System Identification Toolbox

# The System Identification Problem

Basic Questions About System Identification

What is System Identification?

System Identification allows you to build mathematical models of a dynamic system based on measured data.

How is that done?

Essentially by adjusting parameters within a given model until its output coincides as well as possible with the measured output.

How do you know if the model is any good?

A good test is to take a close look at the model's output compared to the measured one on a data set that wasn't used for the fit ("Validation Data").

Can the quality of the model be tested in other ways?

It is also valuable to look at what the model couldn't reproduce in the data ("the residuals"). This should not be correlated with other available information, such as the system's input.

What models are most common?

The techniques apply to very general models. Most common models are difference equations descriptions, such as ARX and ARMAX models, as well as all types of linear state-space models.

Do you have to assume a model of a particular type?

For parametric models, you have to specify the structure. This could be as easy as just selecting a single integer, the model order, or may involve several choices.If you just assume that the system is linear, you can directly estimate its impulse or step response using Correlation Analysis or its frequency response using Spectral Analysis. This allows useful comparisons with other estimated models.

What does the System Identification Toolbox contain?

It contains all the common techniques to adjust parameters in all kinds of linear models. It also allows you to examine the models' properties, and to check if they are any good, as well as to preprocess and polish the measured data.

Isn't it a big limitation to work only with linear models?

No, actually not. Many common model nonlinearities are such that the measured data should be nonlinearly transformed (like squaring a voltage input if you think that it's the power that is the stimuli). Use physical insight about the system you are modeling and try out such transformations on models that are linear in the new variables, and you will cover a lot!

How do I get started?

If you are a beginner, browse through The Graphical User Interface. Then try out a couple of the data sets that come with the toolbox. Use the graphical user interface (GUI) and check out the built-in help functions to understand what you are doing.

Is this really all there is to System Identification?

Actually, there is a huge amount written on the subject. Experience with real data is the driving force to understand more. It is important to remember that any estimated model, no matter how good it looks on your screen, has only picked up a simple reflection of reality. Surprisingly often, however, this is sufficient for rational decision making.

 About the Author Common Terms Used in System Identification