Direct and two-step methods for closed-loop identification: a comparison of asymptotic and finite data set performance

The asymptotic and finite data behavior of some closed-loop identification methods are investigated. It is shown that, when the output power is limited, closed-loop identification can generally identify models with smaller variance than open-loop identification. Several variations on some two-step identification methods are compared with the direct identification method. High order FIR models are used as process models to avoid bias issues arising from inadequate model structures for the processes. Comparisons are, therefore, made based on the variance of the identified process models both for asymptotic situations and for finite data sets. Process model bias resulting from improper selection of the noise and sensitivity function models is also investigated. In this context, the results support the use of direct identification methods on closed-loop data.