Closed-loop system identification for small samples with constraints

Traditional approaches to closed-loop identification of transfer function models require a sufficiently large data set and model forms that are general enough while at the same time requiring application of some form of external excitation (a "dither signal") to the process. In the limit, as the dither signal dominates the control actions, identification becomes easier, but the operation of the process becomes closer to that of an uncontrolled (i.e., open-loop) process, which may be unacceptable. This article proposes a closedloop system identification procedure that aims to improve model parameter estimates by incorporating prior knowledge about the process in the form of constraints without using a dither signal. A Monte Carlo simulation study is presented to illustrate the small-sample benefits of adding various forms of constraints. It is shown how constraints based on process knowledge, which is relatively easy to gain from prior experience, result in best identified models among the class of constraints considered. In particular, prior knowledge of the input-output delay of the process is shown to be the most important for identifying a process operating in closed-loop. An example based on a real process illustrates the advantages of the proposed method over the dither signal approach.