System Identification Toolbox

The Basic Steps of System Identification

The System Identification problem is to estimate a model of a system based on observed input-output data. Several ways to describe a system and to estimate such descriptions exist. This section gives a brief account of the most important approaches.

The procedure to determine a model of a dynamical system from observed input-output data involves three basic ingredients:

• The input-output data
• A set of candidate models (the model structure)
• A criterion to select a particular model in the set, based on the information in the data (the identification method)

The identification process amounts to repeatedly selecting a model structure, computing the best model in the structure, and evaluating this model's properties to see if they are satisfactory. The cycle can be itemized as follows:

1. Design an experiment and collect input-output data from the process to be identified.
2. Examine the data. Polish it so as to remove trends and outliers, and select useful portions of the original data. Possibly apply filtering to enhance important frequency ranges.
3. Select and define a model structure (a set of candidate system descriptions) within which a model is to be found.
4. Compute the best model in the model structure according to the input-output data and a given criterion of fit.
5. Examine the obtained model's properties
6. If the model is good enough, then stop; otherwise go back to Step 3 to try another model set. Possibly also try other estimation methods (Step 4) or work further on the input-output data (Steps 1 and 2).

The System Identification Toolbox offers several functions for each of these steps.

For Step 2 there are routines to plot data, filter data, and remove trends in data, as well as to resample and reconstruct missing data.

For Step 3 the System Identification Toolbox offers a variety of nonparametric models, as well as all the most common black-box input-output and state-space structures, and also general tailor-made linear state-space models in discrete and continuous time.

For Step 4 general prediction error (maximum likelihood) methods, as well as instrumental variable methods and sub-space methods are offered for parametric models, while basic correlation and spectral analysis methods are used for nonparametric model structures.

To examine models in Step 5, many functions allow the computation and presentation of frequency functions and poles and zeros, as well as simulation and prediction using the model. Functions are also included for transformations between continuous-time and discrete-time model descriptions and to formats that are used in other MATLAB toolboxes, like the Control System Toolbox and the Signal Processing Toolbox.

Terms to Characterize the Model Properties

A Startup Identification Procedure