A Hysteresis Dynamic Mathematical Model Approach to Parametric Estimation System

The main contribution of this paper is the proposal of a recent hysteresis dynamic model which is successfully employed within a posited signal modulator. The modulation of signals is a commonly required stage in many engineering applications, such as telecommunications, power electronics, and control, among others. In this paper, the effectiveness of a signal modulator based on the well-known Delta modulator when it contains a dynamic hysteresis system within its main structure is presented. To do that, it is resorted to an application of the granted Hysteresis-Delta Modulator. This application consists of including the modulator within an adaptive scheme, since it is well known that the persistent excitation condition is required, for instance, in parameter estimation tasks. Hence, the main functional property of the modulator with hysteresis is its ability of producing a modulated signal with uniform high-frequency content even when its input is not a permanent persistent excitation signal. To highlight the main contribution of this paper, a numerical experiment of a parameter estimation system is developed to compare the performance of the modulator with the proposed hysteresis model and two other previously reported hysteresis systems. That is, three different scenarios have been tested in the parameter estimation of a nonminimum phase system. Finally, the numerical experiments confirm that the proposed hysteresis model along with the modulator provides the best performance as expected.