Preface xiii -- Acknowledgments xv -- Abbreviations xvii -- 1 Identification 1 -- 1.1 Introduction 1 -- 1.2 Illustration of Some Important Aspects of System Identification 2 -- Exercise 1 .a (Least squares estimation of the value of a resistor) 2 -- Exercise 1 .b (Analysis of the standard deviation) 3 -- Exercise 2 (Study of the asymptotic distribution of an estimate) 5 -- Exercise 3 (Impact of noise on the regressor (input) measurements) 6 -- Exercise 4 (Importance of the choice of the independent variable or input) 7 -- Exercise 5.a (combining measurements with a varying SNR: Weighted least squares estimation) 8 -- Exercise 5.b (Weighted least squares estimation: A study of the variance) 9 -- Exercise 6 (Least squares estimation of models that are linear in the parameters) 11 -- Exercise 7 (Characterizing a 2-dimensional parameter estimate) 12 -- 1.3 Maximum Likelihood Estimation for Gaussian and Laplace Distributed Noise 14 -- Exercise 8 (Dependence of the optimal cost function on the distribution of the disturbing noise) 14 -- 1.4 Identification for Skew Distributions with Outliers 16 -- Exercise 9 (Identification in the presence of outliers) 16 -- 1.5 Selection of the Model Complexity 18 -- Exercise 10 (Influence of the number of parameters on the model uncertainty) 18 -- Exercise 11 (Model selection using the AIC criterion) 20 -- 1.6 Noise on Input and Output Measurements: The IV Method and the EIV Method 22 -- Exercise 12 (Noise on input and output: The instrumental variables method applied on the resistor estimate) 23 -- Exercise 13 (Noise on input and output: the errors-in-variables method) 25 -- 2 Generation and Analysis of Excitation Signals 29 -- 2.1 Introduction 29 -- 2.2 The Discrete Fourier Transform (DFT) 30 -- Exercise 14 (Discretization in time: Choice of the sampling frequency: ALIAS) 31 -- Exercise 15 (Windowing: Study of the leakage effect and the frequency resolution) 31 -- 2.3 Generation and Analysis of Multisines and Other Periodic Signals 33.

Exercise 16 (Generate a sine wave, noninteger number of periods measured) 34 -- Exercise 17 (Generate a sine wave, integer number of periods measured) 34 -- Exercise 18 (Generate a sine wave, doubled measurement time) 35 -- Exercise 19.a (Generate a sine wave using the MATLAB IFFT instruction) 37 -- Exercise 19.b (Generate a sine wave using the MATLAB IFFT instruction, defining only the first half of the spectrum) 37 -- Exercise 20 (Generation of a multisine with flat amplitude spectrum) 38 -- Exercise 21 (The swept sine signal) 39 -- Exercise 22.a (Spectral analysis of a multisine signal, leakage present) 40 -- Exercise 22.b (Spectral analysis of a multisine signal, no leakage present) 40 -- 2.4 Generation of Optimized Periodic Signals 42 -- Exercise 23 (Generation of a multisine with a reduced crest factor using random phase generation) 42 -- Exercise 24 (Generation of a multisine with a minimal crest factor using a crest factor minimization algorithm) 42 -- Exercise 25 (Generation of a maximum length binary sequence) 45 -- Exercise 26 (Tuning the parameters of a maximum length binary sequence) 46 -- 2.5 Generating Signals Using The Frequency Domain Identification Toolbox (FDIDENT) 46 -- Exercise 27 (Generation of excitation signals using the FDIDENT toolbox) 47 -- 2.6 Generation of Random Signals 48 -- Exercise 28 (Repeated realizations of a white random noise excitation with fixed length) 48 -- Exercise 29 (Repeated realizations of a white random noise excitation with increasing length) 49 -- Exercise 30 (Smoothing the amplitude spectrum of a random excitation) 49 -- Exercise 31 (Generation of random noise excitations with a user-imposed power spectrum) 50 -- Exercise 32 (Amplitude distribution of filtered noise) 51 -- 2.7 Differentiation, Integration, Averaging, and Filtering of Periodic Signals 52 -- Exercise 33 (Exploiting the periodic nature of signals: Differentiation, integration, +averaging, and filtering) 52 -- 3 FRF Measurements 55 -- 3.1 Introduction 55.

3.2 Definition of the FRF 56 -- 3.3 FRF Measurements without Disturbing Noise 57 -- Exercise 34 (Impulse response function measurements) 57 -- Exercise 35 (Study of the sine response of a linear system: transients and steady-state) 58 -- Exercise 36 (Study of a multisine response of a linear system: transients and steady-state) 59 -- Exercise 37 (FRF measurement using a noise excitation and a rectangular window) 61 -- Exercise 38 (Revealing the nature of the leakage effect in FRF measurements) 61 -- Exercise 39 (FRF measurement using a noise excitation and a Hanning window) 64 -- Exercise 40 (FRF measurement using a noise excitation and a diff window) 65 -- Exercise 41 (FRF measurements using a burst excitation) 66 -- 3.4 FRF Measurements in the Presence of Disturbing Output Noise 68 -- Exercise 42 (Impulse response function measurements in the presence of output noise) 69 -- Exercise 43 (Measurement of the FRF using a random noise sequence and a random phase multisine in the presence of output noise) 70 -- Exercise 44 (Analysis of the noise errors on FRF measurements) 71 -- Exercise 45 (Impact of the block (period) length on the uncertainty) 73 -- 3.5 FRF Measurements in the Presence of Input and Output Noise 75 -- Exercise 46 (FRF measurement in the presence of input/output disturbances using a multisine excitation) 75 -- Exercise 47 (Measuring the FRF in the presence of input and output noise: Analysis of the errors) 75 -- Exercise 48 (Measuring the FRF in the presence of input and output noise: Impact of the block (period) length on the uncertainty) 76 -- 3.6 FRF Measurements of Systems Captured in a Feedback Loop 78 -- Exercise 49 (Direct measurement of the FRF under feedback conditions) 78 -- Exercise 50 (The indirect method) 80 -- 3.7 FRF Measurements Using Advanced Signal Processing Techniques: The LPM 82 -- Exercise 51 (The local polynomial method) 82 -- Exercise 52 (Estimation of the power spectrum of the disturbing noise) 84 -- 3.8 Frequency Response Matrix Measurements for MIMO Systems 85.

Exercise 53 (Measuring the FRM using multisine excitations) 85 -- Exercise 54 (Measuring the FRM using noise excitations) 86 -- Exercise 55 (Estimate the variance of the measured FRM) 88 -- Exercise 56 (Comparison of the actual and theoretical variance of the estimated FRM) 88 -- Exercise 57 (Measuring the FRM using noise excitations and a Hanning window) 89 -- 4 Identification of Linear Dynamic Systems 91 -- 4.1 Introduction 91 -- 4.2 Identification Methods that Are Linear-in-the-Parameters. The Noiseless Setup 93 -- Exercise 58 (Identification in the time domain) 94 -- Exercise 59 (Identification in the frequency domain) 96 -- Exercise 60 (Numerical conditioning) 97 -- Exercise 61 (Simulation and one-step-ahead prediction) 99 -- Exercise 62 (Identify a too-simple model) 100 -- Exercise 63 (Sensitivity of the simulation and prediction error to model errors) 101 -- Exercise 64 (Shaping the model errors in the time domain: Prefiltering) 102 -- Exercise 65 (Shaping the model errors in the frequency domain: frequency weighting) 102 -- 4.3 Time domain Identification using parametric noise models 104 -- Exercise 66 (One-step-ahead prediction of a noise sequence) 105 -- Exercise 67 (Identification in the time domain using parametric noise models) 108 -- Exercise 68 (Identification Under Feedback Conditions Using Time Domain Methods) 109 -- Exercise 69 (Generating uncertainty bounds for estimated models) 111 -- Exercise 70 (Study of the behavior of the BJ model in combination with prefiltering) 113 -- 4.4 Identification Using Nonparametric Noise Models and Periodic Excitations 115 -- Exercise 71 (Identification in the frequency domain using nonparametric noise models) 117 -- Exercise 72 (Emphasizing a frequency band) 119 -- Exercise 73 (Comparison of the time and frequency domain identification under feedback) 120 -- 4.5 Frequency Domain Identification Using Nonparametric Noise Models and Random Excitations 122 -- Exercise 74 (Identification in the frequency domain using nonparametric noise models and a random excitation) 122.

4.6 Time Domain Identification Using the System Identification Toolbox 123 -- Exercise 75 (Using the time domain identification toolbox) 124 -- 4.7 Frequency Domain Identification Using the Toolbox FDIDENT 129 -- Exercise 76 (Using the frequency domain identification toolbox FDIDENT) 129 -- 5 Best Linear Approximation of Nonlinear Systems 137 -- 5.1 Response of a nonlinear system to a periodic input 137 -- Exercise 77.a (Single sine response of a static nonlinear system) 138 -- Exercise 77.b (Multisine response of a static nonlinear system) 139 -- Exercise 78 (Uniform versus Pointwise Convergence) 142 -- Exercise 79.a (Normal operation, subharmonics, and chaos) 143 -- Exercise 79.b (Influence initial conditions) 146 -- Exercise 80 (Multisine response of a dynamic nonlinear system) 147 -- Exercise 81 (Detection, quantification, and classification of nonlinearities) 148 -- 5.2 Best Linear Approximation of a Nonlinear System 150 -- Exercise 82 (Influence DC values signals on the linear approximation) 151 -- Exercise 83.a (Influence of rms value and pdf on the BLA) 152 -- Exercise 83.b (Influence of power spectrum coloring and pdf on the BLA) 154 -- Exercise 83.c (Influence of length of impulse response of signal filter on the BLA) 156 -- Exercise 84.a (Comparison of Gaussian noise and random phase multisine) 158 -- Exercise 84.b (Amplitude distribution of a random phase multisine) 160 -- Exercise 84.c (Influence of harmonic content multisine on BLA) 162 -- Exercise 85 (Influence of even and odd nonlinearities on BLA) 165 -- Exercise 86 (BLA of a cascade) 167 -- 5.3 Predictive Power of The Best Linear Approximation 172 -- Exercise 87.a (Predictive power BLA - static NL system) 172 -- Exercise 87.b (Properties of output residuals - dynamic NL system) 174 -- Exercise 87.c (Predictive power of BLA - dynamic NL system) 178 -- 6 Measuring the Best Linear Approximation of a Nonlinear System 183 -- 6.1 Measuring the Best Linear Approximation 183 -- Exercise 88.a (Robust method for noisy FRF measurements) 186.

Exercise 88.b (Robust method for noisy input/output measurements without reference signal) 190 -- Exercise 88.c (Robust method for noisy input/output measurements with reference signal) 195 -- Exercise 89.a (Design of baseband odd and full random phase multisines with random harmonic grid) 197 -- Exercise 89.b (Design of bandpass odd and full random phase multisines with random harmonic grid) 197 -- Exercise 89.c (Fast method for noisy input/output measurements - open loop example) 203 -- Exercise 89.d (Fast method for noisy input/output measurements - closed loop example) 207 -- Exercise 89.e (Bias on the estimated odd and even distortion levels) 211 -- Exercise 90 (Indirect method for measuring the best linear approximation) 215 -- Exercise 91 (Comparison robust and fast methods) 216 -- Exercise 92 (Confidence intervals for the BLA) 219 -- Exercise 93 (Prediction of the bias contribution in the BLA) 221 -- Exercise 94 (True underlying linear system) 222 -- 6.2 Measuring the nonlinear distortions 224 -- Exercise 95 (Prediction of the nonlinear distortions using random harmonic grid multisines) 225 -- Exercise 96 (Pros and cons full-random and odd-random multisines) 230 -- 6.3 Guidelines 233 -- 6.4 Projects 233 -- 7 Identification of Parametric Models in the Presence of Nonlinear Distortions 239 -- 7.1 Introduction 239 -- 7.2 Identification of the Best Linear Approximation Using Random Excitations 240 -- Exercise 97 (Parametric estimation of the best linear approximation) 240 -- 7.3 Generation of Uncertainty Bounds? 243 -- Exercise 98 243 -- 7.4 Identification of the best linear approximation using periodic excitations 245 -- Exercise 99 (Estimate a parametric model for the best linear approximation using the Fast Method) 246 -- Exercise 100 (Estimating a parametric model for the best linear approximation using the robust method) 251 -- 7.5 Advises and conclusions 252 -- References 255 -- Subject Index 259 -- Reference Index 263.