System Identification

System Identification covers a very wide range of techniques for obtaining a system model from inputs and outputs to the system. They can be classed into parametric (e.g. Recursive Least Squares) or non-parametric (e.g. frequency testing).

Recursive Least Squares

Pseudo-Random Binary Sequence (PRBS)

Articles on System Identification

Internet Resources on Identification

Commercial Companies

• Here's a simle Matlab script for SISO RLS - it will need some modification to be embedded within your own code. But the basics are all there. There are three RLS algorithms available. A MIMO script is also available, as are 'C' code modules for the above.

• Within Matlab/Simulink the only way to get a PRBS generating M-file is within the Frequency Domain System Identification Toolbox (called mlbs - Maximum Length Binary Sequence) or in the System Identification Toolbox v4.0 (called idinput). Here's a simple Matlab script written by Rob Lynch to do just that:-
Subject: Re: help.. how to generate a PRBS signal in Matlab??
Date: 1997/11/10
Author: Rob Lynch <lynch@accesscom.com>

Here is a simple program to generate pseudo-random bit sequences (you can find polynomials for different-length PRBS' in, for example, Peterson and Weldon, "Error-Correcting Codes" and many other books).

function z=prbs(init,g)
%  z=prbs(init,g)
% 2^n-1-bit PRBS based on initial string 'init'
% and polynomial represented by vector g (e.g., g=[7 1] => x^7+x+1).
% Rob Lynch  Quinta Corporation  3/31/97
z=init;
n=length(init);
for i=(n+1):(2^n-1)
q=z(i-g(1));
for j=2:length(g)
q=xor(q,z(i-g(j)));
end
z=[z q];
end

• "Identification in Closed Loop : A Powerful Design Tool", I.D.Landau, IFAC Journal of Control Engineering Practice, 2001. Describes recent developments in closed loop system identification and how it can yield better, more accurate models for controller design. Also presents robust controllers designed using such identified models, for an experimental drive and flexible transmission system.
• "NNSYSID and NNCTRL: Tools for System Identification and Control with Neural Networks", M.Norgaard, O.Ravn and N.K.Poulsen, IEE Computing & Control Journal, February 2001. Describes two toolboxes for use with Matlab that give neural network system identification and control design, including training algorithms, model validation and model structure selection. These toolboxes are freely downloadable at nnsysid.html and nnctrl.html.
• "Multivariable System Identification for Process control", by Yucai Zhu, published by Elsevier Science Ltd, UK, Oct 2001. 372 pages, ISBN: 0-08-043985-3. Matlab software for this book are available for download.
• "Interaction Between Identification and Robust Control", Paul van den Hof, Delf University of Technology

• Industrial Computer Aided Identification (ICAI) Toolbox is aimed at industrial users who are not necessarily specialists in identification.  It is programmed for MATLAB/SIMULINK, and has a guided tour to identification based on the simplified use of advanced identification methods and an ergonomically designed graphical user interface (GUI).
• Self-Tuning Controllers Simulink Library contains various discrete single input single output (SISO) controllers. All controllers contain an on-line identification of a controlled process using the second or the third order model and thus are also suitable for a control of time varying processes.
• CUEDSID: Cambridge University System Identification Toolbox - algorithms for identification of linear and bilinear dynamic systems using balanced parametrizations or subspace methods.
• Interactive Statistical Calculation Pages on Regression, Correlation, Least Squares Curve-fitting - extensive set of list of web-pages of files and code for regression, least squares. etc.
• Closed-loop Identification Toolbox (CLOSID) for Matlab authored by Paul Van den Hof, Delf University of Technology. To be used in conjunction with the System Identification Toolbox (SITB)
• Advanced System Identification Course Lecture Notes by Dr. V. M. Becerra, Department of Cybernetics, The University of Reading.
• System Identification Course from Department of Systems and Control, Uppsala University. Contains course material and Matlab examples.

• Tai-Ji Control is a control technology company specialized in industrial process identification. It produces a package called Tai-Ji ID for automatic closed-loop identification based on the ASYM method of identification developed by Yucai Zhu.
• Adaptics Inc. makers of ADAPTx an automated multivariable system identification and time series analysis software.