Parametric identification of output error model for sampled systems with integer‐type time delay subject to load disturbance with unknown dynamics

In this paper, a bias‐eliminated output error (OE) model identification method is proposed for single‐input‐single‐output sampled systems with integer‐type time delay subject to load disturbance with unknown dynamics. By viewing the load disturbance response as a time‐variant parameter, an iterative least‐squares identification algorithm is established to estimate the rational model parameters together with an integer‐type delay parameter, while the disturbance response could be simultaneously estimated. To overcome the adverse effect of stochastic noise involved with output measurement, an auxiliary model is constructed to predict the noise‐free system response. Moreover, a set of adaptive forgetting factors is introduced to expedite the convergence rate of model parameter estimation and the tracking performance of load disturbance response, respectively. In addition, a monotonically rising profile for evaluating the delay parameter is proposed for implementing the above iterative least‐squares algorithm, in order to avoid the occurrence of multiple local minima of the loss function for model fitting. The asymptotic convergence on estimating the rational model parameters together with the delay parameter is analysed with a proof. An illustrative example is given to demonstrate the effectiveness and advantage of the proposed method.