System Identification Toolbox

Step 3: Examining the Difficulties

There may be several reasons why the comparisons in Step 2 did not look good. This section discusses the most common ones, and how they can be handled.

Model Unstable

The ARX or state-space model may turn out to be unstable, but could still be useful for control purposes. Change to a 5- or 10-step ahead prediction instead of simulation in the Model Output View.

Feedback in Data

If there is feedback from the output to the input, due to some regulator, then the spectral and correlations analysis estimates are not reliable. Discrepancies between these estimates and the ARX and state-space models can therefore be disregarded in this case. In the Model Residuals View of the parametric models, feedback in data can also be visible as correlation between residuals and input for negative lags.

Disturbance Model

If the state-space model is clearly better than the ARX model at reproducing the measured output, this is an indication that the disturbances have a substantial influence, and it will be necessary to model them carefully.

Model Order

If a fourth order model does not give a good Model Output plot, try eighth order. If the fit clearly improves, it follows that higher order models will be required, but that linear models could be sufficient.

Additional Inputs

If the Model Output fit has not significantly improved by the tests so far, think over the physics of the application. Are there more signals that have been, or could be, measured that might influence the output? If so, include these among the inputs and try again a fourth order ARX model from all the inputs. (Note that the inputs need not at all be control signals, anything measurable, including disturbances, should be treated as inputs).

Nonlinear Effects

If the fit between measured and model output is still bad, consider the physics of the application. Are there nonlinear effects in the system? In that case, form the nonlinearities from the measured data and add those transformed measurements as extra inputs. This could be as simple as forming the product of voltage and current measurements, if you realize that it is the electrical power that is the driving stimulus in, say, a heating process, and temperature is the output. This is of course application dependent. It does not take very much work, however, to form a number of additional inputs by reasonable nonlinear transformations of the measured ones, and just test if inclusion of them improves the fit.

Still Problems?

If none of these tests leads to a model that is able to reproduce the Validation Data reasonably well, the conclusion might be that a sufficiently good model cannot be produced from the data. There may be many reasons for this. It may be that the system has some quite complicated nonlinearities, which cannot be realized on physical grounds. In such cases, nonlinear, black-box models could be a solution. Among the most used models of this character are the Artificial Neural Networks (ANN).

Another important reason is that the data simply do not contain sufficient information, e.g., due to bad signal to noise ratios, large and nonstationary disturbances, varying system properties, etc.

Otherwise, use the insights of which inputs to use and which model orders to expect and proceed to Step 4.

Step 2: Getting a Feel for the Difficulties

Step 4: Fine Tuning Orders and Disturbance Structures