The Analysis of Closed-Loop Dynamic-Stochastic Systems

In the process industries data must often be obtained under conditions of closedloop operation; that is, under conditions where feedback control is being applied. In the analysis of such data care is needed to properly take account of the manner of its generation. In particular, if standard open-looped procedures of model identification, estimation and diagnostic checking are applied to closed-loop data incorrect models niay result and lack of fit not be detected. This paper discusses the identification, estimation and diagnostic checking of closedloop systems and illustrates the ideas on two real sets of data.