Closed-loop identification of systems with uncertain time delays using ARX–OBF structure

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.

► We proposed an ARX–OBF model structure for direct closed-loop identification.
► The model parameters are easily determined using least square method.
► Unlike most classical model structures, the proposed structure does not require prior knowledge of time delay during model estimation.
► OBF–ARX model is much more effective, for multi-step ahead prediction of systems with uncertain time delay, than ARX model.