System Identification Toolbox

Feedback in Data

If the system was operating in closed loop (feedback from the past outputs to the current input) when the data were collected, some care has to be exercised.

Basically, all the prediction error methods work equally well for closed-loop data. Note, however, that the Output-Error model (3-17) and the Box-Jenkins model (3-18) are normally capable of giving a correct description of the dynamics G, even if H (which equals 1 for the output error model) does not allow a correct description of the disturbance properties. This is no longer true for closed-loop data. You then need to model the disturbance properties more carefully. Another thing to be cautious about is that impulse response effects at delay 0 very well could be traced to the feedback mechanism and not to the system itself.

The spectral analysis method and the instrumental variable techniques (with default instruments) as well as n4sid may give unreliable results when applied to closed-loop data. These techniques should be avoided when feedback is present.

To detect if feedback is present, use the basic method of applying impulse to estimate the impulse response. Significant values of the impulse response at negative lags is a clear indication of feedback. When a parametric model has been estimated and the resid command is applied, a graph of the correlation between residuals and inputs is given. Significant correlation at negative lags again indicates output feedback in the generation of the input. Testing for feedback is, therefore, a natural part of model validation.

Filtering Data: Focus

Delays