Mastering System Identification in 100 Exercises

by Schoukens, Johan; Pintelon, Rik; Rolain, Yves

• ISBN13: 9780470936986
• ISBN10: 0470936983
• Edition: 1st
• Format: Paperback
• Copyright: 2012-03-26
• Publisher: Wiley-IEEE Press

Summary

This book enables readers to understand system identification and linear system modeling through 100 practical exercises without requiring complex theoretical knowledge. The contents encompass state-of-the-art system identification methods, with both time and frequency domain system identification methods covered, including the pros and cons of each. Each chapter features MATLAB exercises, discussions of the exercises, accompanying MATLAB downloads, and larger projects that serve as potential assignments in this learn-by-doing resource.

Author Biography

Johan Schoukens, PhD, serves as a full-time professor in the ELEC Department at the Vrije Universiteit Brussel. He has been a Fellow of IEEE since 1997 and was the recipient of the 2003 IEEE Instrumentation and Measurement Society Distinguished Service Award.

Rik Pintelon, PhD, serves as a full-time professor at the Vrije Universiteit Brussel in the ELEC Department. He has been a Fellow of IEEE since 1998 and is the recipient of the 2012 IEEE Joseph F. Keithley Award in Instrumentation and Measurement (IEEE Technical Field Award).

Yves Rolain, PhD, serves as a full-time professor at the Vrije Universiteit Brussel in the ELEC department. He has been a Fellow of IEEE since 2006 and was the recipient of the 2004 IEEE Instrumentation and Measurement Society Technical Award.

Table of Contents

Preface	p. xiii
Acknowledgments	p. xv
Abbreviations	p. xvii
Identification	p. 1
Introduction	p. 1
Illustration of Some Important Aspects of System Identification	p. 2
(Least squares estimation of the value of a resistor)	p. 2
(Analysis of the standard deviation)	p. 3
(Study of the asymptotic distribution of an estimate)	p. 5
(Impact of noise on the regressor (input) measurements)	p. 6
(Im portance of the choice of the independent variable or input)	p. 7
(combining measurements with a varying SNR: Weighted least squares estimation)	p. 8
(Weighted least squares estimation: A study of the variance)	p. 9
(Least squares estimation of models that are linear in the parameters)	p. 11
(Characterizing a 2-dimensional parameter estimate)	p. 12
Maximum Likelihood Estimation for Gaussian and Laplace Distributed Noise	p. 14
(Dependence of the optimal cost function on the distribution of the disturbing noise)	p. 14
Identification for Skew Distributions with Outliers	p. 16
(Identification in the presence of outliers)	p. 16
Selection of the Model Complexity	p. 18
(Influence of the number of parameters on the model uncertainty)	p. 18
(Model selection using the AIC criterion)	p. 20
Noise on Input and Output Measurements: The IV Method and the EIV Method	p. 22
(Noise on input and output: The instrumental variables method applied on the resistor estimate)	p. 23
(Noise on input and output: the errors-in-variables method)	p. 25
Generation and Analysis of Excitation Signals	p. 29
Introduction	p. 29
The Discrete Fourier Transform (DFT)	p. 30
(Discretization in time: Choice of the sampling frequency: ALIAS)	p. 31
(Windowing: Study of the leakage effect and the frequency resolution)	p. 31
Generation and Analysis of Multisines and Other Periodic Signals	p. 33
(Generate a sine wave, noninteger number of periods measured)	p. 34
(Generate a sine wave, integer number of periods measured)	p. 34
(Generate a sine wave, doubled measurement time)	p. 35
(Generate a sine wave using the MATLAB IFFT instruction)	p. 37
(Generate a sine wave using the MATLAB IFFT instruction, defining only the first half of the spectrum)	p. 37
(Generation of a multisine with flat amplitude spectrum)	p. 38
(The swept sine signal)	p. 39
(Spectral analysis of a multisine signal, leakage present)	p. 40
(Spectral analysis of a multisine signal, no leakage present)	p. 40
Generation of Optimized Periodic Signals	p. 42
(Generation of a multisine with a reduced crest factor using random phase generation)	p. 42
(Generation of a multisine with a minimal crest factor using a crest factor minimization algorithm)	p. 42
(Generation of a maximum length binary sequence)	p. 45
(Tuning the parameters of a maximum length binary sequence)	p. 46
Generating Signals Using The Frequency Domain Identification Toolbox (FDIDENT)	p. 46
(Generation of excitation signals using the FDIDENT toolbox)	p. 47
Generation of Random Signals	p. 48
(Repeated realizations of a white random noise excitation with fixed length)	p. 48
(Repeated realizations of a white random noise excitation with increasing length)	p. 49
(Smoothing the amplitude spectrum of a random excitation)	p. 49
(Generation of random noise excitations with a user-imposed power spectrum)	p. 50
(Amplitude distribution of filtered noise)	p. 51
Differentiation, Integration, Averaging, and Filtering of Periodic Signals	p. 52
(Exploiting the periodic nature of signals: Differentiation, integration, +averaging, and filtering)	p. 52
FRF Measurements	p. 55
Introduction	p. 55
Definition of the FRF	p. 56
FRF Measurements without Disturbing Noise	p. 57
(Impulse response function measurements)	p. 57
(Study of the sine response of a linear system: transients and steady-state)	p. 58
(Study of a multisine response of a linear system: transients and steady-state)	p. 59
(FRF measurement using a noise excitation and a rectangular window)	p. 61
(Revealing the nature of the leakage effect in FRF measurements)	p. 61
(FRF measurement using a noise excitation and a Hanning window)	p. 64
(FRF measurement using a noise excitation and a diff window)	p. 65
(FRF measurements using a burst excitation)	p. 66
FRF Measurements in the Presence of Disturbing Output Noise	p. 68
(Impulse response function measurements in the presence of output noise)	p. 69
(Measurement of the FRF using a random noise sequence and a random phase multisine in the presence of output noise)	p. 70
(Analysis of the noise errors on FRF measurements)	p. 71
(Impact of the block (period) length on the uncertainty)	p. 73
FRF Measurements in the Presence of Input and Output Noise	p. 75
(FRF measurement in the presence of input/output disturbances using a multisine excitation)	p. 75
(Measuring the FRF in the presence of input and output noise: Analysis of the errors)	p. 75
(Measuring the FRF in the presence of input and output noise: Impact of the block (period) length on the uncertainty)	p. 76
FRF Measurements of Systems Captured in a Feedback Loop	p. 78
(Direct measurement of the FRF under feedback conditions)	p. 78
(The indirect method)	p. 80
FRF Measurements Using Advanced Signal Processing Techniques: The LPM	p. 82
(The local polynomial method)	p. 82
(Estimation of the power spectrum of the disturbing noise)	p. 84
Frequency Response Matrix Measurements for MIMO Systems	p. 85
(Measuring the FRM using multisine excitations)	p. 85
(Measuring the FRM using noise excitations)	p. 86
(Estimate the variance of the measured FRM)	p. 88
(Comparison of the actual and theoretical variance of the estimated FRM)	p. 88
(Measuring the FRM using noise excitations and a Hanning window)	p. 89
Identification of Linear Dynamic Systems	p. 91
Introduction	p. 91
Identification Methods that Are Linear-in-the-Parameters. The Noiseless Setup	p. 93
(Identification in the time domain)	p. 94
(Identification in the frequency domain)	p. 96
(Numerical conditioning)	p. 97
(Simulation and one-step-ahead prediction)	p. 99
(Identify a too-simple model)	p. 100
(Sensitivity of the simulation and prediction error to model errors)	p. 101
(Shaping the model errors in the time domain: Prefiltering)	p. 102
(Shaping the model errors in the frequency domain: frequency weighting)	p. 102
Time domain Identification using parametric noise models	p. 104
(One-step-ahead prediction of a noise sequence)	p. 105
(Identification in the time domain using parametric noise models)	p. 108
(Identification Under Feedback Conditions Using Time Domain Methods)	p. 109
(Generating uncertainty bounds for estimated models)	p. 111
(Study of the behavior of the BJ model in combination with prefiltering)	p. 113
Identification Using Nonparametric Noise Models and Periodic Excitations	p. 115
(Identification in the frequency domain using nonparametric noise models)	p. 117
(Emphasizing a frequency band)	p. 119
(Comparison of the time and frequency domain identification under feedback)	p. 120
Frequency Domain Identification Using Nonparametric Noise Models and Random Excitations	p. 122
(Identification in the frequency domain using nonparametric noise models and a random excitation)	p. 122
Time Domain Identification Using the System Identification Toolbox	p. 123
(Using the time domain identification toolbox)	p. 124
Frequency Domain Identification Using the Toolbox FDIDENT	p. 129
(Using the frequency domain identification toolbox FDIDENT)	p. 129
Best Linear Approximation of Nonlinear Systems	p. 137
Response of a nonlinear system to a periodic input	p. 137
(Single sine response of a static nonlinear system)	p. 138
(Multisine response of a static nonlinear system)	p. 139
(Uniform versus Pointwise Convergence)	p. 142
(Normal operation, subharmonics, and chaos)	p. 143
(Influence initial conditions)	p. 146
(Multisine response of a dynamic nonlinear system)	p. 147
(Detection, quantification, and classification of nonlinearities)	p. 148
Best Linear Approximation of a Nonlinear System	p. 150
(Influence DC values signals on the linear approximation)	p. 151
(Influence of rms value and pdf on the BLA)	p. 152
(Influence of power spectrum coloring and pdf on the BLA)	p. 154
(Influence of length of impulse response of signal filter on the BLA)	p. 156
(Comparison of Gaussian noise and random phase multisine)	p. 158
(Amplitude distribution of a random phase multisine)	p. 160
(Influence of harmonic content multisine on BLA)	p. 162
(Influence of even and odd nonlinearities on BLA)	p. 165
(BLA of a cascade)	p. 167
Predictive Power of The Best Linear Approximation	p. 172
(Predictive power BLA — static NL system)	p. 172
(Properties of output residuals — dynamic NL system)	p. 174
(Predictive power of BLA — dynamic NL system)	p. 178
Measuring the Best Linear Approximation of a Nonlinear System	p. 183
Measuring the Best Linear Approximation	p. 183
(Robust method for noisy FRF measurements)	p. 186
(Robust method for noisy input/output measurements without reference signal)	p. 190
(Robust method for noisy input/output measurements with reference signal)	p. 195
(Design of baseband odd and full random phase multisines with random harmonic grid)	p. 197
(Design of bandpass odd and full random phase multisines with random harmonic grid)	p. 197
(Fast method for noisy input/output measurements — open loop example)	p. 203
(Fast method for noisy input/output measurements — closed loop example)	p. 207
(Bias on the estimated odd and even distortion levels)	p. 211
(Indirect method for measuring the best linear approximation)	p. 215
(Comparison robust and fast methods)	p. 216
(Confidence intervals for the BLA)	p. 219
(Prediction of the bias contribution in the BLA)	p. 221
(True underlying linear system)	p. 222
Measuring the nonlinear distortions	p. 224
(Prediction of the nonlinear distortions using random harmonic grid multisines)	p. 225
(Pros and cons full-random and odd-random multisines)	p. 230
Guidelines	p. 233
Projects	p. 233
Identification of Parametric Models in the Presence of Nonlinear Distortions	p. 239
Introduction	p. 239
Identification of the Best Linear Approximation Using Random Excitations	p. 240
(Parametric estimation of the best linear approximation)	p. 240
Generation of Uncertainty Bounds?	p. 243
	p. 243
Identification of the best linear approximation using periodic excitations	p. 245
(Estimate a parametric model for the best linear approximation using the Fast Method)	p. 246
(Estimating a parametric model for the best linear approximation using the robust method)	p. 251
Advises and conclusions	p. 252
References	p. 255
Subject Index	p. 259
Reference Index	p. 263
Table of Contents provided by Publisher. All Rights Reserved.