Discrete-Time Dynamic Models

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ISBN: 9780195121988 | 0195121988
Cover: Hardcover
Copyright: 12/2/1999

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Fueled by advances in computer technology, model-based approaches to the control of industrial processes are now widespread. While there is an enormous literature on modeling, the difficult first step of selecting an appropriate model structure has received almost no attention. This book fills the gap, providing practical insight into model selection for chemical processes and emphasizing structures suitable for control system design.

Motivations and Perspectives

(54)

Modeling complex systems

(17)

Fundamental models

(3)

Assumptions, approximations, and simplifications

(2)

Continuous- vs. discrete-time models

(3)

Empirical models

(3)

Gray-box models

(2)

Indirect empirical modeling

(1)

Inherently nonlinear behavior

(14)

Harmonic generation

(4)

Subharmonic generation

(3)

Chaotic response to simple inputs

(1)

Input-dependent stability

(2)

Asymmetric responses to symmetric inputs

(1)

Steady-state multiplicity

(2)

Example 1: distillation columns

(7)

Hammerstein models

(2)

Wiener models

(2)

A bilinear model

(1)

A polynomial NARMAX model

(1)

Example 2: chemical reactors

(11)

Hammerstein and Wiener models

(2)

Bilinear models

(1)

Polynomial NARMAX models

(1)

Linear multimodels

(1)

The Uryson model

(3)

Organization of this book

(4)

Linear Dynamic Models

(36)

Four second-order linear models

(2)

Realizations of linear models

(8)

Autoregressive moving average models

(3)

Moving average and autoregressive models

(2)

State-space models

(1)

Exponential and BIBO stability of linear models

(2)

Characterization of linear models

(4)

Infinite-dimensional linear models

(8)

Continuous-time examples

(2)

Discrete-time slow decay models

(3)

Fractional Brownian motion

(3)

Time-varying linear models

(9)

First-order systems

(4)

Periodically time-varying systems

(4)

Summary: the nature of linearity

(4)

Four Views of Nonlinearity

(47)

Bilinear models

(17)

Four examples and a general result

(7)

Completely bilinear models

104

(4)

Stability and steady-state behavior

108

(3)

Homogeneous models

111

(10)

Homogeneous functions and homogeneous models

111

(4)

Homomorphic systems

115

(2)

Homogeneous ARMAX models of order zero

117

(4)

Positive homogeneous models

121

(8)

Positive-homogeneous functions and models

121

(4)

PH0-ARMAX models

125

(2)

TARMAX models

127

(2)

Static-linear models

129

(8)

Definition of the model class

129

(3)

A static-linear Uryson model

132

(1)

Bilinear models

133

(2)

Mallows' nonlinear data smoothers

135

(2)

Summary: the nature of nonlinearity

137

(3)

NARMAX Models

140

(69)

Classes of NARMAX models

140

(3)

Nonlinear moving average models

143

(9)

Two NMAX model examples

144

(4)

Qualitative behavior of NMAX models

148

(4)

Nonlinear autoregressive models

152

(16)

A simple example

153

(3)

Responses to periodic inputs

156

(2)

NARX model stability

158

(3)

Steady-state behavior of NARX models

161

(2)

Differences between NARX and NARX* models

163

(5)

Additive NARMAX Models

168

(12)

Wiener vs. Hammerstein models

170

(4)

EXPAR vs. modified EXPAR models

174

(3)

Stability of additive models

177

(2)

Steady-state behavior of NAARX models

179

(1)

Polynomial NARMAX models

180

(6)

Robinson's AR-Volterra model

182

(2)

A more general example

184

(2)

Rational NARMAX models

186

(9)

Zhu and Billings model

189

(3)

Another rational NARMAX example

192

(3)

More Complex NARMAX Models

195

(8)

Projection-pursuit models

196

(2)

Neural network models

198

(3)

Cybenko's approximation result

201

(1)

Radial basis functions

202

(1)

Summary: the nature of NARMAX models

203

(6)

Volterra Models

209

(34)

Definitions and basic results

210

(8)

The class V(N,M) and related model classes

210

(3)

Four simple examples

213

(3)

Stochastic characterizations

216

(2)

Four important subsets of V (N,M)

218

(6)

The class H(N,M)

219

(1)

The class UT(N,M)

219

(2)

The class W(N,M)

221

(1)

The class Pt(N,M)

222

(2)

Block-oriented nonlinear models

224

(3)

Block-oriented model structures

224

(2)

Equivalence with the class V (N,M)

226

(1)

Pruned Volterra models

227

(5)

The class of pruned Volterra models

227

(1)

An example: prunings of V(2,2)

228

(2)

The PPOD model structure

230

(2)

Infinite-dimensional Volterra models

232

(3)

Infinite-dimensional Hammerstein models

233

(1)

Robinson's AR-Volterra model

234

(1)

Bilinear models

235

(5)

Matching conditions

236

(2)

The completely bilinear case

238

(1)

A superdiagonal example

238

(2)

Summary: the nature of Volterra models

240

(3)

Linear Multimodels

243

(52)

A motivating example

244

(4)

Three classes of multimodels

248

(5)

Johansen-Foss discrete-time models

248

(2)

A modifed Johansen-Foss model

250

(1)

Tong's TARSO model class

251

(2)

Two important details

253

(2)

Local model selection criteria

253

(1)

Affine vs. linear models

254

(1)

Input-selected multimodels

255

(8)

Input-selected moving average models

255

(1)

Steady states of input-selected models

256

(1)

J-F vs. modified J-F models

256

(3)

Two input-selected examples

259

(4)

Output-selected multimodels

263

(4)

Output-selected autoregressive models

263

(1)

Steady-state behavior

264

(1)

Two output-selected examples

264

(3)

More general selection schemes

267

(9)

Johanssen-Foss and modified models

268

(3)

The isola model

271

(3)

Wiener and Hammerstein models

274

(2)

TARMAX models

276

(15)

The first-order model

277

(3)

The multimodel representation

280

(1)

Steady-state behavior

281

(3)

Some representation results

284

(3)

Positive systems

287

(1)

PHADD models

287

(4)

Summary: the nature of multimodels

291

(4)

Relations between Model Classes

295

(74)

Inclusions and exclusions

296

(6)

The basic inclusions

297

(3)

Some important exclusions

300

(2)

Basic notions of category theory

302

(8)

Definition of a category

303

(1)

Classes vs. sets

304

(2)

Some illuminating examples

306

(3)

Some simple ``non-examples''

309

(1)

The discrete-time dynamic model category

310

(8)

Composition of morphisms

310

(4)

The category DTDM and its objects

314

(2)

The morphism sets in DTDM

316

(2)

Restricted model categories

318

(11)

Subcategories

319

(1)

Linear model categories

320

(3)

Structural model categories

323

(3)

Behavioral model categories

326

(3)

Empirical modeling and IO subcategories

329

(8)

IO subcategories

329

(4)

Example 1: the category Affss

333

(1)

Example 2: the category Gauss

334

(1)

Example 3: the category Median

335

(2)

Structure-behavior relations

337

(10)

Joint subcategories

337

(1)

Linear model characterizations

338

(4)

Volterra model characterizations

342

(2)

Homomorphic system characterizations

344

(3)

Functors, linearization and inversion

347

(6)

Basic notion of a functor

347

(2)

Linearization functors

349

(2)

Inverse NARX models

351

(2)

Isomorphic model categories

353

(5)

Autoregressive vs. moving average models

353

(3)

Discrete- vs. continuous-time

356

(2)

Homomorphic systems

358

(6)

Relation to linear models

358

(1)

Relation to homogeneous models

359

(1)

Constructing new model categories

360

(4)

Summary: the utility of category theory

364

(5)

The Art of Model Development

369

(82)

The model development process

370

(20)

Parameter estimation

371

(5)

Outliers, disturbances and data pretreatment

376

(9)

Goodness-of-fit is not enough

385

(5)

Case study 1---bilinear model identification

390

(5)

Model structure selction

395

(9)

Structural implications of behavior

396

(3)

Behavioral implications of structure

399

(5)

Input sequence design

404

(19)

Effectiveness criteria and practical constraints

405

(4)

Design parameters

409

(5)

Random step sequences

414

(3)

The sine-power sequences

417

(6)

Case study 2---structure and inputs

423

(22)

The Eaton-Rawlings reactor model

424

(1)

Exact discretization

425

(3)

Linear approximations

428

(4)

Nonlinear approximations

432

(13)

Summary: the nature of empirical modeling

445

(6)

Bibliography

451

(10)

Index

461

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Discrete-Time Dynamic Models

Summary

Table of Contents

Supplemental Materials

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Discrete-Time Dynamic Models

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