Identification of continuous systems [10] 0444703160, 9780444703163

Table of contents :
Cover......Page 1
Identification of Continous Systems......Page 3
ISBN 0444703160 9780444703163......Page 4
Table Of Contents......Page 5
PREFACE......Page 13
ACKNOWLEDGMENTS......Page 15
1.1 System Identification and Continuous Models......Page 17
1.2 Identification and Parameter Estimation......Page 20
1.3 A Brief Overview of the Field......Page 21
1.3.2 Parametric methods......Page 23
1.3.3 Systems with nonlinear, time-varying and time-delay elements and system structure......Page 28
1.3.4 Distributed parameter systems......Page 29
1.4 Scope of the Book......Page 30
2. Continuous-Time Models of Dynamical Systems......Page 39
2.1.1 Linear time-invariant systems (LTIVS)......Page 40
2.1.3 Nonlinear systems (NLS)......Page 42
2.2.1.1 State space models......Page 44
2.2.1.2 The weighting matrix of LTIV systems......Page 45
2.2.1.3 Solution in frequency-domain......Page 46
2.2.1.4 Canonical forms for LTIV systems......Page 47
2.2.1.5 Diagonalization of the system matrix......Page 51
2.2.2 Linear time-varying (LTV ) systems, nonlinear systems and delay systems......Page 54
2.2.2.1 Zadeh's system function......Page 55
2.2.2.2 State space representation of LTV systems......Page 56
2.2.2.3 Solution of the state equations of LTV systems......Page 57
2.2.2.4 Transformation of state equations......Page 58
2.2.2.5 Systems with separability properties......Page 59
2.2.2.6 Systems with separable nonlinear elements......Page 60
2.2.2.8 Some useful methods of parametrization of nonlinear and time-varying models......Page 61
2.3.3 The special 'innovations' Kalman filter......Page 63
2.4 Models of DistribuJed Parameter Systems (DPS)......Page 64
3.1.1.1 One-sided Laplace transform......Page 67
3.1.1.2 Two-sided Laplace transform......Page 68
3.1.1.4 One-sided z-transform......Page 69
3.1.1.5 Two-sided z-transform......Page 70
3.1.2 Generalized functions or distributions......Page 71
3.2.1.1 Countable basis......Page 72
3.2.2 Systems of orthogonal polynomials......Page 74
3.2.3 Systems of piecewise constant basis-functions (PCBF)......Page 86
3.2.3.3 Walsh functions (WF)......Page 87
3.2.3.4 Haar functions (HF)......Page 91
3.2.4 Multidimensional expansions in term s of systems of orthogonal functions......Page 93
3.2.5.1 Some important properties of correlation functions......Page 97
3.2.5.2 Some examples of power density spectra......Page 99
3.3.2 Multidimensional Poisson moment functionals (MDPMF)......Page 101
4.1 The Role of Nonparametric Models in Continuous System ldentification......Page 105
4.2.1 Some important deterministic signals......Page 106
4.2.2.1 Random telegraph signal......Page 108
4.2.2.2 Quantized binary random signal......Page 109
4.2.2.3 Quantized binary and ternary pseudorandom signals......Page 110
4.3.1.1 Measurements using a block-pulse input......Page 113
4.3.1.2 Measurements using a saturated ramp function (time integral of block-pulse function) input......Page 114
4.3.1.3 Measurements using an arbitrary deterministic signal......Page 115
4.3.2.1 Evaluation of impulse response or weighting function......Page 117
4.3.2.2 Correlation analysis with binary and ternary random signals......Page 120
4.3.2.3 Numerical solution of the basic equation......Page 125
4.4.1.1 Basic definitions and numerical evaluation......Page 126
4.4.1.2 Coherence function......Page 131
4.4.1.3 The periodogram......Page 132
4.4.2 Identification of a system in closed-loop......Page 133
4.4.3 Direct determination of frequency response by correlation......Page 135
4.5.1.1 The method of flexion tangents and times required to reach certain percent (of steady state) values......Page 137
4.5.1.2 The method of moments......Page 152
4.5.2 From nonparametric models in frequency-domain to transfer functions......Page 153
4.5.2.1 Method of Bode asymptotes......Page 154
4.5.2.2 Approximation of given frequency response to transfer function in rational form......Page 155
4.5.2.3 Least squares approaches for transfer function synthesis from frequency response data......Page 159
4.6.1 Basic relations......Page 167
4.6.2 Determination of frequency response from step response......Page 171
4.6.3 Extension to the case of input signals other than step functions......Page 173
4.6.4 Determination of step response from frequency response......Page 176
5.1 Introduction......Page 183
5.2.1 An introductory example......Page 186
5.2.2 The method (modulating) function technique......Page 188
5.2.3 The Poisson moment functional (PMF) method......Page 189
5.2.4 Method of orthogonal funtions......Page 191
5.2.5.1 The PMF algorithm (Method 2)......Page 193
5.2.5.2 The orthogonal function method......Page 198
5.2.5.3 The method of linear filters......Page 209
5.3.1 Scheme for parameter es timation and model structures......Page 215
5.3.2.1 Direct solution......Page 221
5.3.2.2 Recursive solution......Page 224
5.3.3 The instrumental variable (IV-) method......Page 227
5.3.4 The maximum like li ho od (ML-) method......Page 230
5.3.5 Weighted parameter estimation......Page 234
5.3.6 Normalized PMF's......Page 236
5.3.7 Examples......Page 237
6. Identification of Linear Systems Using Adaptive Models......Page 253
6.1.1 The parallel model approach......Page 254
6.1.2 The series (reciprocal) model approach......Page 261
6.1.3 The series-parallel model approach......Page 263
6.1.4 Stability of model adaptation using gradient methods......Page 266
6.2 Model adaptation in frequency-domain......Page 269
6.3.1.1 The basics of the technique......Page 274
6.3.1.2 A general design method for the series-parallel model approach......Page 276
6.3.1.3 A general design method for the parallel model approach......Page 280
6.3.2.1 A brief introduction to hyperstability theory......Page 283
6.3.2.2 Stable identification with adaptive models on the basis of hyperstability theory......Page 291
6.4.1 The method based on Liapunov's stability theory......Page 299
6.4.2 The method based on hyperstability theory......Page 305
7.1.1 The total (or MIMO) model......Page 315
7.1.2 The MISO model decomposition......Page 317
7.1.3 The SISO model decomposition......Page 319
7.1.4 General formulation of recursive algorithm for MISO models......Page 320
7.1.5 The Poisson moment functional (PMF) algorithm......Page 322
7.1.6 The orthogonal functions method......Page 323
7.2.1 A simple example for illustration......Page 327
7.2.2 The general algorithm......Page 330
7.3.1 The output error approach......Page 335
7.3.2 The equation error approach......Page 337
7.3.3 The iterative shift algorithm (ISA)......Page 339
7.3.4 Identification when the unknown delay is known to be small......Page 343
7.4 Identification of systems with unknown nonlinear elements......Page 346
7.4.1 The PMF approach......Page 347
7.4.2 The orthogonal functions approach......Page 348
7.4.3 Identification of systems with piecewise linear models......Page 349
7.5 Identification of distributed parameter systems (DPS)......Page 352
7.5.1 The multi-dimensional PMF approach......Page 353
7.5.2 The use of multi-dimensional systems of orthogonal functions......Page 357
7.6.1 Matrix rank methods (MRM)......Page 365
7.6.2 Parameter error function approach......Page 368
Notation and Symbols......Page 377
Author Index......Page 379
Subject Index......Page 383