Fuzzy Logic, Identification, And... | Buy

The complexity and sensitivity of modern industrial processes and systems increasingly require adaptable advanced control protocols. These controllers have to be able to deal with circumstances demanding "judgement" rather than simple "yes/no", "on/off" responses, circumstances where an imprecise linguistic description is often more relevant than a cut-and-dried numerical one. The ability of fuzzy systems to handle numeric and linguistic information within a single framework renders them efficacious in this form of expert control system. Divided into two parts, Fuzzy Logic, Identification and Predictive Control first shows you how to construct static and dynamic fuzzy models using the numerical data from a variety of real-world industrial systems and simulations. The second part demonstrates the exploitation of such models to design control systems employing techniques like data mining. Fuzzy Logic, Identification and Predictive Control is a comprehensive introduction to the use of fuzzy methods in many different control paradigms encompassing robust, model-based, PID-like and predictive control. This combination of fuzzy control theory and industrial serviceability will make a telling contribution to your research whether in the academic or industrial sphere and also serves as a fine roundup of the fuzzy control area for the graduate student. Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.

Jairo Espinosa had a considerable experience of the practitioner side of advanced control systems and fuzzy systems in particular working with such companies as Zenith Data Systems in his native Colombia. There, he also won prizes for his academic work and for electronic design. He now works for IPCOS a company specialising in the design of advanced control systems for many process industries. This wil allow the author to draw on a good selection of industrial situations in writing the book. Vincent Wertz is now head of the Automatic Control Group at Louvain where he is particularly active in Ph.D. supervision work (his contributions to the book will ensure relevance to the graduate market) and the book reflects all of his main research interests.

Part I Fuzzy Modeling

1 Fuzzy Modeling

3

(18)

1.1 Function Approximation

4

(14)

1.1.1 System Description

4

(2)

1.1.2 Approximation Error

6

(2)

1.1.3 Constructing Units in the Fuzzy Models

8

(10)

1.2 Approximation Capabilities of Takagi-Sugeno Fuzzy Models

18

(2)

1.3 Conclusion and Summary

20

(1)

2 Constructing Fuzzy Models from Input-Output Data

21

(38)

2.1 Mosaic or Table Lookup Scheme

22

(4)

2.1.1 Illustrative Example

25

(1)

2.2 Using Gradient Descent

26

(12)

2.2.1 Gradient Updating for Trapezoidal Membership Functions

30

(1)

2.2.2 Gradient Updating for Triangular Membership Functions with Overlap ½

31

(1)

2.2.3 Gradient Updating for Polynomial Membership Functions

32

(1)

2.2.4 Gradient Updating for Polynomial Membership Functions with Overlap ½ and c i/j = m i/j

33

(1)

2.2.5 Gradient Updating for Gaussian Membership Functions

34

(1)

2.2.6 Illustrative Example

34

(4)

2.3 Using Clustering and Gradient Descent

38

(8)

2.3.1 Algorithm for Mamdani Models

38

(1)

2.3.2 Algorithm for Takagi-Sugeno Models

39

(1)

2.3.3 Illustrative Example

39

(7)

2.4 Using Evolutionary Strategies

46

(4)

2.5 Generalization and Consequences Estimation

50

(5)

2.5.1 Consequence Initialization

50

(1)

2.5.2 Consequence Estimation

51

(4)

2.6 Example of an Industrial Application

55

(3)

2.7 Conclusions

58

(1)

3 Fuzzy Modeling with Linguistic Integrity: A Tool for Data Mining

59

(32)

3.1 Introduction

59

(2)

3.2 Structure of the Fuzzy Model

61

(2)

3.3 The AFRELI Algorithm

63

(5)

3.4 The FuZion Algorithm

68

(3)

3.5 Examples

71

(18)

3.5.1 Modeling a Two-Input Nonlinear Function

71

(6)

3.5.2 Modeling of a Three-Input Nonlinear Function

77

(3)

3.5.3 Predicting Chaotic Time Series

80

(5)

3.5.4 Modeling of the Quality Properties on a High-Density Polyethylene (HDPE) Reactor

85

(4)

3.6 Complexity of the AFRELI Algorithm

89

(1)

3.7 Conclusions

89

(2)

4 Nonlinear Identification Using Fuzzy Models

91

(32)

4.1 System Identification

92

(1)

4.2 Basic Structure of the Fuzzy System

93

(2)

4.3 Experiment Design for System Identification

95

(3)

4.4 Choosing the Regressors

98

(7)

4.4.1 Search Methods

98

(3)

4.4.2 Regressors Evaluation

101

(4)

4.5 Choosing the Structure

105

(1)

4.6 Calculating the Parameters

106

(2)

4.7 Validation

108

(1)

4.8 Example Identification of the Box and Jenkins Gas Furnace Data Set

109

(9)

4.9 Identification of Takagi Sugeno Fuzzy Models Using Local Linear Identification

118

(1)

4.10 Conclusions

119

(4)

Part II Fuzzy Control

5 Fuzzy Control

123

(28)

5.1 Model-Free Fuzzy Control

124

(5)

5.1.1 Heuristic Trial-and-Error Design

124

(1)

5.1.2 Design of PID-like Fuzzy Controllers

124

(5)

5.2 Model Based Fuzzy Control

129

(17)

5.2.1 Using Adaptive Methods

129

(5)

5.2.2 Using Direct Synthesis

134

(12)

5.3 Conclusions and Future Perspectives

146

(5)

6 Predictive Control Based on Fuzzy Models

151

(44)

6.1 The Predictive Control Strategy

152

(2)

6.2 Unconstrained Nonlinear Predictive Control

154

(13)

6.2.1 Estimation of the Step Response to Construct G(t)

157

(1)

6.2.2 Example Predictive Control of a CSTR Using a Fuzzy Model

158

(9)

6.3 Constrained Nonlinear Predictive Control

167

(24)

6.3.1 The Constrained Nonlinear Predictive Control Problem

168

(5)

6.3.2 Approach Using Estimated Step Response

173

(4)

6.3.3 Approach Using Takagi-Sugeno Fuzzy Models

177

(1)

6.3.4 Approach Using Takagi-Sugeno Fuzzy Models and Multiple Models in the Predictor

178

(3)

6.3.5 Example Predictive Control of a Steam Generator Using a Fuzzy Model

181

(6)

6.3.6 Example: Nonlinear Predictive Control of a Gas-Phase High-Density Polyethylene (HDPE) Reactor

187

(4)

6.4 Conclusions

191

(4)

7 Robust Nonlinear Predictive Control Using Fuzzy Models

195

(12)

7.1 Introduction

195

(1)

7.2 Robust Quadratic Programming

196

(2)

7.3 Problem Description

198

(1)

7.4 Nominal Solution

199

(2)

7.5 Formulation of the MPC Problem as a Robust QP

201

(1)

7.6 The Control Algorithm

202

(1)

7.7 Uncertainty Description in Fuzzy Models

202

(3)

7.7.1 Local Uncertainty Described on Each Rule

203

(1)

7.7.2 Using the Active Rules

204

(1)

7.7.3 Using All the Rules

204

(1)

7.7.4 Using the Reachable Set

205

(1)

7.8 Conclusions and Perspectives

205

(2)

8 Conclusions and Future Perspectives

207

(8)

8.1 Conclusions and Summary

207

(3)

8.2 Perspectives and Future Work

210

(5)

Part III Appendices

A Fuzzy Set Theory

215

(10)

A.1 Introduction

215

(1)

A.2 Fuzzy Sets

215

(1)

A.2.1 Some Examples of Membership Functions

215

(1)

A.3 Basic Definitions of Fuzzy Sets

216

(1)

A.3.1 Support

216

(1)

A.3.2 Core

216

(1)

A.3.3 Height

217

(1)

A.3.4 Normal Fuzzy Set

217

(1)

A.3.5 &lpha;-Cut

217

(1)

A.3.6 Strict α-Cut

217

(1)

A.3.7 Convexity

217

(1)

A.4 Operations on Fuzzy Sets

217

(2)

A.4.1 A Is Contained in B

217

(1)

A.4.2 Complement, Negation

217

(1)

A.4.3 Intersection

218

(1)

A.4.4 Union

218

(1)

A.5 Fuzzy relations

219

(1)

A.5.1 Projection of Fuzzy Relations

220

(1)

A.5.2 Composition of Relations

220

(1)

A.6 Approximate Reasoning

220

(1)

A.6.1 Introduction

220

(1)

A.6.2 Linguistic Variables

221

(1)

A.7 General Structure of a Fuzzy Inference System

221

(4)

A.7.1 Control Rules as a Knowledge Representation

221

(2)

A.7.2 Defuzzification

223

(2)

B Clustering Methods

225

(6)

B.1 Fuzzy C-Means [2]

225

(1)

B.2 Using Fuzzy Covariance Matrix: Gustafson and Kessel Algorithm [3]

226

(2)

B.3 Mountain Clustering [4]

228

(3)

C Gradients Used in Identification with Fuzzy Models

231

(12)

C.1 Gradient for the Singleton Consequences

231

(3)

C.1.1 With Trapezoidal Membership Functions

232

(1)

C.1.2 With Polynomial Membership Functions

233

(1)

C.1.3 With Gaussian Membership Functions

233

(1)

C.2 Gradient for the Parameters of the Membership Functions

234

(13)

C.2.1 With Trapezoidal Membership Functions

234

(1)

C.2.2 With Polynomial Membership Functions

235

(2)

C.2.3 With Gaussian Membership Functions

237

(1)

C.2.4 With Triangular Membership Functions with 0.5 Overlap

237

(2)

C.2.5 With Polynomial Membership Functions with 0.5 Overlap

239

(4)

D Discrete Linear Dynamical System Approximation Theorem

243

(4)

E Fuzzy Control for a Continuously Variable Transmission

247

(8)

E.1 Introduction and Process Description

247

(1)

E.2 Performance Specifications

248

(1)

E.3 A Physical Model for the CVT

249

(2)

E.4 Design of the Controller

251

(1)

E.5 Stability Analysis

252

(1)

E.6 Conclusions

253

(2)

References

255

(6)

Index

261

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