Modeling and Identification of Dynamic Systems (vimmd312, 2018) Textbook background of the curriculum taken. In parenthesis: material not reviewed due to time shortage, but which is suggested to be read and can be easily understood based on the lectures. Dots: material skept. Mastering System Identification in 100 Exercises 1. Identification 1.1 Introduction 1.2 Illustration of some important aspects of system identification 1.2.1 Least squares estimation: A basic approach to system identification 1.2.2 Systematic errors in least squares estimation 1.2.3 Weighted least squares: optimal combination of measurements of different quality 1.2.4 Models that are linear-in-the-parameters.. 1.2.6 What we have learned. Further reading 1.3 Maximum likelihood estimation for Gaussian and Laplace distributed noise (1.5 Selection of the model complexity) (1.6 Noise on input and output measurements: the IV method and the EIV method) 2. Generation and analysis of excitation signals 2.1 Introduction 2.2 The Discrete Fourier Transform 2.3 Generation and analysis of multisines and other periodic signals 2.3.1 Generation and analysis of sine wave signals 2.3.2 Generation of multisine signals 2.3.4 Spectral analysis of multisine signals 2.3.5 What we have learned. Further reading 2.4 Generation of optimized periodic signals 2.4.1 Optimized multisines 2.4.3 What we have learned. Further reading 2.6 Generation of random signals 2.6.1 Generation, analyzing, and shaping random excitations 2.6.2 What we have learned. Further reading 3. FRF measurements 3.1 Introduction 3.2 Definition of the FRF
3.3 FRF measurements without disturbing noise 3.3.1 Direct measurement of the impulse response 3.3.2 Transient and steady-state response for periodic excitations 3.3.3 FRF measurements using random excitations 3.3.4 What we have learned. Further reading 3.4 FRF measurements in the presense of disturbing output noise 3.4.1 Impulse response function measurements in the presence of output noise 3.4.2 FRF measurement in the presence of output noise using noise and multisine excitations 3.4.3 What we have learned. Further reading 3.5 FRF measurements in the presence of input and output noise 3.5.1 What we have learned. Further reading 3.6 FRF measurements of systems captured in a feedback loop 3.6.1 Measurements in the loop: The direct method 3.6.2 Use of an external reference signal: The indirect method 3.6.3 What we have learned. Further reading 3.7 FRF measurements using advanced signal processing techniques: the LPM 3.7.1 Measuring the FRF using the local polynomial method 3.7.2 Estimating a nonparametric noise model using the local polynomial method 3.7.3 What we have learned. Further reading 3.8 Frequency response matrix measurements for MIMO systems 3.8.1 Introduction 3.8.2 Measuring the FRM using a rectangular window 3.8.3 Measuring the FRM using random noise excitations and a Hanning window 3.8.4 What we have learned. Further reading 4. Identification of linear dynamic systems 4.1 Introduction 4.2 Identification methods that are linear-in-the-parameters. The noiseless setup 4.2.1 Introduction 4.2.2 Introduction to time and frequency domain identification.. 4.2.6 What we have learned. Further reading 4.3 Time domain identification using parametric noise models 4.3.1 Introduction 4.3.2 Parametric noise models 4.3.3 Identification of parametric plant and noise models.. 4.3.7 What we have learned. Further reading 4.4 Identification using nonparametric noise models and periodic excitations 4.4.1 Identification using nonparametric noise models and periodic excitations.. 4.4.4 What we have learned. Further reading 4.6 Time domain identification using the system identification toolbox 4.7 Frequency domain identification using the toolbox fdident
5. Best Linear Approximation of nonlinear systems 5.1 Response of a nonlinear system to a periodic input 5.1.1 Static nonlinear systems 5.1.2 Dynamic nonlinear systems 5.1.3 Detection, qualification, and classification of nonlinear distortions 5.1.4 What we have learned. Further reading 5.2 Best Linear Approximation of nonlinear systems 5.2.1 Static nonlinear systems 5.2.2 Dynamic nonlinear systems 5.2.3 What we have learned. Further reading 6. Measuring the Best Linear Approximation of a nonlinear system 6.1. Measuring the best linear approximation 6.1.1 Robust method 6.1.2 Fast method 6.1.3 The indirect method for measuring the best linear approximation 6.1.4 Comparison of the fast and robust methods. 6.1.7 What we have learned. Further reading 6.2 Measuring the nonlinear distortions 6.2.1 What we have learned. Further reading 6.3 Guidelines System Identification. A Frequency Domain Approach (Pintelon, Schoukens) 1. An introduction to identification 1.1 What is identification? 1.2 Identification: a simple example 1.3 Description of the stochastic behavior of estimators 1.4 Basic steps in the identification process 1.5 A statistical approach to the estimation problem 2. Measurements of frequency response function 2.1 Introduction 2.2 An introduction to the Discrete Fourier Transform 2.3 Spectral representations of periodic signals 2.4 Analysis of FRF measurements using periodic excitations 2.5 Reducing FRF measurement errors for periodic excitations 2.6 FRF measurements using random excitations 2.8 Guidelines for FRF measurements 3. Frequency Response Function measurements in the presence of nonlinear distortions 4. Design of excitation signals 10. Basic choices in system identification
11. Guidelines for the user System Identification. Theory for the User, 2nd ed. (Ljung) 1. Introduction 1.1 Dynamic systems 1.2 Models 1.3 An archetypical problem - ARX model and the linear least squares method 1.4 The system identification procedure 2. Time-Invariant Linear Systems 2.1 Impulse responses, disturbances, and transfer functions 2.2 Frequency domain expressions 2.3 Signal spectra (2.4 Single realization behavior and ergodicity results) 2.6 Summary 3. Simulation and Prediction (3.1 Simulation) 3.2 Prediction (3.3 Observers) 3.4 Summary 4. Models of Linear Time-Invariant Systems 4.1 Linear models and sets of linear models 4.2 A family of transfer-function models 4.5 Model sets, model structures, and identifiability: some formal aspects (pages 112-113) 4.6 Identifiability of some model structures (pages 115-118) 5. Models for Time-Varying and Nonlinear Systems (5.1 Linear time-varying models) 5.2 Models with nonlinearities (pages 143-145) 6. Nonparametric Time- and Frequency-Domain Methods 6.1 Transient-response analysis and correlation analysis 6.2 Frequency-response analysis 6.3 Fourier analysis (6.4 Spectral analysis) (6.5 Estimating the disturbance spectrum) 6.6 Summary 7.Parameter Estimation Methods 7.1 Guiding principles behind parameter estimatiom methods 7.2 Minimizing prediction error 7.3 Linear regressions and the least-squares method 7.4 A statistical framework for parameter estimation and the maximum likelihood method 7.5 Correlating prediction errors with past data 7.6 Instrumental-variable methods (pages 224-225) 7.7 Using frequency domain data to fit linear models (pages 228-233) 7.8 Summary
8.Convergence and Consistency 8.1 Introduction 8.2 Conditions on the data set (pages 251-253) 8.3 Prediction-error approach (pages 253-254) 8.4 Consistency and identifiability (page 258) 8.5 Linear time-invariant models: a frequency-domain description of the limit model (pages 263-267) 9. Asymptotic Distribution of Parameter Estimates 9.1 Introduction 9.2 The prediction-error approach: basic theorem 9.3 Expressions for the asymptotic variance (pages 283-284) (9.6 Use and relevance of asymptotic variance expressions) (10. Computing the Estimate) (10.1 Linear regressions and least squares (pages 317-321)) (10.2 Numerical solutions by iterative search methods) (10.3 Computing gradients (pages 329-331)) (10.4 Local solutions and initial values) (11. Recursive Estimation Methods) (11.1 Introduction) (11.2 The recursive least-squares algorithm) (12. Options and Objectives) 13. Experiment Design 13.1 Some general considerations 13.2 Informative experiments (13.3 Input design for open loop experiments) (13.4 Identification in closed loop: identifiability) (13.5 Approaches to closed loop identification) (14. Preprocessing data) 15. Choice of Identification Criterion 15.1 General aspects (15.2 Choice of norm: robustness) (16. Model Structure Selection and Model Validation) (16.1 General aspects of the choice of model structure) (16.2 A priori considerations) (16.3 Model structure selection based on preliminary data analysis) (16.4 Comparing model structures) (16.5 Model validation) (16.6 Residual analysis)
Papers J. Schoukens, Y. Rolain, and R. Pintelon Analysis of windowing/leakage effects in frequency response function measurements T. McKelvey and G. Guérin, Non-parametric frequency response estimation using a local rational model B. Fragniere, J. Wartmann, Local Polynomial Method Frequency-Response Calculation for Rotorcraft Applications J. Schoukens, R. Pintelon, T. Dobrowiecki, Y. Rolain, Identification of linear systems withnonlinear distortions J. Schoukens, A. Marconato, R. Pintelon, Y. Rolain, M. Schoukens, K. Tiels, L. Vanbeylen, G. Vandersteen, A. Van Mulders, System Identification in a Real World