On-line delay estimation for stable, unstable and integrating systems under step response

A simple but effective on-line method to estimate the delay from step response, which can be used for stable, unstable and integrating systems, is proposed in this paper. The estimation and control are made simultaneously since the nominal delay is updated in closed-loop based on certain calculus on the output signal. Moreover, the approach is based on a Modified Smith Predictor and the delay estimation is implemented using a multi-model scheme with fixed models. Additionally, the convergence properties of the estimation algorithm and the stability analysis of the closed-loop are well-defined. Simulation examples show the effectiveness of the proposed method, where the delay estimation leads to an optimal and robust controller, tackling the uncertainty in the delay.