Low-order plus time-delay models are useful in several applications within the industry context, with many methods being developed based on their use. As the processes are of higher order, the few parameters used need to capture the main dynamics of the identified process. In this work, a straightforward methodology for the generation of discrete-time optimal Laguerre plus time-delay (OLPTD) models is suggested. They take advantage of the orthonormal properties of the Laguerre functions, have the estimate quality maximized by means of a computation of the optimal pole directly from the collected data and allow the possibility of using a time-delay term to avoid using more parameters to model the true or apparent delays. The models are generated from the system step response, so that necessary information such as rough estimates of settling time and dominant time constant may be inferred from the identification experiment itself. Models up to third-order were analysed and the results were used to highlight, besides the feasibility of the methodology, that the second-order models grant enough flexibility to approximate dynamics induced by zeros in the transfer function with similar performance as compared to third-order models, which provide good approximations often without including any time-delay.
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