Table of Contents
Series Introduction iii
Preface v
I Identification
1 Introduction to Identification 3
1.1 Where are models needed? 3
1.2 What kinds of models are there? 4
1.2.1 Identification vs. first-principle modeling 7
1.3 Steps of identification 8
1.4 Outline of the book 11
2 Linear Regression 13
2.1 Linear systems 13
2.2 Method of least squares 17
2.2.1 Derivation 18
2.2.2 Algorithm 20
2.2.3 Matrix representation 21
2.2.4 Properties 25
2.3 Recursive LS method 28
2.3.1 Derivation 28
2.3.2 Algorithm 31
2.3.3 A posteriori prediction error 33
2.4 RLS with exponential forgetting 34
2.4.1 Derivation 36
2.4.2 Algorithm 36
2.5 Kalman filter 37
2.5.1 Derivation 40
2.5.2 Algorithm 42
2.5.3 Kalman filter in parameter estimation 44
3 Linear Dynamic Systems 47
3.1 Transfer function 47
3.1.1 Finite impulse response 47
3.1.2 Transfer function 50
3.2 Deterministic disturbances 53
3.3 Stochastic disturbances 53
3.3.1 Offset- in noise 55
3.3.2 Box-Jenkins 55
3.3.3 Autoregressive exogenous 57
3.3.4 Output error 59
3.3.5 Other structures 61
3.3.6 Diophantine equation 66
3.3.7 i-step-ahead predictions 69
3.3.8 Remarks 74
4 Non-linear Systems 77
4.1 Basis function networks 78
4.1.1 Generalized basis function network 78
4.1.2 Basis functions 79
4.1.3 Function approximation 81
4.2 Non-linear black-box structures 82
4.2.1 Power series 83
4.2.2 Sigmoid neural networks 89
4.2.3 Nearest neighbor methods 95
4.2.4 Fuzzy inference systems 98
5 Non-linear Dynamic Structures 113
5.1 Non-linear time-series models 114
5.1.1 Gradients of non-linear time-series models 117
5.2 Linear dynamics and static non-linearities 120
5.2.1 Wiener systems 121
5.2.2 Hammerstein systems 124
5.3 Linear dynamics and steady-state models 125
5.3.1 Transfer function with unit steady-state gain 126
5.3.2 Wiener and Hammerstein predictors 126
5.3.3 Gradients of the Wiener and Hammerstein predictors 128
5.4 Remarks 132
5.4.1 Inverse of Hammerstein and Wiener systems 133
5.4.2 ARX dynamics 134
6 Estimation of Parameters 137
6.1 Prediction error methods 138
6.1.1 First-order methods 139
6.1.2 Second-order methods 140
6.1.3 Step size 141
6.1.4 Levenberg-Marquardt algorithm 142
6.2 Optimization under constraints 149
6.2.1 Equality constraints 149
6.2.2 Inequality constraints 151
6.3 Guided random search methods 153
6.3.1 Stochastic learning automaton 155
6.4 Simulation examples 159
6.4.1 Pneumatic valve: identification of a Wiener system 160
6.4.2 Binary distillation column: identification of Hammerstein model under constraints 167
6.4.3 Two-tank system: Wiener modeling under constraints 172
6.4.4 Conclusions 176
II Control
7 Predictive Control 181
7.1 Introduction to model-based control 181
7.2 The basic idea 182
7.3 Linear quadratic predictive control 183
7.3.1 Plant and model 184
7.3.2 i-step ahead predictions 185
7.3.3 Cost function 186
7.3.4 Remarks 187
7.3.5 Closed-loop behavior 188
7.4 Generalized predictive control 189
7.4.1 ARMAX/ARIMAX model 190
7.4.2 i-step-ahead predictions 191
7.4.3 Cost function 193
7.4.4 Remarks 195
7.4.5 Closed-loop behavior 197
7.5 Simulation example 197
8 Multivariate Systems 203
8.1 Relative gain array method 204
8.1.1 The basic idea 204
8.1.2 Algorithm 206
8.2 Decoupling of interactions 209
8.2.1 Multivariable Pi-controller 210
8.3 Multivariable predictive control 213
8.3.1 State-space model 213
8.3.2 i-step ahead predictions 216
8.3.3 Cost function 217
8.3.4 Remarks 218
8.3.5 Simulation example 219
9 Time-varying and Non-linear Systems 223
9.1 Adaptive control 223
9.1.1 Types of adaptive control 225
9.1.2 Simulation example 228
9.2 Control of Hammerstein and Wiener systems 232
9.2.1 Simulation example 233
9.2.2 Second order Hammerstein systems 242
9.3 Control of non-linear systems 247
9.3.1 Predictive control 248
9.3.2 Sigmoid neural networks 248
9.3.3 Stochastic approximation 252
9.3.4 Control of a fermenter 254
9.3.5 Control of a tubular reactor 266
III Appendices
A State-Space Representation 273
A.1 State-space description 273
A.1.1 Control and observer canonical forms 274
A.2 Controllability and observability 275
A.2.1 Pole placement 276
A.2.2 Observers 280
B Fluidized Bed Combustion 283
B.1 Model of a bubbling fluidized bed 283
B.1.1 Bed 285
B.1.2 Freeboard 286
B.1.3 Power 286
B.1.4 Steady-state 287
B.2 Tuning of the model 288
B.2.1 Initial values 288
B.2.2 Steady-state behavior 288
B.2.3 Dynamics 290
B.2.4 Performance of the model 291
B.3 Linearization of the model 293
Bibliography 299
Index 307
