Identification of dual‐rate sampled systems with time delay subject to load disturbance

A discrete‐time model identification method is proposed for dual‐rate sampled systems with time delay subject to load disturbance with unknown dynamics. By viewing the output response arising from such load disturbance as a dynamic parameter for estimation, two recursive least‐squares identification algorithms are developed to estimate the linear model parameters and the load disturbance response, respectively, while the integer delay parameter is derived by using a one‐dimensional searching approach to minimise the output fitting error. An auxiliary model is constructed to estimate the unknown noise‐free output such that consistent estimation of the model parameters can be obtained under stochastic noise in the output measurement. Moreover, two adaptive forgetting factors are introduced to expedite the convergence rates of estimating the model parameters and the load disturbance response, respectively. Theoretical analysis is given to clarify the convergence of parameter estimation. Two illustrative examples are presented to demonstrate the effectiveness and merit of the proposed identification method.