions ordered by the increasing quality of the model information used; novel PID control concepts for multivariable processes. PID Control will be useful to industry-based engineers wanting a better understanding of what is involved in the steps to a new generation of PID controller techniques. Academics wishing to have a broader perspective of PID control research and development will find useful pedagogical material and research ideas in this text.

Editorial Responsibilities

xix

Notation

xxv

1 PID Control Technology

(46)

Learning Objectives

(1)

1.1 Basic Industrial Control

(5)

1.1.1 Process Loop Issues - a Summary Checklist

(1)

1.2 Three-Term Control

(10)

1.2.1 Parallel PID Controllers

(1)

1.2.2 Conversion to Time constant PID Forms

(2)

1.2.3 Series PID Controllers

(2)

1.2.4 Simple PID Tuning

(3)

1.3 PID Controller Implementation Issues

(12)

1.3.1 Bandwidth-Limited Derivative Control

(4)

1.3.2 Proportional Kick

(2)

1.3.3 Derivative Kick

(2)

1.3.4 Integral Anti-Windup Circuits

(3)

1.3.5 Reverse-Acting Controllers

(1)

1.4 Industrial PID Control

(17)

1.4.1 Traditional Industrial PID Terms

(2)

1.4.2 Industrial PID Structures and Nomenclature

(1)

1.4.3 The Process Controller Unit

(2)

1.4.4 Supervisory Control and the SCADA PID Controller

(11)

Acknowledgements

(1)

References

(1)

2 Some PID Control Fundamentals

(62)

Learning Objectives

(1)

2.1 Process System Models

(9)

2.1.1 State Space Models

(3)

2.1.2 Convolution Integral Process Models

(1)

2.1.3 Laplace Transfer Function Models

(2)

2.1.4 Common Laplace Transform Process Models

(2)

2.2 Controller Degrees of Freedom Structure

(3)

2.2.1 One Degree of Freedom Control

(1)

2.2.2 Two Degree of Freedom Control

(2)

2.2.3 Three Degree of Freedom Structures

(1)

2.3 PID Control Performance

(28)

2.3.1 Controller Performance Assessment - General Considerations

(6)

2.3.2 Controller Assessment - the Effectiveness of PID Control

(7)

2.3.3 Classical Stability Robustness Measures

(6)

2.3.4 Parametric Stability Margins for Simple Processes

(9)

2.4 State Space Systems and PID Control

(11)

2.4.1 Linear Reference Error Feedback Control

(2)

2.4.2 Two Degree of Freedom Feedback Control System

(1)

2.4.3 State Feedback With Integral Error Feedback Action

(4)

2.4.4 State Space Analysis for Classical PI Control Structure

(4)

2.5 Multivariable PID Control Systems

(7)

2.5.1 Multivariable Control

100

(3)

2.5.2 Cascade Control Systems

103

(3)

Acknowledgements

106

(1)

References

106

(3)

3 On-line Model-Free Methods

109

(38)

Learning Objectives

109

(1)

3.1 Introduction

110

(4)

3.1.1 A Model-Free Control Design Paradigm

110

(4)

3.2 Iterative Feedback Tuning

114

(10)

3.2.1 Generating the Cost Function Gradient

114

(3)

3.2.2 Case Study - a Wastewater Process Example

117

(5)

3.2.3 Some Remarks on Iterative Feedback Tuning

122

(2)

3.3 The Controller Parameter Cycling Tuning Method

124

(19)

3.3.1 Generating the Gradient and Hessian - Some Theory

125

(6)

3.3.2 Issues for a Controller Parameter Cycling Algorithm

131

(4)

3.3.3 The Controller Parameter Cycling Algorithm

135

(1)

3.3.4 Case Study - Multivariable Decentralised Control

136

(7)

3.4 Summary and Future Directions

143

(1)

Acknowledgements

144

(1)

Appendix 3.A

144

(1)

References

145

(2)

4 Automatic PID Controller Tuning - the Nonparametric Approach

147

(36)

Learning Objectives

147

(1)

4.1 Introduction

148

(1)

4.2 Overview of Nonparametric Identification Methods

149

(3)

4.2.1 Transient Response Methods

149

(1)

4.2.2 Relay Feedback Methods

150

(1)

4.2.3 Fourier Methods

150

(1)

4.2.4 Phase-Locked Loop Methods

151

(1)

4.3 Frequency Response Identification with Relay Feedback

152

(14)

4.3.1 Basic Idea

153

(2)

4.3.2 Improved Estimation Accuracy

155

(6)

4.3.3 Estimation of a General Point

161

(3)

4.3.4 Estimation of Multiple Points

164

(1)

4.3.5 On-line relay tuning

164

(2)

4.4 Sensitivity Assessment Using Relay Feedback

166

(5)

4.4.1 Control Robustness

166

(1)

4.4.2 Maximum Sensitivity

167

(1)

4.4.3 Construction of the 2 -0 Chart

168

(2)

4.4.4 Stability Margins Assessment

170

(1)

4.5 Conversion to Parametric Models

171

(3)

4.5.1 Single and Multiple Lag Processes

172

(2)

4.5.2 Second-Order Modelling

174

(1)

4.6 Case Studies

174

(6)

Case Study 4.1: Improved Estimation Accuracy for the Relay Experiment

176

(1)

Case Study 4.2: Estimation of a General Point

177

(1)

Case Study 4.3: Estimation of Multiple Points

177

(2)

Case Study 4.4: On-line Relay Tuning

179

(1)

Case Study 4.5: Sensitivity Assessment

179

(1)

References

180

(3)

5 Relay Experiments for Multivariable Systems

183

(30)

Learning Objectives

183

(1)

5.1 Introduction

184

(1)

5.2 Critical Points of a System

185

(2)

5.2.1 Critical Points for Two-Input, Two-Output Systems

185

(1)

5.2.2 Critical Points for MIMO Systems

186

(1)

5.3 Decentralised Relay Experiments for Multivariable Systems

187

(10)

5.3.1 Finding System Gains at Particular Frequencies

188

(2)

5.3.2 Decentralised Relay Control Systems - Some Theory

190

(1)

5.3.3 A Decentralised Two-Input, Two-Output PID Control System Relay-Based Procedure

191

(6)

5.4 A Decentralised Multi-Input, Multi-Output PID Control System Relay-Based Procedure

197

(5)

5.5 PID Control Design at Bandwidth Frequency

202

(5)

5.6 Case Studies

207

(3)

5.6.1 Case Study 1: The Wood and Berry Process System Model

207

(3)

5.6.2 Case Study 2: A Three-Input, Three-Output Process System

210

(1)

5.7 Summary

210

(1)

References

211

(2)

6 Phase-Locked Loop Methods

213

(46)

Learning Objectives

213

(1)

6.1 Introduction

214

(7)

6.1.1 The Relay Experiment

215

(1)

6.1.2 Implementation Issues for the Relay Experiment

216

(4)

6.1.3 Summary Conclusions on the Relay Experiment

220

(1)

6.2 Some Constructive Numerical Solution Methods

221

(8)

6.2.1 Bisection Method

222

(2)

6.2.2 Prediction Method

224

(3)

6.2.3 Bisection and Prediction Method - a Comparison and Assessment

227

(2)

6.3 Phase-Locked Loop Identifier Module - Basic Theory

229

(26)

6.3.1 The Digital Identifier Structure

230

(12)

6.3.2 Noise Management Techniques

242

(6)

6.3.3 Disturbance Management Techniques

248

(7)

6.4 Summary and Discussion

255

(1)

References

256

(3)

7 Phase-Locked Loop Methods and PID Control

259

(38)

Learning Objectives

259

(1)

7.1 Introduction - Flexibility and Applications

260

(1)

7.2 Estimation of the Phase Margin

260

(1)

7.3 Estimation of the Parameters of a Second-Order Underdamped System

261

(4)

7.4 Identification of Systems in Closed Loop

265

(5)

7.4.1 Identification of an Unknown System in Closed Loop with an Unknown Controller

265

(3)

7.4.2 Identification of an Unknown System in Closed Loop with a Known Controller

268

(2)

7.5 Automated PI Control Design

270

(24)

7.5.1 Identification Aspects for Automated PID Control Design

271

(4)

7.5.2 PI Control with Automated Gain and Phase Margin Design

275

(11)

7.5.3 PI Control with Automated Maximum Sensitivity and Phase Margin Design

286

(8)

7.6 Conclusions

294

(1)

References

295

(2)

8 Process Reaction Curve and Relay Methods Identification and PID Tuning

297

(42)

Learning Objectives

297

(1)

8.1 Introduction

298

(4)

8.2 Developing Simple Models from the Process Reaction Curve

302

(8)

8.2.1 Identification Algorithm for Oscillatory Step Responses

303

(2)

8.2.2 Identification Algorithm for Non-Oscillatory Responses Without Overshoot

305

(5)

8.3 Developing Simple Models from a Relay Feedback Experiment

310

(10)

8.3.1 On-line Identification of FOPDT Models

312

(2)

8.3.2 On-line Identification of SOPDT Models

314

(1)

8.3.3 Examples for the On-line Relay Feedback Procedure

315

(2)

8.3.4 Off-line Identification

317

(3)

8.4 An Inverse Process Model-Based Design Procedure for PID Control

320

(9)

8.4.1 Inverse Process Model-Based Controller Principles

320

(3)

8.4.2 PI/PID Controller Synthesis

323

(2)

8.4.3 Autotuning of PID Controllers

325

(4)

8.5 Assessment of PI/PID Control Performance

329

(7)

8.5.1 Achievable Minimal IAE Cost and Rise Time

329

(3)

8.5.2 Assessment of PI/PID Controllers

332

(4)

References

336

(3)

9 Fuzzy Logic and Genetic Algorithm Methods in PID Tuning

339

(22)

Learning Objectives

339

(1)

9.1 Introduction

340

(1)

9.2 Fuzzy PID Controller Design

340

(10)

9.2.1 Fuzzy PI Controller Design

342

(1)

9.2.2 Fuzzy D Controller Design

343

(1)

9.2.3 Fuzzy PID Controller Design

344

(1)

9.2.4 Fuzzification

345

(1)

9.2.5 Fuzzy Control Rules

346

(1)

9.2.6 Defuzzification

346

(3)

9.2.7 A Control Example

349

(1)

9.3 Multi-Objective Optimised Genetic Algorithm Fuzzy PID Control

350

(5)

9.3.1 Genetic Algorithm Methods Explained

351

(2)

9.3.2 Case study A: Multi-Objective Genetic Algorithm Fuzzy PID Control of a Nonlinear Plant

353

(1)

9.3.3 Case study B: Control of Solar Plant

354

(1)

9.4 Applications of Fuzzy PID Controllers to Robotics

355

(2)

9.5 Conclusions and Discussion

357

(1)

Acknowledgments

358

(1)

References

358

(3)

10 Tuning PID Controllers Using Subspace Identification Methods

361

(28)

Learning Objectives

361

(1)

10.1 Introduction

362

(1)

10.2 A Subspace Identification Framework for Process Models

363

(5)

10.2.1 The Subspace Identification Framework

363

(3)

10.2.2 Incremental Subspace Representations

366

(2)

10.3 Restricted Structure Single-Input, Single-Output Controllers

368

(3)

10.3.1 Controller Parameterisation

369

(1)

10.3.2 Controller Structure and Computations

370

(1)

10.4 Restricted-Structure Multivariable Controller Characterisation

371

(1)

10.4.1 Controller Parameterisation

371

(1)

10.4.2 Multivariable Controller Structure

372

(1)

10.5 Restricted-Structure Controller Parameter Computation

372

(4)

10.5.1 Cost Index

373

(1)

10.5.2 Formulation as a Least-Squares Problem

373

(1)

10.5.3 Computing the Closed-Loop System Condition

374

(1)

10.5.4 Closed-Loop Stability Conditions

375

(1)

10.5.5 The Controller Tuning Algorithm

375

(1)

10.6 Simulation Case Studies

376

(11)

10.6.1 Activated Sludge Wastewater Treatment Plant Layout

377

(1)

10.6.2 Case study 1: Single-Input, Single-Output Control Structure

378

(1)

10.6.3 Case Study 2: Control of Two Reactors with a Lower Triangular Controller Structure

379

(3)

10.6.4 Case Study 3: Control of Three Reactors with a Diagonal Controller Structure

382

(3)

10.6.5 Case Study 4: Control of Three Reactors with a Lower Triangular Controller Structure

385

(2)

References

387

(2)

11 Design of Multi-Loop and Multivariable PID Controllers

389

(40)

Learning Objectives

389

(1)

11.1 Introduction

390

(4)

11.1.1 Multivariable Systems

390

(1)

11.1.2 Multivariable Control

391

(1)

11.1.3 Scope of the Chapter and Some Preliminary Concepts

392

(2)

11.2 Multi-Loop PID Control

394

(14)

11.2.1 Biggest Log-Modulus Tuning Method

394

(1)

11.2.2 Dominant Pole Placement Tuning Method

395

(9)

11.2.3 Examples

404

(4)

11.3 Multivariable PID Control

408

(18)

11.3.1 Decoupling Control and Design Overview

409

(3)

11.3.2 Determination of the Objective Loop Performance

412

(9)

11.3.3 Computation of PID Controller

421

(1)

11.3.4 Examples

422

(4)

11.4 Conclusions

426

(1)

References

427

(2)

12 Restricted Structure Optimal Control

429

(44)

Learning Objectives

429

(1)

12.1 Introduction to Optimal LQG Control for Scalar Systems

430

(6)

12.1.1 System Description

431

(1)

12.1.2 Cost Function and Optimisation Problem

432

(4)

12.2 Numerical Algorithms for SISO System Restricted Structure Control

436

(5)

12.2.1 Formulating a Restricted Structure Numerical Algorithm

436

(3)

12.2.2 Iterative Solution for the SISO Restricted Structure LQG Controller

439

(1)

12.2.3 Properties of the Restricted Structure LQG Controller

440

(1)

12.3 Design of PID Controllers Using the Restricted Structure Method

441

(3)

12.3.1 General Principles for Optimal Restricted Controller Design

442

(1)

12.3.2 Example of PID Control Design

443

(1)

12.4 Multivariable Optimal LQG Control: An Introduction

444

(9)

12.4.1 Multivariable Optimal LQG Control and Cost Function Values

448

(3)

12.4.2 Design Procedures for an Optimal LQG Controller

451

(2)

12.5 Multivariable Restricted Structure Controller Procedure

453

(8)

12.5.1 Analysis for a Multivariable Restricted Structures Algorithm

454

(4)

12.5.2 Multivariable Restricted Structure Algorithm and Nested Restricted Structure Controllers

458

(3)

12.6 An Application of Multivariable Restricted Structure Assessment - Control of the Hotstrip Finishing Mill Looper System

461

(9)

12.6.1 The Hotstrip Finishing Mill Looper System

461

(2)

12.6.2 An Optimal Multivariable LQG Controller for the Looper System

463

(2)

12.6.3 A Controller Assessment Exercise for the Hotstrip Looper System

465

(5)

12.7 Conclusions

470

(1)

Acknowledgements

471

(1)

References

472

(1)

13 Predictive PID Control

473

(58)

Learning Objectives

473

(1)

13.1 Introduction

474

(1)

13.2 Classical Process Control Model Methods

475

(10)

13.2.1 Smith Predictor Principle

475

(2)

13.2.2 Predictive PI With a Simple Model

477

(3)

13.2.3 Method Application and an Example

480

(5)

13.3 Simple Process Models and GPC-Based Methods

485

(15)

13.3.1 Motivation for the Process Model Restriction

485

(1)

13.3.2 Analysis for a GPC PID Controller

486

(4)

13.3.3 Predictive PID Control: Delay-Free System h = 0

490

(1)

13.3.4 Predictive PID Control: Systems with Delay h > 0

491

(2)

13.3.5 Predictive PID Control: An Illustrative Example

493

(7)

13.4 Control Signal Matching and GPC Methods

500

(24)

13.4.1 Design of SISO Predictive PID Controllers

500

(3)

13.4.2 Optimal Values of Predictive PID Controller Gains

503

(12)

13.4.3 Design of MIMO Predictive PID controllers

515

(9)

Acknowledgements

524

(1)

Appendix 13.A

524

(5)

13.A.1 Proof of Lemma 13.1

524

(2)

13.A.2 Proof of Theorem 13.1

526

(1)

13.A.3 Proof of Lemma 13.2

527

(2)

References

529

(2)

About the Contributors

531

(8)

Index

539

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Pid Control

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