Closed-loop Identification of Systems with Uncertain Time Delays using ARX-OBF Structures

Closed-loop identification of systems with known time delays can be effectively carried out with simple
model structures like Autoregressive with Exogenous Input (ARX) and Autoregressive Moving Average
with Exogenous Input (ARMAX). However, when the system contains large uncertain time delay, such
structures may lead to inaccurate models with significant bias if the time delay estimate used in the
identification is less accurate. On the other hand, conventional orthonormal basis filter (OBF) model
structures are very effective in capturing the dynamics of systems with uncertain time delays. However,
they are not effective for closed-loop identification. In this paper, an ARX–OBF model structure which is
obtained by modifying the ARX structure is shown to be effective in handling closed-loop identification
of systems with uncertain time delays. In addition, the paper shows that this advantage of ARX–OBF
models over simple ARX model is considerable in multi-step ahead predictions.