Closed-loop identification: the role of the noise model and prefilters

The main closed-loop identifiability results for linear SISO systems are reviewed and illustrated with examples. A frequency domain expression for the asymptotic prediction error sum of squares is used to reinterpret some of these results, and to analyse the role of the noise model and data prefilters on the identifiability of the process dynamic model. Unlike the case of open-loop identification it is shown that in closed-loop identification the process model can only be identified if the correct noise model or prefilter is also identified. The process model biases that result from the specification of incorrect noise models are illustrated by simulation examples and explained using the asymptotic theory. The effect of operator intervention (manual feedback) during ‘open-loop’ experiments is shown to be equivalent to feedback under certain conditions.