A Hysteresis Dynamic Mathematical Model Approach to Parametric Estimation System

Nubia Ilia Ponce De León Puig,José Rodellar,Leonardo Acho,Francesco Tornabene

doi:10.1155/2021/6628380

Nubia Ilia Ponce De León Puig, José Rodellar + Show 2 more

Open Access

https://doi.org/10.1155/2021/6628380

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Abstract

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.

Highlights

In recent years, the comprehension of the hysteresis phenomenon and the development of adequate mathematical tools to describe it have attracted the attention of many researchers [1,2,3,4,5,6]. e main reason is that hysteresis is encountered in many different physical and mathematical fields
Hysteresis can be described as a nonlinear phenomenon that, under zero-bias and low-frequency periodic excitation, its output has a periodic response with the same frequency of its input [4, 6]
E signal modulation method carried out here follows the main idea of the standard one-bit-analog-to-digital Delta modulator converter [23]. is kind of modulator has had a great variety of applications in digital communication transmission [23], secure communication design [24, 25], and some patents related to sinusoidal signal generators [26] and sensors for measurements [27]. This proposed hysteresis model is integrated into a Delta modulator structure and applied to a parameter estimation process. erefore, according to our numerical experiments, this development increases the Delta modulator performance in this specific application

Summary

Introduction

The comprehension of the hysteresis phenomenon and the development of adequate mathematical tools to describe it have attracted the attention of many researchers [1,2,3,4,5,6]. e main reason is that hysteresis is encountered in many different physical and mathematical fields. The common alternative is to develop simple hysteresis models which, not giving the best description of the physical hysteresis behaviour of the system, do keep relevant input-output features useful for characterization, design, and control purposes [4, 5, 15]. Is kind of modulator has had a great variety of applications in digital communication transmission [23], secure communication design [24, 25], and some patents related to sinusoidal signal generators [26] and sensors for measurements [27] As mentioned before, this proposed hysteresis model is integrated into a Delta modulator structure and applied to a parameter estimation process. (1) To propose a recent hysteresis dynamic model that may be applied in different engineering systems (2) To redesign a Hysteresis Delta Modulator that is able to improve the performance of a parameter estimation algorithm. Numerical experiments are well implemented to highlight the main dynamics’ characteristics of each model

Case 1

Case 2