Identification and fine tuning and closed-loop processes under discrete EWMA and PI adjustments

Conventional process identification techniques of a open-loop process use the cross-correlation function between historical values of the process input and of the process output. If the process is operated under a linear feedback controller, however, the cross-correlation function has no information on the process transfer function because of the linear dependency of the process input on the output. In this paper, several circumstances where a closed-loop system can be identified by the autocorrelation function of the output are discussed. It is assumed that a proportional integral controller with known parameters is acting on the process while the output data were collected. The disturbance is assumed to be a member of a simple yet useful family of stochastic models, which is able to represent drift. It is shown that, with these general assumptions, it is possible to identify some dynamic process models commonly encountered in manufacturing. After identification, our approach suggests to tune the controller to a near-optimal setting according to a well-known performance criterion.