1. SylabUZ
2. Faculty of Computer Science, Electrical Engineering and Automatics
3. winter term 2018/2019
4. WIEiA - oferta ERASMUS / Automatic Control and Robotics - Second-cycle Erasmus programme
5. System modelling and identification

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System modelling and identification - course description

Aim of the course

To provide fundamental knowledge in system identification, including: input signal selection, model order selection, non-recursive and recursive identification methods.

To develop skills in building system models based on structure knowledge and input-output measurements, including nonparametric identification methods, parametric identification methods, neural networks and fuzzy models.

Prerequisites

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Signals and dynamic systems, Control engineering, Artificial intelligence methods

Scope

Introduction. Plants and their models. Model using. System identification and mathematical modelling. Equivalence of models and model equivalence criteria. Parameter estimation. Identifications error definitions. Building system models based on structure knowledge and measurements. Identification algorithm scheme.

Nonparametric identification methods. Transient states analysis. Frequency identification methods. Correlation methods. Power spectrum analysis.

Least squares method. Linear static models. Least squares problem. Normal equations. Analysis of least squares estimator. Best linear unbiased estimator. Confidence intervals of parameter estimates. Model complexity. Finding the least squares solution with orthogonal-triangular decomposition. Recursive least squares algorithm.

Models of dynamic systems. Model classification. General structure of linear model. AR, AR, MA, ARMA, FIR, ARX, ARMAX, OE, and Box-Jenkins models. Multi-input multi-output models. Nonlinear models. Wiener and Hammerstein models. Volterra and Kolmogorov-Gabor models. State-space models. Model structure selection.

Input signals. Deterministic signals. Stochastic signals. Input signals used in system identification. Persistent excitation condition.

Prediction error method. Simulation and prediction. Optimal predictors. Least-squares estimation of ARX model parameters. Parameter consistency problem. Instrumental variables method. Choice of instrumental variables. Prediction error method.

Recursive identification. Properties of recursive identification algorithms. Recursive least squares method. Exponential forgetting. Recursive instrumental variables method. Recursive prediction error method. Parameter adaptation of self-tuning controller.

Closed-loop identification. Identifiability of closed-loop systems. Direct identification methods. Indirect identification methods. Influence of feedback loop on estimation accuracy.

Modeling of static and dynamic nonlinear systems using neural networks and fuzzy models. Neural network models of static and dynamic nonlinear systems. Learning algorithms. Generalization.

Neural network model testing and validation. Optima architecture selection. Fuzzy logic. Fuzzy models. Mamdani, Takagi-Sugeno-Kang and Tsukamoto inference methods. Neuro-fuzzy models. Parameter optimization. Rule base optimization. Operator optimization. Examples of neural network and fuzzy modelling.

Teaching methods

Lecture, laboratory exercises.

Learning outcomes and methods of theirs verification

Outcome description	Outcome symbols	Methods of verification	The class form

Assignment conditions

Lecture – the main condition to get a pass are sufficient marks in written or oral tests conducted at least once per semester.

Laboratory – the passing condition is to obtain positive marks from all laboratory exercises to be planned during the semester.

Calculation of the final grade: lecture 50% + laboratory 50%

Recommended reading

1. Ljung L.: System identification. Theory for the User. Prentice Hall, Upper Saddle River, 1999

2. Nelles O.: Nonlinear System Identification. From Classical Approaches to Neural Networks and Fuzzy models. Springer, New York, Berlin, Heidelberg, 2001

3. Soderstrom T., Stoica P.: System Identification. Prentice Hall, Upper Saddle River, 1994

Further reading

1. Norgaard M., Ravn O., Poulsen N.K., Hansen L.K.: Neural Networks for Modelling and Control of Dynamic Systems. Springer, London, 2000

Notes

Modified by dr hab. inż. Wojciech Paszke, prof. UZ (last modification: 29-04-2020 12:07)