An Experimental Study of the Empirical Identification Method to Infer an Unknown System Transfer Function

Identification is considered a very important procedure, within the control area, to estimate the best-possible approximate model among different designs. Its significance comes from the fact that more than 75% of the cost associated with an advanced control project is aimed at obtaining a precise mathematical modeling. Therefore, in this work, an exhaustive analysis was carried out to determine the appropriate input stimulus for an unknown real system that must be controlled, with the aim of accurately estimating its transfer function (TF) using the empirical identification method (gray-box). The analysis was performed quantitatively by means of three tests: (i) the PID controller step response was evaluated theoretically; (ii) the controller performance was assessed in a Cartesian robot by tracking a trajectory defined through a Gaussian acceleration profile; (iii) the efficiency of the determined input stimulus with the best performance on inferring the TF for the system to be controlled was verified by assessing its operation in a real system, through repeatability tests, utilizing the integral errors.