On this page a comprehensive set of hands-on examples, demos, and exercises will be provided using MATLAB® Live Scripts. The purpose of the Hands-On pages is to illustrate many aspects of system identification using ‘simple’ but generic examples that provide a deeper understanding of the theory. General conclusions and user guidelines are provided at the end of each section.

I would like to thank Tadeusz Dobrowiecki (Budapest University of Technology and Economics) for reading early versions of these Hands-On illustrations and pointing out some errors and unclear points. He also gave me proposals for additional ideas. 

The material is presented in the following sub-sections:

Table of contents

Statistics Refresher
This section is intended for readers less familiar with statistics. We illustrate the use of the sample mean, sample variance, covariance matrix, and central limit theorem in system identification.

System Identification
The three lead actors in system identification data, model, and cost are introduced. The user aspects, how to make a proper selection between different options is illustrated. Typical questions that are addressed are: How to design an experiment? What are the important aspects of a model? Should we always use a least squares cost function?

Design of Excitation Signals
Good measurements make it much easier to obtain good models. In this section we discuss how to design a good excitation for the identification of linear systems. It will be shown that periodic signals, when they can be applied, offer considerable advantages. A detailed introduction to the design and processing of these signals is given.

Nonparametric Identification
The frequency response and the impulse response functions are nonparametric models for a SISO linear system. An extensive overview, ranging from the classical approaches to the very recent methods will be given.

Identification of Linear Systems
In this section we learn how to identify a model for a single-input single-output (SISO) linear dynamic system, starting from the measured input and output signals. Also, the power spectrum of the unmodeled disturbances is identified and used to generate uncertainty bounds on the estimated model.

Identification in the Presence of Nonlinear Distortions
How to identify a linear model if we know nonlinear distortions are present? How to select the excitation signals? What model quality can be expected? What is the level and the nature of the nonlinear distortions? What is the dominating disturbance: noise or nonlinear distortions? These aspects are discussed and illustrated by means of a series of examples.

Identification of Nonlinear Systems
The full nonlinear system identification process, the model structure selection, the identification and the validation is discussed in full detail.

A list of publications that provide more detailed information, mathematical explanations and formal proofs on the topics being discussed is provided. It is not the aim to provide a comprehensive overview of the existing literature or a list of the most recent publications in the field.